Recall the half-angle identity for cosine:
cos²(x) = 1/2 (1 + cos(2x))
Then we can rewrite the integrand as
cos³(4x) = cos(4x) cos²(4x) = 1/2 cos(4x) (1 + cos(8x))
So we have
[tex]\displaystyle \int \cos^3(4x) \, dx = \frac12 \int (\cos(4x) + \cos(4x)\cos(8x)) \, dx[/tex]
Next, recall the cosine product identity,
cos(a) cos(b) = 1/2 (cos(a - b) + cos(a + b))
so that the integral is equivalent to
[tex]\displaystyle \int \cos^3(4x) \, dx = \frac12 \int \cos(4x) \, dx + \frac14 \int (\cos(4x - 8x) + \cos(4x + 8x)) \, dx[/tex]
[tex]\displaystyle \int \cos^3(4x) \, dx = \frac34 \int \cos(4x) \, dx + \frac14 \int \cos(12x) \, dx[/tex]
Computing the rest is trivial:
[tex]\displaystyle \int \cos^3(4x) \, dx = \boxed{\frac3{16} \sin(4x) + \frac1{48} \sin(4x) + C}[/tex]
A car travelling at a constant speed covers 585 km in 9 hours. In how much time will it cover in 520 km? I want the answer in direct or inverse proportion.
Answer:
It took eight hours to travel 520km
Step-by-step explanation:
Help help help
Help hep help
Answer:
-2
Step-by-step explanation:
-4x-2x ≤ 17-5
-6x ≤ 12 | /(-6)
x ≥ -2
Does anyone know the answer to this? Please help
I need help with number 5 please
Answer:
-4[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I hope this helps!
can you help me to my module
Answer:
Yes, what is your question
Step-by-step explanation:
Answer:
yes what is your question
PLEASE HELP WITH THIS ONE QUESTION
Answer:
The graph moved down 5 units
Step-by-step explanation:
Answer:
Step-by-step explanation:
The best way to get an answer to this question is to study the graph you get when you study the result from Desmos, which is a free graphing program.
Notice the way the graph is laid out. If the graph was simply y = x^2 - 6x then the y value for the minimum value would be x = 3 (just like the 2 values you do get) and y = -9
But y = x^2 - 6x + 3 has you moving up 3 units to y = - 6 and y = x^2 - 6x + 8 moves you to y = - 1. Which way are you going? The difference is 5 units and you are moving down because you start at y = x^2 - 6x + 8 and move down to x^2 - 6x + 3.
Without finding minimums (which is a cumbersome process which needs to be done twice) there's no easy way to do this except graphing.
The answer is B.
-4= 6 + b I need help in this question
What is the slope of the line on the graph?
Answer:
slope: 4/12
Simplified to: 1/3
Negative slope so: -1/3
Y intercept:4
Form: Y=mx+b
Y=-1/3x+4
change the following numbers to decimals and round to the nearest hundredth 3÷4 and ✔10
Answer:
0.75 and 10.00
Step-by-step explanation:
jessie works in an electronics store and earns a 7.5% commission on every item that she sells. How much commission would she earn for selling a computer that costs $1,580?
Work Shown:
7.5% = (7.5)/100 = 0.075
7.5% of $1580 = 0.075*1580 = 118.50
There are two mystery numbers. The sum of 7 times the first number and 8 times the second number is 22. The sum of 5 times the first number and 8 times the second number is 18. What are the two numbers?
Based on the information given, the value of the two numbers will be 2 and 1 respectively.
Let the first number be aLet the second number be bThe equation to solve the question will be:
7a + 8b = 22 .... i
5a + 8b = 18 ..... ii
Subtract equation ii from I
2a= 4
a = 4/2
a = 2
Therefore, 7a + 8b = 22
7(2) + 8b = 22
14 + 8b = 22
8b = 22 - 14.
8b = 8
b = 8/8 = 1
Therefore, the numbers are 2 and 1.
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0.94 written as a fraction in simplest form
Which value for x makes the following equation true?
−2x−4=−6
Answer:
Step-by-step explanation:
−2x − 4 = −6
−2x − 4 + 4 = −6 + 4
−2x = −2
−2x/-2 = −2/-2
x = 1
The equation is,
→ -2x - 4 = -6
Let's solve for the value of x,
→ -2x - 4 = -6
→ -2x = -6 + 4
→ x = (-2)/(-2)
→ x = 2/2
→ [ x = 1 ]
Thus, the value of x is 1.
Y=4x+8 y=-x-7 solve by substitution
Step-by-step explanation:
Alrighty! here you go image.
Answer:x=15
Step-by-step explanation:
Instruction
Active
Constructing Parallel Lines through a Given Point
ty
Construct a line through P that is parallel
to the given line by following these steps.
1. Construct a line through points
Q and P
make two pair of line segment of PQ andQP and construct use of a scale and the parallel line give the point name
Food A 150 calories in 3/4 of a serving. Food B 250 calories in 2/3 of a serving. Find each unit rate. Which food has fewer calories per serving?
A set of house plans is made in the ratio 30:1. if a room is 6m long,how long is this room on the plan
Answer:
0.2
Step-by-step explanation:
30: 1
6:?
cross multiply
(6*1)/30
ans:0.2cm
A banker estimated a customer's worth to be $127,000. The customer was actually worth $120,000.
Find the percent error.
A. 5.5%
B. 5.6%
C. 5.7%
D. 5.8%
Please explain and get 100 points+ Brainlyist
Answer:
the answer is
5.6 I think
What four digit number an i? The sum of my digits is 4. The product of my digits is 1
Answer:
4, 2, 1, 1
Step-by-step explanation:
Construct a linear equation for the linear data presented in the table.
A) y = x + 3
B) y = 2x + 3
C) y=x-3
D) y = 2x - 3
Answer: A) y = x + 3
Step-by-step explanation:
Use two points given in the table and plug them into slope-intercept form y = mx + b.
In order to solve for m, the slope, by plugging them into [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex].
(0, 3) (2, 5)
[tex]\frac{5-3}{2-0}[/tex] = [tex]\frac{2}{2}[/tex] = 1
Use one of the points and plug it into the slope-intercept form y = mx + b.
3 = 1(0) + b
3 = 0 + b
3 = b
The linear equation to the table would be y = x + 3.
I make $20 an hour but I love 30% to taxes. How much do I take home each hour after taxes?
Answer:
$14
Step-by-step explanation:
We can make an equation
30%. . . . . .X
--------- = ---------
100. . . . . . .20
Now we cross multiply
100x = 600
x = 6
Now we subtract to find how much we will take home.
20 - 6 = $14 every hour will be made
____________is the exact average deviation of data values from the mean in squared units, and ____________ is the approximate average deviation of data values from the mean in regular units.
Variance is the exact average deviation of data values from the mean in squared units and the Standard deviation of data values from the mean in regular units.
Variance is a statistical measure of the dispersion of numbers in a data collection. Variance estimates how much more each number in the set deviates from the mean, and from each and every other number in the set.
The variance is a measure of the degree of variability. It is determined by averaging the squared deviations out of the mean.
The greater the spread of the data, the greater the variance in proportion to the mean.
The standard deviation is determined as the square root of variance by calculating the departure of each data point from the mean. The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average.
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Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)
The perimeter of the rectangle is the sum of its dimensions
The dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]
The area is given as:
[tex]\mathbf{A = 1000}[/tex]
Let the dimension be x and y.
So, we have:
[tex]\mathbf{A = xy = 1000}[/tex]
Make x the subject
[tex]\mathbf{x = \frac{1000}{y}}[/tex]
The perimeter is calculated as:
[tex]\mathbf{P = 2(x + y)}[/tex]
Substitute [tex]\mathbf{x = \frac{1000}{y}}[/tex]
[tex]\mathbf{P = 2(\frac{1000}{y} + y)}[/tex]
Expand
[tex]\mathbf{P = \frac{2000}{y} + 2y}[/tex]
Differentiate
[tex]\mathbf{P' = -\frac{2000}{y^2} + 2}[/tex]
Set to 0
[tex]\mathbf{ -\frac{2000}{y^2} + 2 = 0}[/tex]
Rewrite as:
[tex]\mathbf{ -\frac{2000}{y^2} = -2}[/tex]
Divide both sides by -1
[tex]\mathbf{\frac{2000}{y^2} = 2}[/tex]
Multiply y^2
[tex]\mathbf{2000 = 2y^2}[/tex]
Divide by 2
[tex]\mathbf{1000 = y^2}[/tex]
Take square roots of both sides
[tex]\mathbf{y = \sqrt{1000 }}[/tex]
[tex]\mathbf{y = 10\sqrt{10 }}[/tex]
Substitute [tex]\mathbf{y = \sqrt{1000 }}[/tex] in [tex]\mathbf{x = \frac{1000}{y}}[/tex]
[tex]\mathbf{x = \frac{1000}{\sqrt{1000}}}[/tex]
[tex]\mathbf{x = \sqrt{1000}}[/tex]
[tex]\mathbf{x = 10\sqrt{10 }}[/tex]
Hence, the dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]
Read more about perimeters at:
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pls help mee I dont k ow this and if anyone is smort enough can you help me with the 9ther questions (5 i total my last redo)
Answer:
c
Step-by-step explanation:
I think that is the answer
Answer:
c
Step-by-step explanation:
it is equal to.
SOLVE PLZ I give brainlest
17+ -9
A. 26
B. 8
C. -8
D.-26
Answer:
B: 8
Step-by-step explanation:
When you add a negative number, it means you subtract that number.
[tex]17+-9=17-9=8[/tex]
paki sagot po kailangan na kasi..
thank you in advance ☺
1. 5
2.2
3.2,5
4.2,5
5.2
HOPE IT HELPS:)
PLS FOLLOW:)
#BRAINLIEST:)
4. When you _________ the problem, it makes it easier to understand how you solved it.
Answer:
When you explain the problem, it makes it easier to understand how you solved it.
I hope this helped at all.
.79 % of what number of horses is 29 horses
Answer: 37
Cross multiply 100x29 over 79
If sin theta < 0 and cot theta < 0, which quadrant(s)
could the terminal side of theta lie?
Answer:
Step-by-step explanation:
sinθ < 0 means below the x axis
cotθ = cosθ/sinθ < 0
As sinθ is already < 0 means cosθ has to be > 0 meaning right of the y axis.
Right of y and below x is the IV quadrant.
The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).
What is meant by Trigonometric Identities?Trigonometric Identities are equality conditions that hold for all possible values of the variables in the equation and use trigonometry functions. There exists numerous unique trigonometric identities that relate a triangle's side length and angle.
here, we have,
Sine, cosine, and tangent are the fundamental three operations in trigonometry. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical notions exists built.
Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These exists identities that, geometrically speaking, involve certain functions of one or more angles.
we have,
sinθ < 0 means below the x axis
cotθ = cosθ/sinθ < 0
As sinθ is already < 0 means cosθ has to be > 0 meaning right of the y axis.
Right of y and below x is the IV quadrant.
Hence, The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).
To learn more about trigonometric identities refer to:
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What is the area of a square if the Perimeter is 36 inches and each side is X -1
Answer:
Area= 100 inches square.
Step-by-step explanation:
4(x-1)=36
4x-4=36
4x=40
x=10
10×10=100