You need to stabilize a flagpole by string in a guy-wire from the top of a flagpole to the ground. The pole is 15 feet tall and angle of elevation is 70 degrees. Using trig ratios calculate how much wire is needed
Answers
w=h/sinα, we are told that h=15 ft and α=70° so
w=15/sin70° ft
w≈15.96 ft (to nearest hundredth of a foot)
The length of the wire needed is:
15.9625 feet
Step-by-step explanation:We will model this problem with the help of a right angled triangle such that the side opposite to the angle 70 degree is: 15 feet.
Now, we are asked to find the amount of wire used i.e. we are asked to find the hypotenuse of the right angled triangle.
We will use the sine trignometric ratio as follows:
[tex]\sin 70=\dfrac{15}{x}\\\\i.e.\\\\x=\dfrac{15}{\sin 70}\\\\i.e.\\\\x=\dfrac{15}{0.9397}\\\\i.e.\\\\x=15.9625\ feet[/tex]
Related Questions
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
Answers
In the 30°-60°-90° triangle, the side lying opposite to the angle 30° is half the hypotenuse, so:
[tex]a= \frac{x}{2} [/tex]
By the Pythagorean theorem:
[tex]b^2 = c^2-a^2\\ \\b^2=x^2-( \frac{x}{2} )^2 = x^2- \frac{x^2}{4} = \frac{4x^2-x^2}{4}= \frac{3x^2}{4} \\ \\ b= \sqrt{ \frac{3x^2}{4} } = \frac{ \sqrt{3x^2} }{ \sqrt{4} } = \frac{x \sqrt{3} }{2} [/tex]
[tex]\text{Perimeter }=x+ \frac{x}{2} + \frac{x \sqrt{3} }{2}= \frac{2x+x+x \sqrt{3}}{2}= \frac{3x+x \sqrt{3} }{2}[/tex]
For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.
Explanation:In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the
perimeter
of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.
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Evaluate p(7,5) can someone help
Answers
----------------------------------------------
Work Shown:
P(n,r) = (n!)/((n-r)!)
P(7,5) = (7!)/((7-5)!)
P(7,5) = (7!)/(2!)
P(7,5) = (7*6*5*4*3*2*1)/(2*1)
P(7,5) = (5040)/(2)
P(7,5) = 2520
The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.
Answers
The angle EAB is 90+60 = 150.
The law of the cosines helps:
BE^2 = AE^2 + AB^2 - 2*AB*AE*cos(150) = 4^2 + 4^2 - 2*4*4*(-sqrt(3)/2)
BE^2 = 16+16+16*sqrt(3) = 16(2+sqrt(3)),
BE = 4*sqrt( 2 + sqrt(3 ) ) Nice number
BE ~ 7.7274 ... ~ 7.73
In fact, if you take a ruler, one can see that the ratio between AB and BE is ~ 1.95 which s the same number.
Answer: BE = 4*sqrt( 2 + sqrt(3 ) ) ~ 7.73
BE is [tex]7.73[/tex]
What is Square?
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
What is equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.
We have to find BE.
Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]
The angle EAB is [tex]90+60 = 150[/tex]°
Using the law of the cosines, we get
[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]
[tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]
⇒[tex]BE=7.73[/tex]
Hence, we can conclude that BE is [tex]7.73[/tex]
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SOMEONE PLEASE HELP!!!!
Which area formula or formulas show(s) a joint variation?
I A=s^2
II A=pir^2
III A=l*w
Select one:
a. III only
b. II and III
c. II only
d. I, II, and III
Answers
Equation 1
A = s²
Here we have only one variable, 's', and the value of Area will only vary when s varies.
Equation 2
A = πr²
Here the only variable is 'r', which is the radius of a circle. The value of Area, A, varies as radius varies. π is a constant.
Equation 3
A = l×w
Here we have to variables, the 'l' and the 'w'.
We can say that the value of Area, A, will vary jointly as l and w vary
The correct answer is option a)
Answer:
Step-by-step explanation:
What is the solution to the following system?
3x+2y+z=20
x-4y-z=-10
2x+y+2z=15
A. (2, 3, 4)
B. (4, 3, –2)
C. (4, 3, 2)
D. (6, 7, –2)
Answers
Answer:
C. (4, 3, 2)
Step-by-step explanation:
Given : [tex]3x+2y+z=20[/tex]
[tex]x-4y-z=-10[/tex]
[tex]2x+y+2z=15[/tex]
To Find: Solution:
[tex]3x+2y+z=20[/tex] -1
[tex]x-4y-z=-10[/tex] --2
[tex]2x+y+2z=15[/tex] --3
Substitute the value of z from 1 in 2 and 3
So in 2 , [tex]x-4y-(20-3x-2y)=-10[/tex]
[tex]x-4y-20+3x+2y=-10[/tex]
[tex]4x-2y=-10+20[/tex]
[tex]4x-2y=10[/tex] ---4
So, in 3 , [tex]2x+y+2(20-3x-2y)=15[/tex]
[tex]2x+y+40-6x-4y=15[/tex]
[tex]-4x-3y=15-40[/tex]
[tex]-4x-3y=-25[/tex] -5
Now solve 4 and 5
Substitute the value of x from 4 in 5
[tex]-4(\frac{10+2y}{4})-3y=-25[/tex]
[tex]-1(10+2y)-3y=-25[/tex]
[tex]-10-2y-3y=-25[/tex]
[tex]-10-5y=-25[/tex]
[tex]-5y=-15[/tex]
[tex]y=3[/tex]
Now substitute the value of y in 4
[tex]4x-2(3)=10[/tex]
[tex]4x-6=10[/tex]
[tex]4x=10+6[/tex]
[tex]4x=16[/tex]
[tex]x=4[/tex]
Now substitute the value of x and y in 1 to get value of z
[tex]3(4)+2(3)+z=20[/tex]
[tex]12+6+z=20[/tex]
[tex]18+z=20[/tex]
[tex]z=20-18[/tex]
[tex]z=2[/tex]
Thus The solution is (4,3,2)
Hence Option c is correct.
you have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friends to have the same balance?
Answers
140 + 10x = y
95 + 19x = y
You will have the same balance after 5 weeks.
help factoring trinomial
Answers
need 2 numbers when added = 5 and when multiplied = -24
answer is D
-3+8 = 5
-3*8 = -24
-24 = (+8) * (-3)
8 - 3 = 5
so
x^2 + 5x - 24 = (x + 8)(x - 3)
answer is
D.(x - 3)(x + 8)
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
Answers
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18.
Answers: symmetrical, uniform, skewed to the left, skewed to the right.
Answers
x Count
---- ---------
16 2
17 2
18 2
19 2
20 2
21 2
Graph the data set to show the histogram shown below.
It is clear that the data s uniformly distributed.
Answer: uniform
What are the solutions of the equation z2-12z+36=0
Answers
(z - 6)(z - 6) = 0
z - 6 = 0
z = 6
solution is : 6,6
A line passes through (−2, 5) and has slope 13 . What is an equation of the line in point-slope form
Answers
slope(m) = 13
(-2,5)...x1 = -2 and y1 = 5
sub...pay attention to ur signs
y - 5 = 13(x - (-2)...not done yet
y - 5 = 13(x + 2) <== point slope form
The demand function for an auto parts manufacturing company is given by f(x) = 100000 - 2500x , where x represents price and f(x) represents quantity. f^-1 (x) = _______. In the inverse function, the variable X represents _____
Answers
Answer:
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
The variable X represents the quantity.
Step-by-step explanation:
We are given that
The demand function for an auto parts manufacturing company is fiven by
f(x)=100000-25 x
Where x=Represents price
f(x)= Represents quantity
We have to find inverse function [tex]f^{-1}(X)[/tex]
Let f(x)=X
[tex]X=100000-2500 x[/tex]
[tex]2500x=100000-X[/tex]
[tex]x=\frac{100000-X}{2500}[/tex]
Substituting the value of x then we get
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Therefore, the inverse function
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Where X= Represents the quantity
[tex]f^{-1}(X)[/tex]=Represents price
What is the average rate of change from x = 2 to x = 3?
2
3
0
5
Answers
(y_final-y_start)/(x_final-x_start) (also for physics!)
In your case:
average rate of change is:
(-1-(-3))/(3-2) = 2/1=2
You can see it's +, so increasing (yeah).
if you would make the interval very small, from x=2 to x=2.00001, and so n, you'd get the concept of slope and derivative (but that's just to let u know)
Answer:
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
Step-by-step explanation:
The average rate of a function f(x) on the interval [a,b] is defined as
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
The average rate of change from x = 2 to x = 3 is
[tex]m=\frac{f(3)-f(2)}{3-2}[/tex] .... (1)
From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.
Put f(2)=-3 and f(3)=-1 in equation (1).
[tex]m=\frac{-1-(-3)}{3-2}[/tex]
[tex]m=\frac{-1+3}{1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
twice a number added to 4 is 28
Answers
should be
2x + 4 = 28
2x = 28-4
2x = 24
x = 12
hope it helps
Given,
2x + 4 = 28
2x = 24
x = 12
Hence, the number is 12.
87 less than the quotient of an unknown number and 43 is -75.
What is the value of the unknown number?
Answers
x / 43 - 87 = -75
x/43 = -75 + 87
x/43 = 12...multiply both sides by 43
x = 12 * 43
x = 516 <==
The circle shown below has ab and bc as its tangents: ab and bc are two tangents to a circle which intersect outside the circle at a point
b. if the measure of arc ac is 160°, what is the measure of angle abc? 80° 40° 60° 20°
Answers
One of the theorems of circle is that the measure of the intercepted arc is twice as that of its opposite angle. In this case, since the intercepted arc measures 160°, then the measure of angle abc is 160/2 = 80°.
Therefore, the answer is 80°.
Answer:
Answer: 20°
Step-by-step explanation:
You invest $3,756.00 and buy 100 shares of a company's stock. Their value increases by 12%. How much is each share worth?
Answers
$37.56(1.12)
$42.0672
$42.07 (to nearest cent)
Answer:
Each share worth is $42.0672 .
Step-by-step explanation:
As given
You invest $3,756.00 and buy 100 shares of a company's stock.
Their value increases by 12%.
12% is written in the decimal form
[tex]= \frac{12}{100}[/tex]
= 0.12
Share value increase = 0.12 × Investment cost
= 0.12 × 3756
= $450.72
Total value of shares becomes after increases of 12% = Share value increase + Investment cost .
Total value of shares becomes after increases of 12% = $3756+ $450.72
= $4206.72
[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]
[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]
Each shares worth = $42.0672
Therefore the each share worth is $42.0672 .
What is 8q+3(10q^2+2)+8
Answers
= 8q + 30q^2 + 6 + 8
= 30q^2 + 8q + 14
Hope it helped!
Find the area of a regular hexagon with a 48-inch perimeter.
48√3 in2
96√3 in2
192√3 in2
in2 means inches squared
Answers
I need help with this problem and a few others
Answers
What is the solution set of the following equation? -5x + x + 9 = -4x + 12
Answers
-4x + 9 = -4x + 12
-4x + 4x = 12 - 9
0 = 3.....incorrect....NO SOLUTION
What is the solution set of the following equation? -5x + x + 9 = -4x + 12
X=0
which of the following could be the equation of the graph shown below
Answers
2y = 4x - 6
y = 2x - 3....y int = -3 , x int = (3/2,0)
I believe it is going to be : -4x + 2y = -6
Answer:
-4x+2y+-6 and y=3x-2
A shipping company offers various sized shipping boxes to its customers. Some of these boxes are cube-shaped, with equal height, width, and depth. As part of an upcoming sales promotion, the company will offer two cube-shaped boxes for the price of one.
a. Write an expression to represent the total volume of two different sized boxes as a sum of cubes if one of the boxes has sides with a length of 1 foot and the other has sides with a length of x feet.
b. Factor the sum of cubes.
c. Calculate the total volume of the two boxes if x = 3 feet.
Answers
[tex]m*m*m= m^{3} [/tex] foot cubed.
a.
Let v1 be the volume of the box with side length 1 ft.
and v2 be the volume of the box with side length x ft.
[tex]V1=1^{3}=1[/tex] (foot cubed)
[tex]V2=x^{3}[/tex] (foot cubed)
Vtotal=[tex]V1+V2=1+x^{3}[/tex] feet cubed
b.
by the "sum of cubes" identity:
[tex]x^{3}+1=(x+1)( x^{2} -x+1) [/tex],
this identity can be derived by dividing [tex]x^{3}+1[/tex] by (x+1), by long division.
c. Vtotal when x=3 feet is:
Vtotal=[tex]V1+V2=1+3^{3}=1+27=28[/tex] (feet cubed)
What is the area of a regular hexagon with a side of 5 and an apothem of 4.33
Answers
a(n,s)=(ns^2)/(4tan(180/n)), where n=number of sides and s=side length
(notice apothem is not needed :P)
a(6,5)=(6*5^2)/(4tan(180/6)
a(6,5)=37.5/tan30
a(6,5)≈64.95 units (to nearest hundredth of a unit)
The main cables of a suspension bridge are ideally parabolic. the cables over a bridge that is 400 feet logn are attached to towers that 100 feet tall. the lower point of the cable is 40 feet abouve the bdrige. find the equation that can be used to model the cables.
Answers
Let the vertex be on the y axis, exactly, at the point (0, 40)
Another point of this parabola is (200, 100), as can be checked from the figure.
The vertex form of the equation of a parabola is :
[tex]y=a(x-h)^{2}+k [/tex], where (h, k) is the vertex of the parabola,
replacing (h, k) with (0, 40), we have:
[tex]y=ax^{2}+40[/tex]
to find a, we substitute (x, y) with (200, 100):
[tex]100=a200^{2}+40[/tex]
40,000a=60
a=60/40,000=3/(2,000)
So, the equation of the parabola is [tex]y= \frac{3}{2000} x^{2}+40[/tex]
The equation to model the suspension cables of a bridge, where the lowest point of the cable is 40 feet above the bridge, and the towers are 100 feet tall and 200 feet from the center, is y = -0.0015x^2 + 60.
Explanation:To find the equation that models the suspension cable of a bridge, we use the properties of a parabolic shape. Since the cable is attached to towers that are 100 feet tall and the lowest point of the cable is 40 feet above the bridge, we know the vertex of the parabola is 60 feet (100 - 40) below the top of the towers.
Let's define the coordinate system with the origin at the lowest point of the cable. Then the towers are at (-200, 60) and (200, 60) because the bridge is 400 feet long, so each tower is 200 feet horizontally from the center. The parabolic equation takes the general form y = ax^2 + bx + c. Because the vertex is at (0, 60), c = 60.
Using the points (-200, 60), we can substitute into the parabolic equation and write a system to solve for a and b. Since the parabola is symmetric, b = 0. The system becomes 60 = a(-200)^2 + 60, which simplifies to a = -60/40000.
Thus, the equation to model the cables is y = -60/40000x^2 + 60, or simplified, y = -0.0015x^2 + 60.
I REALLY NEED HELP ON THESE QUESTIONS!!!! IM SOOO STUCK!!!!
A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 4 ounces of Celebes Kalossi, and costs $15. The second mixture has 4 ounces of Sumatra and 12 ounces of Celebes Kalossi, and costs $21. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?
Answers
12*x + 4*y=15
4*x + 12*y = 21
Now, solve it. For instance (there are many ways):
Multiply the second equation by (-3):
12*x + 4*y=15
-12*x -36*y = -63
Sum them up (x cancel out. That's why we multiply by -3)
-32y=-48, y = 48/32=6/4=3/2
y = 3/2 and x = go to any equation. Say the second again:
4*x + 12*y = 21
4x + 12*3/2 =21 ----> 4x + 18=21, 4x = 3, x = 3/4.
So cost of Sumatra $ 3/2 per oz, or $ 1.50
Cost of Celebes Kalossi (what a name!) $ 3/4 per oz = $ 0.75 per oz
Let's check it with the first equation:
12*0.75+4*1.5 = 15!
Clear?
How old is molly if she was 52 years old when she was fourteen years ago?
Answers
52+14=x
66=x
We know this equation is true because 14 years ago, she was 52 so 14 years later, she is 66.
The area of a rectangular lot that is 50 feet wide by 100 feet deep is:
Answers
The area of a rectangle can be directly calculated using the formula:
A = l * w
Where l is the length or the depth while w is the width
Therefore,
A = 50 feet * 100 feet
A = 5000 square feet
Explain why two similar right triangles will have the same cosine ratios.
Answers
LET θ’s (opp,adj,hypo)=(AB,BC,AC) and (PQ,QR,PR)
Then by similarity,
sinθ=AB/AC=PQ/PR ,cosθ=BC/AC=QR/PR ,tanθ=AB/BC=PQ/QR
the corresponding ratio of (adjacent side/hypotenuse),and hence
the cosine ratio must be the same
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Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
Answers
The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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