Simplify: 20 sin(2x) cos(2x)
To simplify 20 sin(2x) cos(2x), apply the double-angle trigonometric identities for sine and cosine.
The given expression: 20 sin(2x) cos(2x) can be simplified using the double-angle trigonometric identity for sine and cosine.
Apply the identities sin(2x) = 2sin(x)cos(x) and cos(2x) = cos²(x) - sin²(x).Substitute these identities into the expression and simplify to get the final result.A cylinder storage tank is to contain V=16,000pi cubic feet (about 400,00 gallons). the cost of the tank is proportional to its area, so the minimal-cost tank will be the one with minimum area. The volume (V) of a cylinder of radius r and height h is (pi)(r^2)(h). its surface area is the area of top and bottom, 2(pi)(r^2), plus the side area 2(pi)(r^2)(h). find the dimensions, r and h, of the minimal-area tank
Can someone please answer this?
What's the best five terms to the list?
the letters are going backwards and they use each letter twice
so next 5 should be vt, ut, us, ts, tr
For football tryouts at a local school, 12 coaches and 42 players will split into groups. Each group have the same number of coaches and players. What is the greatest number of groups that can be formed? How many coaches and players will be in each of these groups?
20 friends and 12 invations are left how many has she mailed
20-12 8
She has mailed 8 invitations.
Car cost $40000 it depreciates 12% each year. What is the cars value in 5yrs
14,000 acres of 40,000 acre forest burned in a forest fire. What percentage of the forest was damaged?
A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Another way to state the transformation is D. R0, 360°
Calculations and Parameters
Given that the rotation is:
(x,y) --------> (x,y)
This shows that it goes back to its original position and there is a full rotation occurred.
Based on its full rotation to 360°, it can be noted that option D is another way to state the transformation as other given rotations would give different translations.
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Answer: I can confirm it’s D Ro, 360°
Step-by-step explanation:
1)broccoli is 4lbs for $5 if she buys 3 pounds how much will it cost 2) if she buys 4.2 pounds of it what will be the cost
Martina made 35 hats. Martina made 7 times as many hats as shen. Let h be the number of hats that shen made
The mean incubation time for a type of fertilized egg kept at 100.7100.7â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 22 daysdays. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 1919 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?
A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.
It is stated that the total bill the patient would only pay would be the $25 plus 20% of the original bill. Therefore this would mean that:
25 + 0.2 * X = 200 ---> 1
25 + 0.2 * X = 800 ---> 2
Where X represents the original bill.
Calculating for X in equation 1:
25 + 0.2 * X = 200
0.2 * X = 175
X = 875
Calculating for X in equation 2:
25 + 0.2 * X = 800
0.2 * X = 775
X = 3875
Therefore the original bill ranges from $875 to $3875. The equality equation would be:
$875 ≥ X ≥ $3875
Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.2 (16 – π) in.2 (64 – 16π) in.2 (64 – 4π) in.2Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.2 (16 – π) in.2 (64 – 16π) in.2 (64 – 4π) in.2vvvv
Answer: [tex]64-16\pi[/tex] unit square.
Step-by-step explanation:
Here, four circle are removing from a square from the square of edge 8.
Since, The area of the square= [tex]8^2=64[/tex] square unit ( because, area of square=side×side)
The area of a circle with radius 2 = [tex]\pi(2)^2=4\pi[/tex] square unit.
The area of four circle of radius 2= [tex]4\times4\pi=16\pi[/tex] square unit.
According to the question, these four circle are removed by the above square.
Therefore remaining area of the square after removing these four circle=area of the square- area of four circle of radius 2= [tex]64-16\pi[/tex] square unit.
The remaining area of the square is 64 - 16π.
What is a circle?A circle is a bounded figure in which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius
Area of one circle = 2²π = 4π
Area of four circles = 4 x 4π = 16π
What is a square?A square is a quadrilateral with four equal sides.
Characteristics of a square includes:
Area of a square = length²
= (2x4)²
= 64
The remaining area of the square = 64 - 16π
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if f(x)=3/x+2 -√x-3, complete the following statement (round your answer to the nearest hundredth) f(7)=
The given function [tex]f(x) = \dfrac{ 3}{x + 2} -\sqrt{x-3}[/tex] The value of f(7) would be -1.67.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
The given function
[tex]f(x) = \dfrac{ 3}{x + 2} -\sqrt{x-3}[/tex]
By substitute x = 7 to find f(7)
[tex]f(7) = \dfrac{ 3}{7 + 2} -\sqrt{7-3}\\\\f(7) = \dfrac{ 3}{9} -\sqrt{4}\\\\f(7) = \dfrac{ 1}{3} -2\\\\f(7) = \dfrac{ 1 - 6}{3}\\\\f(7) = \dfrac{ -5}{3}\\[/tex]
f(7)= -5/3 = -1.67
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Traveling at 65 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 125 miles from San Diego to Malibu?
We can establish a proportion:
Since an hour = 60 minutes
If it takes 60 minutes to travel 65 miles (speed)
X minutes it will take to travel 125 miles
X = 125miles*60 minutes/65 miles = 115 minutes approximately
Answer : 115 minutes approximately
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
You want to buy a tent in the shape of a pyramid. The rectangular base is 35 square feet, with a height of 4 feet. What is the volume of the tent? Round your answer to the nearest hundredth.
23.33 cubic feet
46.67 cubic feet
93.33 cubic feet
140 cubic feet
V=(l*w*h)/3
need to find length = square root(35) 5.916
(5.916 *5.916*4)/3 =46.665
round to 46.67 cubic feet
A survey conducted by a song rating service finds that the percentages of listeners familiar with poker face by lady gaga who would give the song ratings of 5, 4, 3, 2, and 1 are, respectively, 50 percent, 18 percent, 19 percent, 8 percent, and 5 percent. assign the numerical values 1, 2, 3, 4, and 5 to the (qualitative) ratings 1, 2, 3, 4, and 5 and find an estimate of the probability distribution of x = this song’s rating by a randomly selected listener who is familiar with the song.
The probability distribution of the song 'Poker Face' ratings by a randomly selected listener familiar with the song can be represented by assigning probabilities to each rating based on the survey percentages. The sum of these probabilities equals 1, confirming a valid distribution.
Explanation:The student is asking about how to find the probability distribution for the ratings given to the song 'Poker Face' by Lady Gaga. To solve this, we assign numerical values to the qualitative ratings: 1, 2, 3, 4, and 5 correspond to the ratings 1 through 5, respectively.
We can list out the probabilities for each rating based on the survey as such:
Rating 5: P(X=5) = 50% or 0.50Rating 4: P(X=4) = 18% or 0.18Rating 3: P(X=3) = 19% or 0.19Rating 2: P(X=2) = 8% or 0.08Rating 1: P(X=1) = 5% or 0.05This list represents the estimation of the probability distribution of a song's rating by a randomly selected listener familiar with the song. In other words, it tells us the likelihood that a listener would rate the song at a certain level.
To confirm this is a valid probability distribution, we must check that the sum of all probabilities adds up to 1:
0.50 + 0.18 + 0.19 + 0.08 + 0.05 = 1.00
Since the sum is equal to 1, we have a valid probability distribution.
the length of a rectangular floor is 5 feet less than twice it's width. the area of the floor is 150 square feet. what is the width of the room?
A minor league baseball team plays 72 games in a season. If the team won 15 more than twice as many games as they lost, how many wins and losses did the team have?
A bicycle store costs $2,400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?
Which property of polynomial addition says that the sum of two polynomials is always a polynomial
Answer:
Closure
Step-by-step explanation:
Which factor do 64x^2+48x+9 and 64x^2 - 9 have in common?
The distance between points
Simplify (7x+42)/(x^2+13x+42)
The simplified expression is given by:
[tex]\dfrac{7}{x+7}[/tex]
Step-by-step explanation:We are asked to simplify the expression which is given in terms of variable x as:
[tex]=\dfrac{7x+42}{x^2+13x+42}[/tex]
The given expression is a rational expression as it is a polynomial expression in the denominator as well as in the numerator.
Now we know that:
[tex]7x+42=7(x+6)[/tex]
and
[tex]x^2+13x+42=x^2+7x+6x+42\\\\\\i.e.\\\\\\x^2+13x+42=x(x+7)+6(x+7)\\\\\\i.e.\\\\\\x^2+13x+42=(x+7)(x+6)[/tex]
Hence, we get:
[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{(x+6)(x+7)}\\\\\\i.e.\\\\\\\dfrac{7x+42}{x^2+13x+42}=\dfrac{7}{x+7}[/tex]
Hence, the simplified expression is:
[tex]\dfrac{7}{x+7}[/tex]
Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.
Final answer:
The question asks for the original vector function given its derivative and an initial condition. Through integration and applying the initial condition, the vector function is found to be r(t) = t⁵i + t⁶j + (t²/2 + 1/2)k.
Explanation:
The question involves finding the vector function r(t) given its derivative r'(t) = 5t⁴i + 6t⁵j + t k and an initial condition r(1) = i + j. To find r(t), integrate each component of r'(t) with respect to t. The integration results in:
The i component: ∫5t4 dt = t⁵/1 + C₁The j component: ∫6t5 dt = t⁶/1 + C₂The k component: ∫t dt = t²/2 + C₃Therefore, r(t) = (t⁵/1 + C₁)i + (t⁶/1 + C₂)j + (t²/2 + C₃)k. Substituting t = 1 and using the initial condition r(1) = i + j to find the constants C₁, C₂, and C₃, we get:
C₁ = 0C₂ = 0C₃ = 1/2Finally, r(t) = t⁵i + t⁶j + (t²/2 +1/2) k.
The function [tex]\( r(t) \)[/tex] is:
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]
[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]
To find [tex]\( r(t) \) given \( r'(t) \) and \( r(1) \)[/tex], we need to integrate[tex]\( r'(t) \)[/tex]with respect to ( t ) and then use the given initial condition ( r(1) ) to determine the constant of integration.
Given:
[tex]\[ r'(t) = 5t^4i + 6t^5j + tk \][/tex]
[tex]\[ r(1) = i + j \][/tex]
First, let's integrate [tex]\( r'(t) \)[/tex] with respect to [tex]\( t \)[/tex] to find [tex]\( r(t) \)[/tex]:
[tex]\[ r(t) = \int 5t^4i \, dt + \int 6t^5j \, dt + \int tk \, dt \][/tex]
[tex]\[ r(t) = \frac{5}{5}t^5i + \frac{6}{6}t^6j + \frac{1}{2}t^2k + C \][/tex]
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k + C \][/tex]
Now, we apply the initial condition [tex]\( r(1) = i + j \)[/tex]:
[tex]\[ r(1) = (1)^5i + (1)^6j + \frac{1}{2}(1)^2k + C = i + j \][/tex]
[tex]\[ i + j + \frac{1}{2}k + C = i + j \][/tex]
Comparing the coefficients of [tex]\( i \), \( j \), and \( k \)[/tex], we get:
Coefficient of [tex]\( i \): \( 1 = 1 \)[/tex] (matches)
Coefficient of [tex]\( j \): \( 1 = 1 \)[/tex] (matches)
Coefficient of [tex]\( k \): \( \frac{1}{2} = 0 \)[/tex] (doesn't match)
So, to make the coefficients match, [tex]\( C = -\frac{1}{2} \)[/tex].
Therefore, the function [tex]\( r(t) \)[/tex] is:
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]
[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]
how much will the toll be after the increase
130% = 1.30
multiply 2.50 x 1.30
2.50 x 1.30 = 3.25
the new toll is 3.25
Professor whata guy surveyed a random sample of 420 statistics students. one of the questions was, "will you take another mathematics class?" the results showed that 252 of the students said yes. what is the sample proportion, p, of students who saud they would take another math class?
The sample proportion, p, of students who said they would take another math class, p = 0.6 or 60%.
To determine the sample proportion, p, you can use the following formula:
p = x/nwhere:
x is the number of students who said yes (successes).n is the total number of students surveyed.From the question,
x = 252n = 420Substituting these values into the formula gives:
p = 252 / 420 = 0.6
Therefore, the sample proportion of students who said they would take another math class is 0.6 or 60%.
Which of theses numbers is the smallest 0.02, 0.24, 0.11, 0, 2
Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? Is this number evidence of a grand design, a massive freak coincidence or something else?