Answer:
The expression that represents the number of hits he got in the rest of the games is [tex]t=52-h[/tex].
Step-by-step explanation:
Given:
Number of hits in one season = 52 hits
Number of hits in one game = 'h'
We need to write expression that represents the number of hits he got in the rest of the games.
Solution:
Let the number of hits he got in the rest of the games be 't'.
Now we can say that;
The number of hits he got in the rest of the games is equal to Number of hits in one season minus Number of hits in one game.
framing in equation form we get;
[tex]t=52-h[/tex]
Hence expression that represents the number of hits he got in the rest of the games is [tex]t=52-h[/tex].
Answer:
52 - h
Step-by-step explanation:
Simplify: 52 - h
There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others
1. True
2. False
ANSWER: True
EXPLANATION:
The statement is true. Any correctly constructed frequency distribution is valid. However, some choices for the categories or classes give more information about the shape of the distribution.
am i correct on this equation??
-- need honest answers!!! --
Unfortunately you are incorrect. The answer is actually tan(y) = 20/21
The tangent of an angle is the ratio of the opposite and adjacent sides.
tan(angle) = opposite/adjacent
tan(K) = JL/LK
tan(y) = 20/21
----------------------
Side note: the tangent of angle x would be the reciprocal of this fraction since the opposite and adjacent sides swap when we move to angle J
tan(angle) = opposite/adjacent
tan(J) = LK/JL
tan(x) = 21/20
Powers of 10 make it very easy to write large and small numbers, but as a result it can also be easy to forget the large differences between different powers. We can compare any two numbers by dividing them. For example, we say that 12 is four times as large as 3 because 12÷3=4. Complete the sentences below comparing pairs of powers of 10.
Answer:let us compare the following pairs of power of 10,9×10^6 ÷3×10^12=3×10^-6
Step-by-step explanation:
Comparing pairs of power of 10 involve applying principle of indices.in what is known as the laws of indices
Law1 states that X^a ×X^b=X^(a+b) meaning that multiplication of indices results to addition of the indexes raise as exponenet of 10, similarly a division as in the answer above always lead to substraction of the indexes as seen in the example 9×10^6/3×10^12 will becomen9÷3×10^(6-12)=3×10^-6.
(Score for Question 2: ___ of 6 points)
2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of
solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(c) 6x + 4x - 6 = 24 + 9x
(d) 25 - 4x = 15 - 3x + 10 - X
(e) 4x + 8 = 2x + 7 + 2x - 20
Answer:
Answer:
The answer to your question is below
Step-by-step explanation:
c) 6x + 4x - 6 = 24 + 9x
6x + 4x - 9x = 24 + 6
x = 30 This equation has one solution, it's an identity
d) 25 - 4x = 15 - 3x + 10 - x
-4x + 3x + x = 15 + 10 - 25
0 = 0 It has infinite number of solutions, it is an identity
e) 4x + 8 = 2x + 7 + 2x - 20
4x - 2x - 2x = 7 - 20 + 8
0 = -5 It has no solution it is a contradiction
I have 200 coins to put into 4 bags I put the coins into each bag so that each bag has 2 mote coins than the one before How many coins are on each bag
First bag has 47 coins and second bag has 49 coins and third bag has 51 coins and fourth bag has 53 coins
Solution:
Given that,
Total number of coins = 200
Number of bags = 4
I put the coins into each bag so that each bag has 2 more coins than the one before
Therefore,
Each bag has 2 more coins than the one before. Based on this we can say,
Let "x" be the number of coins put in first bag
Then, x + 2 is the number of coins put in second bag
Then, x + 4 is the number of coins put in third bag
Then, x + 6 is the number of coins put in fourth bag
We know that,
Total number of coins = 200
[tex]x + x + 2 + x + 4 + x + 6 = 200\\\\4x + 12 = 200\\\\4x = 200-12\\\\4x = 188\\\\x = 47[/tex]
Thus,
Coins put in first bag = x = 47
Coins put in second bag = x + 2 = 47 + 2 = 49
Coins put in third bag = x + 4 = 47 + 4 = 51
Coins put in fourth bag = x + 6 = 47 + 6 = 53
Thus number of coins in each bag are found
Final answer:
By setting up an algebraic equation to distribute 200 coins into 4 bags with each bag having 2 more coins than the previous one, we find the number of coins in each bag are 47, 49, 51, and 53, respectively.
Explanation:
The question involves distributing 200 coins into 4 bags so that each subsequent bag has 2 more coins than the previous one. To find out how many coins are in each bag, let's denote the number of coins in the first bag as x. Consequently, the second bag would have x + 2 coins, the third bag x + 4 coins, and the fourth bag x + 6 coins. The total number of coins across all bags would be x + (x + 2) + (x + 4) + (x + 6) = 200.
Simplifying the equation, we get 4x + 12 = 200, which simplifies further to 4x = 188. Dividing both sides by 4 yields x = 47. Therefore, the number of coins in each bag, starting from the first to the fourth, are 47, 49, 51, and 53, respectively.
Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?
Answer:
The total number of buns Mrs Klein made = 400
Step-by-step explanation:
Question
Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 of the remaining in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?
Given:
Mrs Klein sold [tex]\frac{3}{5}[/tex] of the buns in the morning.
Mrs Klein sold [tex]\frac{1}{4}[/tex] of the remaining buns in the evening.
She sold 200 more buns in the morning than afternoon.
To find the total number of buns she make.
Solution:
Let the total number of buns be = [tex]x[/tex]
Number of buns sold in the morning will be given as = [tex]\frac{3}{5}x[/tex]
Number of buns remaining = [tex]x-\frac{3}{5}x[/tex]
Number of buns sold in the evening will be given as = [tex]\frac{1}{4}(x-\frac{3}{5}x)[/tex]
Difference between the number of buns sold in morning and evening = 200
Thus, the equation to find [tex]x[/tex] can be given as:
[tex]\frac{3}{5}x-\frac{1}{4}(x-\frac{3}{5}x)=200[/tex]
Using distribution:
[tex]\frac{3}{5}x-\frac{1}{4}x+(\frac{1}{4}.\frac{3}{5}x)=200[/tex]
[tex]\frac{3}{5}x-\frac{1}{4}x+\frac{3}{20}x=200[/tex]
Multiplying each term with the least common multiple of the denominators to remove fractions.
The L.C.M. of 4, 5 and 20 = 20.
Multiplying each term with 20.
[tex]20\times \frac{3}{5}x-20\times\frac{1}{4}x+20\times\frac{3}{20}x=20\times 200[/tex]
[tex]12x-5x+3x=4000[/tex]
[tex]10x=400[/tex]
Dividing both sides by 10.
[tex]\frac{10x}{10}=\frac{4000}{10}[/tex]
∴ [tex]x=400[/tex]
Thus, total number of buns Mrs Klein made = 400
Emil's backpack weighs six and three eights pounds. He removes a book that weighs three fourth pound. Then he removes a book that weighs one half pound .How much does Emil's back pack weigh now
Answer:
Emil's back pack weigh now [tex]5\frac{1}{8}\ pounds[/tex].
Step-by-step explanation:
Given:
Total Weight of backpack = [tex]6\frac{3}{8}\ pounds[/tex]
[tex]6\frac{3}{8}\ pounds[/tex] can be Rewritten as [tex]\frac{51}{8}\ pounds[/tex]
Weight of backpack = [tex]\frac{51}{8}\ pounds[/tex]
Weight of Book 1 = [tex]\frac{3}{4}\ pound[/tex]
Weight of Book 2 = [tex]\frac{1}{2}\ pound[/tex]
We need to find weight of back pack after removing books.
Solution:
Now we can say that;
weight of back pack after removing books can be calculated by Subtracting Weight of Book 1 and Weight of Book 2 from Total Weight of backpack.
framing in equation form we get;
weight of back pack after removing books = [tex]\frac{51}{8}-\frac{3}{4}-\frac{1}{2}[/tex]
Now to solve the equation we will first make the denominator common using LCM.
weight of back pack after removing books =[tex]\frac{51\times1}{8\times1}-\frac{3\times2}{4\times2}-\frac{1\times4}{2\times4}=\frac{51}{8}-\frac{6}{8}-\frac{4}{8}[/tex]
Now the denominators are common so we will solve the numerator.
weight of back pack after removing books = [tex]\frac{51-6-4}{8}=\frac{41}{8}\ pounds \ \ OR \ \ 5\frac{1}{8}\ pounds[/tex]
Hence Emil's back pack weigh now [tex]5\frac{1}{8}\ pounds[/tex].
What is the median value of the set R, if for every term in the set, [tex]R_n = R_{n-1} + 3[/tex]? (1) The first term of set R is 15. (2) The mean of set R is 36.
Answer:
36
Step-by-step explanation:
Given that
[tex]R_n = R_{n+1} +3[/tex] is given
First term is 15
This is an arithmetic series with a =15 and d =3
If n is the number of terms, then we have
Sum of n terms = 36 xn = 36n
But as per arithmetic progression rule
[tex]S_n = \frac{n}{2} [2a+(n-1)d]\\= \frac{n}{2} [30+(n-1)3]=36n[/tex]
[tex]72 = 30+3n-3\\n-=15[/tex]
When there are n terms we have middle term is the 8th term
Hence median is 8th term
=[tex]a_8 = 15+7(3) \\=36[/tex]
Find DC
HELP PLEASE!! :(
using sine cosine or tangent
DC=14
Explanation
consider triangle ADB
<BAD=54°
sin<BAD=opposite side/ hypotenuse
sin 54°=BD/BA
BD=BA sin 54°=20*0.8=16
consider triangle BDC
cos <BCD=adjacent side/hypotenuse
=DC/BC
cos 28°=DC/BC
DC=cos28° *BC
=0.88*16=14.08
Find four numbers that form a geometric progression such that the third term is greater than the first by 12 and the fourth is greater than the second by 36.
Answer:
5 , 4.5, 13.5 and 40.5
Step-by-step explanation:
Since the numbers are in geometric progression, their form is essentially:
a, ar, ar^2 and ar^3
Where a and r are first term and common ratio respectively.
From the information given in the catalog:
Third term is greater than the first by 12 while fourth is greater than second by 36.
Let’s now translate this to mathematics.
ar^2 - a = 12
ar^3 - ar = 36
From 1, a(r^2 - 1) = 12 and 2:
ar(r^2 - 1) = 36
From 2 again r[a(r^2 -1] = 36
The expression inside square bracket looks exactly like equation 1 and equals 12.
Hence, 12r = 36 and r = 3
Substituting this in equation 1,
a( 9 - 1) = 12
8a = 12
a = 12/8 = 1.5
Thus, the numbers are 1.5, (1.5 * 3) , (1.5 * 9), (1.5 * 27) = 1.5 , 4.5, 13.5 and 40.5
Final Answer:
The four numbers forming the geometric progression are 1.5, 4.5, 13.5, and 40.5.
Explanation:
Let's start by defining what a geometric progression (GP) is. A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Let's denote the four numbers in the GP as a, ar, ar², and ar³, where:
- a is the first term,
- r is the common ratio.
We've been given two conditions:
1. The third term is greater than the first by 12, which gives us the equation:
ar² = a + 12
2. The fourth term is greater than the second by 36, which leads us to:
ar³ = ar + 36
We need to solve this system of equations to find the values of a and r.
Starting with the first equation:
ar² = a + 12
We can subtract 'a' from each side to get:
ar - a = 12
Factor out 'a' from the left side:
a(r² - 1) = 12
Now notice that r² - 1 is a difference of squares and can be factored to (r + 1)(r - 1):
a(r + 1)(r - 1) = 12
This equation tells us that the product of 'a' and (r + 1)(r - 1) is 12. For now, let's keep this equation aside and look at the second condition.
Proceeding with the second equation:
ar = ar + 36
Subtract 'ar' from each side:
ar³ - ar = 36
Factor out 'ar':
ar(r² - 1) = 36
Again, we recognize a difference of squares in the parentheses, so we factor it:
ar(r + 1)(r - 1) = 36
This equation relates 'ar', and (r + 1)(r - 1), and tells us the product is 36.
Now, because we have a similar term in both equations, (r + 1)(r - 1), we can set the products equal to each other to find a relationship between 'a' and 'ar':
From the first equation, we have a(r + 1)(r - 1) = 12,
From the second equation, we have ar(r + 1)(r - 1) = 36.
Dividing the second equation by the first one gives us:
ar(r + 1)(r - 1) / a(r + 1)(r - 1) = 36 / 12
ar / a = 36 / 12
r = 3
Now that we have the value of 'r', let's substitute it back into either of the original equations to find 'a'. Let's use the first equation:
a(r² - 1) = 12
a(3² - 1) = 12
a(9 - 1) = 12
a(8) = 12
a = 12 / 8
a = 3 / 2
a = 1.5
Now we have both 'a' and 'r', which allows us to determine the four numbers in the GP:
The first number, a, is 1.5.
The second number, ar, is 1.5 * 3 = 4.5.
The third number, ar², is 4.5 * 3 = 13.5.
The fourth number, ar², is 13.5 * 3 = 40.5.
So, the four numbers forming the geometric progression are 1.5, 4.5, 13.5, and 40.5.
A cardboard box manufacturing company is building boxes with length represented by x+ 1, width by 5- x, and height by x -1. The volume of the box is modeled by the function below V(x) 18 14 10 6 24 X 5 6 2 2 3 -2 -6 Over which interval is the volume of the box changing at the fastest average rate? [1,2] A. [1,3.5 B. C. [1,5] r0,3.51 D
Answer:
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
b. [1,3.5]
[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]
c. [1,5]
[tex] m =\frac{0-0}{5-1}=0[/tex]
d. [0,3.5]
[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]
So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
Step-by-step explanation:
Assuming that we have the figure attached for the function. For this case we just need to quantify the slope given by:
[tex] m = \frac{\Delta y}{\Delta x}[/tex]
For each interval and the greatest slope would be the interval on which the volume of the box is changing at the fastest average rate
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
b. [1,3.5]
[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]
c. [1,5]
[tex] m =\frac{0-0}{5-1}=0[/tex]
d. [0,3.5]
[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]
So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
The correct answer is A. [1,2].
To determine over which interval the volume of the box changes at the fastest average rate, we need to find the average rate of change of the volume function ( V(x) ) over the given intervals and compare them.
The volume ( V(x) ) of the box is given by:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \][/tex]
We first need to express ( V(x) ) in a simplified form. Let's expand the expression:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \]\[ V(x) = (x + 1)(x^2 - 6x + 5) \]\[ V(x) = x(x^2 - 6x + 5) + 1(x^2 - 6x + 5) \]\[ V(x) = x^3 - 6x^2 + 5x + x^2 - 6x + 5 \]\[ V(x) = x^3 - 5x^2 - x + 5 \][/tex]
Now, we calculate the average rate of change over each interval. The average rate of change of ( V(x) ) over an interval ([a, b]) is given by:
[tex]\[ \text{Average Rate of Change} = \frac{V(b) - V(a)}{b - a} \][/tex]
We need to compute this for each interval provided.
1. Interval [1, 2]:
[tex]\[ V(1) = (1 + 1)(5 - 1)(1 - 1) = 0 \]\[ V(2) = (2 + 1)(5 - 2)(2 - 1) = 3 \times 3 \times 1 = 9 \]\[ \text{Average Rate of Change} = \frac{V(2) - V(1)}{2 - 1} = \frac{9 - 0}{2 - 1} = 9 \][/tex]
2. Interval [1, 3.5]:
[tex]\[ V(1) = 0 \]\[ V(3.5) = (3.5 + 1)(5 - 3.5)(3.5 - 1) = 4.5 \times 1.5 \times 2.5 = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(1)}{3.5 - 1} = \frac{16.875 - 0}{3.5 - 1} = \frac{16.875}{2.5} = 6.75 \][/tex]
3. Interval [1, 5]:
[tex]\[ V(1) = 0 \]\[ V(5) = (5 + 1)(5 - 5)(5 - 1) = 6 \times 0 \times 4 = 0 \]\[ \text{Average Rate of Change} = \frac{V(5) - V(1)}{5 - 1} = \frac{0 - 0}{5 - 1} = 0 \][/tex]
4. Interval [0, 3.5]:
[tex]\[ V(0) = (0 + 1)(5 - 0)(0 - 1) = 1 \times 5 \times -1 = -5 \]\[ V(3.5) = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(0)}{3.5 - 0} = \frac{16.875 - (-5)}{3.5 - 0} = \frac{16.875 + 5}{3.5} = \frac{21.875}{3.5} \approx 6.25 \][/tex]
Comparing these average rates of change:
[tex]\([1, 2]\): 9\\ \([1, 3.5]\): 6.75\\ \([1, 5]\): 0\\ \([0, 3.5]\): 6.25[/tex]
The interval where the volume of the box is changing at the fastest average rate is [tex]\([1, 2]\)[/tex], with an average rate of change of 9.
Therefore, the correct answer is: A.[tex]\([1, 2]\)[/tex].
Complete question :
The number of ducks and pigs in a field totals 34. The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, determine how many ducks and how many pigs are in the field. (For each answer, enter an exact number.)
Answer: the number of ducks in the field is 25
the number of pigs in the field is 9
Step-by-step explanation:
Let x represent the number of ducks in the field.
Let y represent the number of pigs in the field.
A duck has one head and a pig also has one head.
The number of ducks and pigs in a field totals 34. This means that
x + y = 34
The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, it means that
2x + 4y = 86 - - - - - - - - - - -- - 1
Substituting x = 34 - y into equation 1, it becomes
2(34 - y) + 4y = 86
68 - 2y + 4y = 86
- 2y + 4y = 86 - 68
2y = 18
y = 18/2 = 9
Substituting y = 9 into x = 34 - y, it becomes
x = 34 - 9 = 25
To find the number of ducks and pigs in the field, we can set up a system of equations and solve them. Using the given information and the equations x + y = 34 and 2x + 4y = 86, we can find that there are 25 ducks and 9 pigs in the field.
Explanation:To solve this problem, we can use a system of equations. Let x represent the number of ducks and y represent the number of pigs. From the given information, we can set up two equations:
x + y = 34 (equation 1)
2x + 4y = 86 (equation 2)
Now, we can solve the system of equations. We can start by multiplying equation 1 by 2 to eliminate the x variable:
2(x + y) = 2(34)
2x + 2y = 68
Next, we can subtract equation 2 from this new equation:
(2x + 2y) - (2x + 4y) = 68 - 86
-2y = -18
Dividing both sides of the equation by -2 gives us:
y = 9
Substituting this value back into equation 1:
x + 9 = 34
x = 34 - 9
x = 25
Therefore, there are 25 ducks and 9 pigs in the field.
A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute. Approximately how far will a passenger travel during a 5-minute ride?a. 132 feet
b. 659 feet
c. 1,978 feet
d. 3,956 feet
Step-by-step explanation:
Diameter, D = 42 feet
Circumference = πD = π x 42 = 131.95 feet
Number of rotations per minute = 3
Total time = 5 minutes
Total rotations = 5 x 3 = 15
Distance traveled per rotation = 131.95 feet
Distance traveled in 15 rotations = 15 x 131.95 = 1978 feet
Option C is the correct answer.
Do Now 60: What are the formulas to find area for a square, triangle, rectangle, parallelogram, trapezoid, circle, ellipse and equilaterial triangle?
Answer:
Area of a square = Length × Length
Area of a triangle = 1/2 base × height
Area of a rectangle = Length × breadth
Area of a parallelogram = base × height
Area of a trapezoid = 1/2 × sum of parallel sides × height
Area of circle = π × square of the radius
Area of ellipse = π × product of major and minor radii
Area of equilateral triangle = 1/2 base × height
Step-by-step explanation:
The area of a square is calculated by multiplying the length by itself.
The area of a triangle is calculated by multiplying half the base of the triangle by its height
The area of a rectangle is found by multiplying the length of the rectangle by its breadth
The area of a parallelogram is calculated by multiplying the base of the parallelogram by its height
The area of a trapezoid is found by multiplying half the sum of the two parallel sides by its height
The area of a circle is calculated by multiplying pi by the square of the radius of the circle
The area of an ellipse is found by multiplying pi by the product of the major and minor radii of the ellipse
The area of an equilateral triangle is calculated by multiplying half the base of the triangle by its height. The height is calculated using Pythagoras theorem
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Upper H 0: p less than or equals 0.6 Upper H Subscript a: p greater than 0.6 What type of test is being conducted in this problem?
Answer: right-tailed
Step-by-step explanation:
By considering the given information , we have
Null hypothesis : [tex]H_0: p\leq0.6[/tex]
Alternative hypothesis : [tex]H_a: p>0.6[/tex]
The kind of test (whether left-tailed, right-tailed, or two-tailed.) is based on alternative hypothesis.
Since the given alternative hypothesis([tex]H_a[/tex]) is right-tailed , so out test is a right-tailed test.
Hence, the correct answer is "right-tailed".
A body of constant mass m is projected vertically upward with an initial velocity v0 in a medium offering a resistance k|v|, where k is a constant. Neglect changes in the gravitational force. a. Find the maximum height xm attained by the body and the time tm at which this maximum height is reached.
Answer:
tm = tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }
Xm = Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg})
Step-by-step explanation:
Note, I substituted maximum time tm = tₐ and maximum height Xm = Xₐ
We will use linear ordinary differential equation (ODE) to solve this question.
Remember that Force F = ma in 2nd Newton law, where m is mass and a is acceleration
Acceleration a is also the rate of change in velocity per time. i.e a=dv/dt
Therefore F = m(dv/dt) = m (v₂-v₁)/t
There are two forces involved in this situation which are F₁ and F₂, where F₁ is the gravitational force and F₂ is the air resistance force.
Then, F = F₁ + F₂ = m (v₂-v₁)/t
F₁ + F₂ = -mg-kv = m (v₂-v₁)/t
Divide through by m to get
-g-(kv/m) = (v₂-v₁)/t
Let (v₂-v₁)/t be v¹
Therefore, -g-(kv/m) = v¹
-g = v¹ + (k/m)v --------------------------------------------------(i)
Equation (i) is a inhomogenous linear ordinary differential equation (ODE)
Therefore let A(t) = k/m and B(t) = -g --------------------------------(ia)
b = ∫Adt
Since A = k/m, then
b = ∫(k/m)dt
The integral will give us b = kt/m------------------------------------(ii)
The integrating factor will be eᵇ = e ⁽k/m⁾
The general solution of velocity at any given time is
v(t) = e⁻⁽b⁾ [ c + ∫Beᵇdt ] --------------------------------------(iiI)
substitute the values of b, eᵇ, and B into equation (iii)
v(t) = e⁻⁽kt/m⁾ [ c + ∫₋g e⁽kt/m⁾dt ]
Integrating and cancelling the bracket, we get
v(t) = ce⁻⁽kt/m⁾ + (e⁻⁽kt/m⁾ ∫₋g e⁽kt/m⁾dt ])
v(t) = ce⁻⁽kt/m⁾ - e⁻⁽kt/m⁾ ∫g e⁽kt/m⁾dt ]
v(t) = ce⁻⁽kt/m⁾ -mg/k -------------------------------------------------------(iv)
Note that at initial velocity v₀, time t is 0, therefore v₀ = v(t)
v₀ = V(t) = V(0)
substitute t = 0 in equation (iv)
v₀ = ce⁻⁽k0/m⁾ -mg/k
v₀ = c(1) -mg/k = c - mg/k
Therefore c = v₀ + mg/k ------------------------------------------------(v)
Substitute equation (v) into (iv)
v(t) = [v₀ + mg/k] e⁻⁽kt/m⁾ - mg/k ----------------------------------------(vi)
Now at maximum height Xₐ, the time will be tₐ
Now change V(t) as V(tₐ) and equate it to 0 to get the maximum time tₐ.
v(t) = v(tₐ) = [v₀ + mg/k] e⁻⁽ktₐ/m⁾ - mg/k = 0
to find tₐ from the equation,
[v₀ + mg/k] e⁻⁽ktₐ/m⁾ = mg/k
e⁻⁽ktₐ/m⁾ = {mg/k] / [v₀ + mg/k]
-ktₐ/m = ㏑{ [mg/k] / [v₀ + mg/k] }
-ktₐ = m ㏑{ [mg/k] / [v₀ + mg/k] }
tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }
Therefore tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] } ----------------------------------(A)
we can also write equ (A) as tₐ = m/k ㏑{ [mg/k] [v₀ + mg/k] } due to the negative sign coming together with the In sign.
Now to find the maximum height Xₐ, the equation must be written in terms of v and x.
This means dv/dt = v(dv/dx) ---------------------------------------(vii)
Remember equation (i) above -g = v¹ + (k/m)v
Given that dv/dt = v¹
and -g-(kv/m) = v¹
Therefore subt v¹ into equ (vii) above to get
-g-(kv/m) = v(dv/dx)
Divide through by v to get
[-g-(kv/m)] / v = dv / dx -----------------------------------------------(viii)
Expand the LEFT hand size more to get
[-g-(kv/m)] / v = - (k/m) / [1 - { mg/k) / (mg/k + v) } ] ---------------------(ix)
Now substitute equ (ix) in equ (viii)
- (k/m) / [1 - { mg/k) / (mg/k + v) } ] = dv / dx
Cross-multify the equation to get
- (k/m) dx = [1 - { mg/k) / (mg/k + v) } ] dv --------------------------------(x)
Remember that at maximum height, t = 0, then x = 0
t = tₐ and X = Xₐ
Then integrate the left and right side of equation (x) from v₀ to 0 and 0 to Xₐ respectively to get:
-v₀ + (mg/k) ㏑v₀ = - {k/m} Xₐ
Divide through by - {k/m} to get
Xₐ = -v₀ + (mg/k) ㏑v₀ / (- {k/m})
Xₐ = {m/k}v₀ - {m²g}/k² ㏑(1+{kv₀/mg})
Therefore Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg}) ---------------------------(B)
The question is about an object projected upwards under gravity and a certain resistance. The equations of motion will be non-linear due to the nature of the resistance. Solving these equations metaphorically or numerically will yield the maximum height and time taken to reach that height.
Explanation:The subject matter here is mechanics which falls under Physics. Given that there is a body of constant mass m projected upwards with an initial velocity v0 and the medium being passed through provides a resistance of k|v|, the equations of motion under this resistance will be non-linear.
The question here pertains to the calculations related to an object moving upwards under a given resistance and gravity. To obtain the maximum height achieved by the body xm and the time taken to reach that tm, we employ the trick of non-dimensionalisation. First, we observe the units of all physical quantities and using this, we can introduce reduced physical quantities which are dimensionless.
Unfortunately, these non-linear equations don’t have a neat analytical solution, and methods of approximation or numerical techniques might be necessary to solve them for particular initial conditions.
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Steve starts his hike at an elevation of -261 feet below sea level what was the change in elevation from the start of his hike to the end and elevation is -108 feet below sea level
Answer:
153 feet
Step-by-step explanation:
The change in elevation is the difference between his ending elevation and his starting elevation:
-108 -(-261) = 153 . . . feet
In the context of the BCG (Boston Consulting Group) matrix, the _____ is a poor performer that has only a small share of a slow-growth market. a. cash cow b. question mark c. star d. dog
Answer:
d. dog
Step-by-step explanation:
The BCG matrix is a tool used to assess the performance of the products of an organization on the basis of market share and market growth.
Basically there are 4 classes of products namely; Star, cash cow, question mark and dog.
Dogs are product with low market share and low growth.
Question mark have high growth but low market share while cash cows are the products with high mark share but low growth.
Stars are products with high market share and high market growth.
Hence dog is a poor performer that has only a small share of a slow-growth market. Option d.
A college faculty consists of 400 men and 250 women. The college administration wants to draw a sample of 65 faculty members to ask their opinion about a new parking fee. They draw a simple random sample of 40 men and another simple random sample of 25 women. What type of sample is this?
Answer:
The type of sample is Stratified sampling.
Step-by-step explanation:
Consider the provided information.
Types of sampling.
Random sampling is similar to placing the name of everyone in a hat and pulling out a few names.In Systematic sampling, we list of elements is counted off. Convenience sampling: data which is readily available is used. That is, the first people are running into by the surveyor.In Cluster sampling, we divide the population into groups, usually geographically. In Stratified sampling we divide population into groups called strata. but this time population might be separated into males and females.Here the population is divided into groups of males and females therefore it is stratified sampling.
Hence, the type of sample is Stratified sampling.
Is √m+n = √m + √n for all values of m and n? Explain why or why not.
Step-by-step explanation:
√(m + n) = √m + √n
Square both sides:
m + n = m + 2√(mn) + n
Simplify:
0 = 2√(mn)
mn = 0
The equation is only true if either m or n (or both) is 0.
Final answer:
The square root of the sum of two numbers is not equal to the sum of the square roots of those numbers.
Explanation:
No, √m+n is not equal to √m + √n for all values of m and n. This is because of the nature of square roots and how they interact with addition. Taking the square root of a sum is not the same as the sum of the square roots. For example, for m = 4 and n = 9, √4 + √9 = 2 + 3 = 5, but √(4 + 9) = √13, which is not equal to 5. This example illustrates how the two expressions yield different results, emphasizing the importance of understanding the properties of square roots in mathematical operations.
A company's annual profit, P, is given by P=−x2+195x−2175, where x is the price of the company's product in dollars. What is the company's annual profit if the price of their product is $32?
Answer: the company's annual profit if the price of their product is $32 is $3041
Step-by-step explanation:
A company's annual profit, P, is given by P = −x²+ 195x − 2175, where x is the price of the company's product in dollars.
To determine the company's annual profit if the price of their product is $32, we would substitute x = 32 into the given equation. It becomes
P = −32²+ 195 × 32 − 2175
P = −1024 + 6240 − 2175
P = $3041
F(x)=-1/4x-3, find the value of x for which f(x)=x
Answer:
x = -2.4
Step-by-step explanation:
f(x) = -1/4x -3
x = -1/4x -3 . . . . . the desired value of f(x)
5/4x = -3 . . . . . . . add 1/4x
x = -12/5 . . . . . . . multiply by 4/5, the inverse of 5/4
__
Check
-1/4(-2.4) -3 = 0.6 -3 = -2.4 = x . . . . answer checks OK
Choose the correct solution graph for the inequality.
The correct answer is: Option number 4 (Last Option)
Step-by-step explanation:
Given inequality is:
-6x > 42
In order to solve the inequality,
Dividing both sides by 6
[tex]-\frac{6x}{6} > \frac{42}{6}\\-x > 7[/tex]
Multiplying by -1
[tex]x<7[/tex]
As the solution is x<7, this means that the number 7 will not be included in the solution and all numbers less than 7 will be a part of the solution.
The number which is not included in the solution is marked by a shallow circle on the number line.
Hence,
The correct answer is: Option number 4 (Last Option)
Keywords: Number line, inequality
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A salesman packed 3 shirts and 5 ties. With one shirt, he could wear all 5 ties. With another shirt, he could wear 4 ties. With the third shirt, he could wear only 2 ties. How many different combinations did he have? a) 40 b) 22 c) 11 d) 10
Answer:
11 different combinations
Step-by-step explanation:
A salesman packed 3 shirts and 5 ties.
With one shirt, he could wear all 5 ties = 5 combinations
With another shirt, he could wear 4 ties = 4 combinations
With the third shirt, he could wear only 2 ties= 2 combinations
number of different combinations= [tex]5+4+2=11[/tex]
so answer is 11
The shape of France's production possibilities frontier (PPF) should reflect the fact that as France produces more cars and fewer trucks, the opportunity cost of producing each additional car?
Answer:
the opportunity cost of producing each additional car REMAINS CONSTANT
In March, Delphine's house had 40% more snowfall than in February. Delphine's house had f centimeters of snowfall in February.A. 40 f. B. 40+f C. 1.4f D. 40f+f
Answer:
It's A
Step-by-step explanation:
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The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming the distribution of commuting times is known to be mound-shaped and symmetric, what percentage of these commuting times are between 50 and 110 minutes?
Answer:
81.85% of the workers spend between 50 and 110 commuting to work
Step-by-step explanation:
We can assume that the distribution is Normal (or approximately Normal) because we know that it is symmetric and mound-shaped.
We call X the time spend from one worker; X has distribution N(μ = 70, σ = 20). In order to make computations, we take W, the standarization of X, whose distribution is N(0,1)
[tex] W = \frac{X-μ}{σ} = \frac{X-70}{20} [/tex]
The values of the cummulative distribution function of the standard normal, which we denote [tex] \phi [/tex] , are tabulated. You can find those values in the attached file.
[tex]P(50 < X < 110) = P(\frac{50-70}{20} < \frac{X-70}{20} < \frac{110-70}{20}) = P(-1 < W < 2) = \\\phi(2) - \phi(-1)[/tex]
Using the symmetry of the Normal density function, we have that [tex] \phi(-1) = 1-\phi(1) [/tex] . Hece,
[tex]P(50 < X < 110) = \phi(2) - \phi(-1) = \phi(2) - (1-\phi(1)) = \phi(2) + \phi(1) - 1 = \\0.9772+0.8413-1 = 0.8185[/tex]
The probability for a worker to spend that time commuting is 0.8185. We conclude that 81.85% of the workers spend between 50 and 110 commuting to work.
Max is a diver. He uses positive numbers to represent elevations above the water's surface and negative numbers to represent elevations below the water's surface. Max is standing on the springboard. He represent his location as 3 meters. He lets a ring drop to the bottom of the pool. He represents its location at the bottom of the pool as -4 meters. How many meters below the surface of the water is the ring? A. Less than 4 meters B. More than 4 meters C. Exactly 4 meters D. Exactly 3 meters Please help: :)
Given the pay rate and hours worked, determine the gross earnings. Make sure to include decimals and appropriate zeros. rate 6.50 hours 40
Final answer:
To determine the gross earnings for 40 hours worked at a pay rate of $6.50 per hour, multiply the pay rate by hours. The gross earnings would be $260.00.
Explanation:
To calculate the gross earnings given the pay rate and hours worked, we use a simple multiplication. However, there is an additional consideration mentioned in Exercise 3.1, which states that the employee should receive 1.5 times the hourly rate for hours worked above 40 hours. Therefore, the calculation involves two steps if the number of hours exceeds 40.
Calculation:
If hours ≤ 40, the formula is:In this particular case, the student only worked 40 hours at a pay rate of $6.50 per hour. Using the first formula, the gross earnings would be:
Gross Earnings = $6.50/hour × 40 hours = $260.00
A, B, and C are collinear, and B is between A and C. The ratio of AB to AC is 4:5. If A is at (-3,7) and B is at (1,-5), what are the coordinates of point C?
Answer:
Step-by-step explanation:
AB:AC=4:5
AB:BC=4:5-4 OR 4:1
So B divides AC in the ratio 4:1