Answer:
[tex]V = \frac{\pi^2}{8}[/tex]
[tex]V = 1.23245[/tex]
Step-by-step explanation:
Given
[tex]y = \cos 2x[/tex]
[tex]y = 0; x = 0; x = \frac{\pi}{4}[/tex]
Required
Determine the volume of the solid generated
Using the disk method approach, we have:
[tex]V = \pi \int\limits^a_b {R(x)^2} \, dx[/tex]
Where
[tex]y = R(x) = \cos 2x[/tex]
[tex]a = \frac{\pi}{4}; b =0[/tex]
So:
[tex]V = \pi \int\limits^a_b {R(x)^2} \, dx[/tex]
Where
[tex]y = R(x) = \cos 2x[/tex]
[tex]a = \frac{\pi}{4}; b =0[/tex]
So:
[tex]V = \pi \int\limits^a_b {R(x)^2} \, dx[/tex]
[tex]V = \pi \int\limits^{\frac{\pi}{4}}_0 {(\cos 2x)^2} \, dx[/tex]
[tex]V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx[/tex]
Apply the following half angle trigonometry identity;
[tex]\cos^2(x) = \frac{1}{2}[1 + \cos(2x)][/tex]
So, we have:
[tex]\cos^2(2x) = \frac{1}{2}[1 + \cos(2*2x)][/tex]
[tex]\cos^2(2x) = \frac{1}{2}[1 + \cos(4x)][/tex]
Open bracket
[tex]\cos^2(2x) = \frac{1}{2} + \frac{1}{2}\cos(4x)[/tex]
So, we have:
[tex]V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx[/tex]
[tex]V = \pi \int\limits^{\frac{\pi}{4}}_0 {[\frac{1}{2} + \frac{1}{2}\cos(4x)]} \, dx[/tex]
Integrate
[tex]V = \pi [\frac{x}{2} + \frac{1}{8}\sin(4x)]\limits^{\frac{\pi}{4}}_0[/tex]
Expand
[tex]V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})] - [\frac{0}{2} + \frac{1}{8}\sin(4*0)])[/tex]
[tex]V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})] - [0 + 0])[/tex]
[tex]V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})])[/tex]
[tex]V = \pi ([{\frac{\pi}{8} + \frac{1}{8}\sin(\pi)])[/tex]
[tex]\sin \pi = 0[/tex]
So:
[tex]V = \pi ([{\frac{\pi}{8} + \frac{1}{8}*0])[/tex]
[tex]V = \pi *[{\frac{\pi}{8}][/tex]
[tex]V = \frac{\pi^2}{8}[/tex]
or
[tex]V = \frac{3.14^2}{8}[/tex]
[tex]V = 1.23245[/tex]
Find the missing side or angle.
Round to the nearest tenth.
C=53°
B= 80°
a=2
b=[?]
Answer:
2.69 approximately 3
Step-by-step explanation:
53⁰+80⁰+A=180⁰(sum of angles on a triangle)
133⁰+A=180
A=180-133
A=47⁰
using sine rule
2/sin 47 = b/sin 80
b sin47 = 2 sin 80
b= 1.9696/0.7314
b=2.69 approximately 3
Identify the transformation that was applied to this letter.
HELPoo
Why 117+3 = 5! is correct
Answer:
5!= 5×4×3×2×1
117+3=120
5×4×3×2×1= 120
therefore 117+3=5! is correct
The statement 117+3 = 5! is correct because;
The left hand side and right hand side give the same solution of 120.
We want to find out why 117 + 3 = 5! is correct.
Let us first find the left hand side of the equation;
117 + 3 = 120
Now, for the right hand side, 5! simply means 5 factorial.
Factorial of a number is a term used in maths to denote the product of all
positive integers less than or equal to that number. For example; n!. That is
factorial and it means the product of all positive integers below n.
Let's apply the concept of factorial to 5!.
All positive integers less than or equal to 5 are; 5, 4 , 3, 2, 1
Thus; 5! = 5 × 4 × 3 × 2 × 1 = 120
This 5! = 120 and it is the same as 117 + 3 = 120. Thus the given statement in the question is true.
Read more at; https://brainly.com/question/24115376
what is the circumference?
Answer:
Circumference is the area around the whole circle
Step-by-step explanation:
Answer:
The circumference is 50.2
Step-by-step explanation
I worked it out by
C = 2 * π *
pls answer me this all question correctly pls I beg you pls friends pls pls pls pls pls pls pls pls
Answer:
[tex]a. \: 28[/tex]
[tex]b. \: 5[/tex]
Step-by-step explanation:
[tex]a. \: 88 \div 3 \frac{1}{7} [/tex]
[tex]88 \div \frac{22}{7} [/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]88 \div \frac{7}{22} [/tex]
[tex]4 \times 7[/tex]
[tex]28[/tex]
[tex]b. \: 49 \frac{2}{9} \div 9 \frac{4}{9} [/tex]
[tex] \frac{425}{9} \div \frac{85}{9} [/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex] \frac{425}{9} \times \frac{9}{85} [/tex]
[tex]5[/tex]
Hope it is helpful...A group consisting of 10 children an adult went to a movie theater children tickets cost 5 each and adults tickets cost 8 each and the total cost for 10 people was 62.how much children were in the group
9514 1404 393
Answer:
6 children
Step-by-step explanation:
If all of the group were adults, the total cost of tickets would be 8×$10 = $80. The actual cost was $80 -62 = $18 less than that. Since each children's ticket saves $3 off the cost of an adult ticket, there were $18/$3 = 6 children's tickets.
There were 6 children in the group.
_____
If you want an equation, you can let c represent the number of children. Then the cost of tickets is ...
8(10 -c) +5c = 62 . . . . 10-c is the number of adults
-3c = -18 . . . . . . . subtract 80
c = -18/-3 = 6 . . . divide by 3
n is an integer with -5 <2n< 6
Write down all the values of n
Answer:
it is -2,-1,0,1,2
30 POINTS!!!!! I NEED IT NOW!!!!!!Find the maximun, minimum,range,medium,mean,mode and the other stuff on the picture if you can if not its ok.
Answer:
34
Step-by-step explanation:
What angles are adjacent to angle 4
Answer:
2,3
Step-by-step explanation:
They are the closest angles to 4.
How do I solve
tan x= 3/5
Answer:
30.96375653
Step-by-step explanation:
if using a calculator, type in;
shift tan (3/5)
so basically shift tan (0.6)
bracket is important
if writing;
tan^-1 (0.6) = 30.96375653
Which of the following is the inverse relation of the set?
{(3, 1), (4, 2), (5, 3), (6, 4)} ?
A)
{(3, 1), (4, 2), (5, 3), (6, 4)}
B)
{(2, 4), (3, 3), (5, 4), (6, 1)}
C)
{(1, 3), (2, 4), (3, 5), (4, 6)}
D)
{(2, 1), (4, 3), (5, 3), (6, 4)}
Answer:
c number because even or odd numbers are equal i hope help you
please mark me brainlist
Answer:
C is the Correct answer.
Step-by-step explanation:
please no link answers you will be reported
Which of the following equations describes this graph?
A. y = x2 - 8x+18
B. y = x2 - 6x+10
C. y = x2 +6x+10
D. y = 2x2 - 12x+19
Answer:
B
Step-by-step explanation:
You can use the key features (such as the vertex) to determine which is the correct equation
8 more than 5 times a number is equal to 6 more than 3 times that number.What is the number?
A. 1
B. 2
C. 3
D. 4
HELP PLs thANKS
Answer:
A. 1
Step-by-step explanation:
8 - 5x = 6 - 3x
-5x + 3x = 6 - 8
-2x = -2
divide through by -2
x = 1
Answer:
A. 1
Step-by-step explanation:
5x -8 = 3x -6
5x = 3x +2
2x = 2
x = 1
Check:
5-8 = 3-6
-3 = -3
In the French Honor Society, there are 12 girls and 8 boys.
This summer, they are taking a trip to France and only 8
people can go. Find the probability that each of the
following groups will be randomly selected to go on the trip
to France.
a) All girls
b) All boys
c) 4 girls and 4 boys
d) 3 girls and 5 boys
e) At least one boy
f) At least two girls
Answer:
a) All girls - 12C8 /20 C8
b) All boys - 8C8/20C8
c) 4 girls and 4 boys - 8C4 * 12C4/20 C8
d) 3 girls and 5 boys - 8C5 * 12C3/20 C8
e) At least one boy - 1 - 12C8 /20 C8
f) At least two girls 1 - (1 - 8C8 /20 C8)
Step-by-step explanation:
Given -
Total girls - 12
Total boys - 8
a) All girls - 12C8 /20 C8
b) All boys - 8C8/20C8
c) 4 girls and 4 boys - 8C4 * 12C4/20 C8
d) 3 girls and 5 boys - 8C5 * 12C3/20 C8
e) At least one boy - 1 - 12C8 /20 C8
f) At least two girls 1 - (1 - 8C8 /20 C8)
suppose that a population parameter is 0.2, and many samples are taken from the population. As the size of each sample increases, the mean of the sample proportions would approach which of the following values?
A. 0.1
B. 0.3
C. 0.4
D. 0.2
Answer:
D 0.2
Step-by-step explanation:
YES THIS IS RIGHT
The required, mean of the sample proportions would approach is 0.2.
What is a normal distribution?Normal distributions can be altered to standard normal distributions by the formula:
Z = (X - μ)/σ
As the size of each sample increases, the mean of the sample proportions would approach the population parameter, which in this case is 0.2. This is known as the central limit theorem.
Therefore, the answer is D. 0.2.
Learn more about normal distribution here: https://brainly.com/question/12421652
#SPJ2
Petra is making necklaces to sell at a craft fair. The hardware for each necklace costs $3.75,
and each bead costs $0.50. The number of beads Petra needs depends on the design she
chooses. Which expression gives the total cost to make 30 necklaces with b beads?
30 (4.25b)
30 (3.75b + 0.5)
30 (0.55 +3.75)
30 (0.5b) + 3.75
How do you graph 4x + 2y = 3
Answer
x =0,3/4
Y=3/2,0
Step-by-step explanation:
hope this helps
Which is nearest to the perimeter of WXYZ?
W: -4, 3) X: (1,4) Y (2,-2) Z (-3,-1)
A. 21 units
B. 11 units
C. 20 units
D. 9 units
Answer:
segment XY = 6
segment XW = 5
segment WZ = 4
segment ZY = 5
6 + 5 + 4 + 5 = 20 units :))))
There are 32 founding members of an organization. The function y 3x + 32 can be used to determine the number of members in the organization
after 3 months.
Answer:
https://studyandanswers.com/mathematics/question22956714
Step-by-step explanation:
I am not the bot btw. This is the only way I can help you. If you don't like it well to bad
Which set of data has the smallest difference between the mean and the median?
O A 13, 42, 17, 26, 38
OB. 28, 7, 36, 8, 17
OC 14, 29, 38, 7, 13
OD 23, 36, 25, 38, 30
Answer:
D 23, 36, 25, 38, 30
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all it's values divided by the number of values.
Median of a data-set:
The median of a data-set is the value that separates the lower 50% from the upper 50% on the ordered set.
If the cardinality n is odd, as in this case, the median is the element at the position (n+1)/2. Since in this case, n = 5, the median is the 3rd element in the ordered set.
A 13, 42, 17, 26, 38
Ordered set: 13, 17, 26, 38, 42
Median: 26
Mean: (13+17+26+38+42)/5 = 27.2
Difference: 27.2 - 26 = 1.2
B. 28, 7, 36, 8, 17
Ordered set: 7, 8, 17, 28, 36
Median: 17
Mean: (7+8+17+28+36)/5 = 19.2
Difference: 19.2 - 17 = 2.2
C 14, 29, 38, 7, 13
Ordered set: 7, 13, 14, 29, 38
Median: 14
Mean: (7+13+14+29+38)/5 = 20.2
Difference: 20.2 - 14 = 6.2
D 23, 36, 25, 38, 30
Ordered set: 23, 25, 30, 36, 38
Median: 30
Mean: (23+25+30+36+38)/5 = 30.4
Difference: 30.4 - 30 = 0.4
Option d has the smallest difference.
What annual rate of interest would you have to earn on an investment of $5500 to ensure receiving $434.50 interest after one year?
PLEASE HELPPPP
x was a sacrifice
,,,,,,,,,,,,,,,
Answer:
yes next y will be a sacrifice
Step-by-step explanation:
i did it
A coordinate plane with a straight line with a positive slope. The line starts at (0, 0) and passes through points labeled A at (2, 1) and B at (4, 2) and through (8, 4). There is a vertical dashed line starting at point A extending two units to the right and one unit up to point B.
What is the vertical change from Point A to Point B?
What is the horizontal change from Point A to Point B?
What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary
Answer:
On edge 2021
Step-by-step explanation:
!st:1
2nd:2
3rd:0.5
Answer:
A coordinate plane with a straight line with a positive slope. The line starts at (0, 0) and passes through points labeled A at (2, 1) and B at (4, 2) and through (8, 4). There is a vertical dashed line starting at point A extending two units to the right and one unit up to point B.
What is the vertical change from Point A to Point B?
1
What is the horizontal change from Point A to Point B?
2
What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary
0.5
Step-by-step explanation:
does the graph represent a function
3.
a box has 10 red cubes, 5 blue cubes
and 2 green cubes. If a cube is
randomly picked from the box, which
coloured cube is:
(a) least likely to be picked?
(b) most likely to be picked?
Answer:
The Answer is is option B.
2+9n=72
how do you find what n equals?
Answer:
the correct answer is 7.78
Aiden wants to make 1/2 of a batch of muffins the recipe calls for 2/3 cup of milk for whole batch how much milk should aiden use?
Answer:
Quantity of milk Aiden needs = 1/3 cup of milk
Step-by-step explanation:
Given:
Aiden wants to make muffins = 1/2 batch
Full batch muffins need = 2/3 cup of milk
Find:
Quantity of milk Aiden needs
Computation:
Quantity of milk Aiden needs = Number of batch Aiden make x Amount of milk need for a batch
Quantity of milk Aiden needs = [1/2] x [2/3]
Quantity of milk Aiden needs = 1/3 cup of milk
a box of 10 chocolates cost $7.30. How much does one chocolate cost?
p.s I will make you brainliest only if you explain GOOD!!
Answer:
One costs $0.73
Step-by-step explanation:
When looking at this, you should divide 7.30/10. This will show each individual bar. The quotient is 0.73 which is the price of each one chocolate.
The area of a rectangle is 200 square feet. Find its length if its width is 10 feet.
Answer:
20
Step-by-step explanation:
In area you have to multiply so 10 x ? = 200
10 x 20 = 200
four causes of solar eclips
Answer:
A solar eclipse occurs when the moon gets between Earth and the sun, and the moon casts a shadow over Earth. A solar eclipse can only take place at the phase of new moon, when the moon passes directly between the sun and Earth and its shadows fall upon Earth's surface