Integrate :
[tex]\red{\footnotesize\displaystyle\bf \int cos^3 4x\:\:dx}[/tex]
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]
Which table represents a linear function?
The table that represents a linear function, having a slope value of 2 is: Table 4 (see image attached below)
Recall:
A function that is linear has a dependent and independent variable, such that y = mx + b.The "m" represents the slope which is the same all through the points given.m = change in y / change in xThus, the fourth table has the following slope (m) that is the same across all points.
Using two pairs of points, (0, 1) and (1, 3):
Slope = 3 - 1/1 - 0 = 2/1
Slope (m) = 2
Any two pairs of points we use will give us the same slope (m) of 2.
Table 1, 2 and 3 will give us different slopes across the points on each table, meaning they do not represent a linear function.Therefore, the table that represents a linear function, having a slope value of 2 is: Table 4 (see image attached below).
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the bottom the range has the same numbers so I just need the domain and range help plz!!
How to identify domain and range from co-ordinate pairs?
If a pair be (x,y)Domain=x
Range=y
Hence.
In the graph here
[tex]\\ \sf\longmapsto D_f=0\leqslant x\leqslant y[/tex]
[tex]\\ \sf\longmapsto R_f=0\leqslant y\leqslant 14[/tex]
7x+3y=m, solve for y
What is the image of the point (-3, 4) after a rotation of 180° counterclockwise
about the origin?
Answer:
-3 ,-4
Step-by-step explanation:
Answer: ( 3 , -4)
Step-by-step explanation:
i got it wrong at first and it told me the right answer
Use the function g(x)=11 to find the following values
g(-3)
Answer: https://www.bing.com/search?q=https%3A%2F%2Fwww.chegg.com%2Fhomework-help%2Fquestions-and...%0A&form=IPRV10
Step-by-step explanation: There you will find your answer
The value of g(-3) comes to be 11 because g(x) is a constant function.
Given function is:
g(x) =11
Function g(x) is a constant function because g(x) is independent of x.
How graph of a constant function look like?The graph of a constant function is parallel to the y-axis and gives the same output for any input given to the function.
So, The value of g(-3) will be the same as the value of g(x) i.e. 11
So, value of g(-3) = 11
Therefore, The value of g(-3) comes to be 11 because g(x) is a constant function.
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What is the numerical answer?
length = inches
Answer:
31.5 inches
Step-by-step explanation:
If 2 centimeters is 9 inches, then 1 centimeter is 4.5 inches. Then, just multiply by 7.
1. In the expression at aⁿ,n is called
a. exponent
b.base
c. variable
d.number
HELP ASAP
In math class, the girl to boy ratio is 8 to 6. If there are 24 girls in the class, how many boys are there?
A
20
B
30
C
18
D
16
Answer:
C, 18.
Step-by-step explanation:
Since 24 divided by 8 is 3, which means that
8x3 = 24, then the amount of boys must be solved using the equation 6x3 which equals 18.
Please find the correct answer will give high points, mark brainliest, give 4 stars, and hearts. PLS
there are 350,000 in a warehouse predict the number of light bulbs that are likely to have no defects
Answer:
175000.(or around that number)
Step-by-step explanation:
half of 350,000 is 175000.
In the xy-plane, a line crosses the y-axis at the point (2, 2) and passes through
the paint (-3, -13). Which of the following is an equation of the line?
Write the equation of the line in y=mx + b form
Answer:
y=-4x+2
Step-by-step explanation:
all you need to do is find the x-axis and y-axis. That information is already there, so put It together
I DONT KNOW THIS QUESTION
Use your work from above to find the sum of 501+502+503+…+800
Answer:
Step-by-step explanation:
Gauss n(n+1)/2
which is n? the last number of the sum
500(500 + 1)/2 = 125,250
800(800+1)/2 = 320,400
uh oh forgot to read the last one, give me a minute. done
(800 - 501 + 1)(800 + 501)/2
300(1301)/2 = 195,150
or
320,400 - 125,250 = 195,150
If an object's position over time is given by the function d(t)=(t^2 +3)e^-1/2 for greater than 0 , on what interval is the object's position increasing and concave down ?
Answer:
Step-by-step explanation:
[tex]d(t)=(t^2+3)e^\frac{-1}{2} \\d'(t)=2t e^{-\frac{1}{2} }\\it~ is~ increasing ~if~d'(t)>0\\e^{-\frac{1}{2} } =\frac{1}{e^\frac{1}{2} } >0\\so~t>0\\and~decreasing~if~t<0\\[/tex]
so it is concave upward at t=0
SOMEONE PLEASE HELP ME
Answer:
D
Step-by-step explanation:
0.4 = 4/10 = 2/5
3|x + 7| + 6 = 18 How many solutions are there to the equation?
Answer:
There are two solutions.
Step-by-step explanation:
x = -3
x = -11
What is the volume of a cylinder in cubic feet of a cylinder with a height of 3ft and a base diameter of 18ft, round to the nearest tenths place
Answer:
763.4 ft^3 to the nearest tenth.
Step-by-step explanation:
The base radius = 1/2 * 18 = 9 ft.
The volume = π r^2 h
= π * 9^2 * 3
= 763.407 f^3.
A department store sells a pair of shoes with a 15% discount. The original price of the shoes is $75. What is the sale price?
Answer:
$63.75
Step-by-step explanation:
10% = 7.5
5% = 3.75
15% = 11.25
75.00
-11.25
63.75
The length of a rectangle is 10 times its width. If the area of the rectangle is 52yd^2, find its approximate width.
Answer:
76377/9338912
Step-by-step explanation:
Umm how to do rates
The definition of a rate in math is, the speed of something being gained in a problem, let's say we have a hot pipe that can full up a pool in 6 hours, our rate would be 1/6 of the pool per hour.
Vhich number line represents the solution of 4x - 9> -21?
Answer:4x -9 >= -21
4x >= -12
x >= -12/4
x >= -3
so this number line started with -3 and go away till + infinity
hope this will help you
Step-by-step explanation:
Frame a linear equation for each of the following statements.
1. [tex]b[/tex]47 is 23 more than two times p.
2.[tex]b[/tex]One-fourth of p decreased by 3 gives −12
3.[tex]b[/tex]2 times p exceeds 15 by 3.
4. [tex]b[/tex]One-fifth of p decreased by 4 gives 6
Answer: chopstick
Step-by-step explanatio
You need to purchase supplies for an employee appreciation picnic. Your boss gives you the shopping list below and asks that you get the best deal by buying from one grocer, either Quality Groceries or Fresh Market. You call both grocers, and they provide the price information that you put into the table. Which grocer will provide all these picnic supplies for the lowest cost, and what is that cost without sales tax?
Answer:
Hi there, this is what I got but sorry if it is incorrect.
Hamburger Patties Package of 10 $15.50 Package of 8 $12.40
Hot Dogs Package of 12 $6.23 Package of 10 $4.99
Hamburger Buns Package of 8 $3.79 Package of 8 $3.55
Hot Dog Buns Package of 12 $2.75 Package of 8 $2.55
Potato Salad Gallon $4.33 Gallon $5.55
Ice Cream Gallon $7.55 Gallon $6.99
Answer:
its )B
Step-by-step explanation:
What is 59.56 rounded to the nearest whole number?
Answer:
60
Step-by-step explanation:
150-5r is greater than or equal to 87.5
Find the value of r?
Answer:
R=12.5
Step-by-step explanation:
Which graph represents a proportional relationship?
Answer: The first graph
Step-by-step explanation:
A proportional graph always goes through the origin
Answer:
The first graph
Step-by-step explanation:
10) Bernice recived the followine scores
on 5 Science test : 96, 7, 82, 96
and 89. Which of the following statements
is true
a) The mean and median of the set of
Scores are the same t to sonho
b) The mode of the set score is 96
of The median of the set score is 82
do the mean of the set is greater
than the median
The mode of the set score is 96
The correct answer is b) The mode of the set score is 96.
What is mean, median and mode?The "mean" is the "average" of the set of values.
The "median" is the "middle" value in the list of numbers.
The "mode" is the value that occurs most often.
Now the given scores on 5 Science test are,
96, 7, 82, 96 and 89
So, Sum of all the scores = 96+7+82+96+89= 370
Mean :
Mean = Sum of all the scores / Number of tests
⇒ Mean = 370 / 5
⇒ Mean = 74
Median :
Median is the middle value after rearrangement
So, rearranging the scores we get,
7, 82,) 89,( 96, 96
Hence the median of the scores is 89
Mode :
Mode is the number occurring the most. Since 96 occurs the most, hence the mode is 96.
Thus, from the given option, the correct option is b) The mode of the set score is 96
Hence, the correct answer is b) The mode of the set score is 96.
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Which of the following statements are correct?
Please help
Answer:
True A. angles one and five are corresponding angles.
True B. angles three and six are alternate interior angles.
False C. angles two and seven are alternate interior angles.
Angles two and seven are alternate exterior angles.
False D. angles five and eight are alternate exterior angles.
Angles five and Eight are verticle angles.
False E. angles two and four are same-sided consecutive angles.
Angles two and four are supplementary angles
True F. angles four and six are same side consecutive angles.
True G. angles one and eight are alternate exterior angles.