In circle C above, the length of EG is 34 in. What is the length of CF?
find the volume of the solid formed by revolving the region bounded by the graphs of y = 4x - x^2 and f(x) = x^2 from [0,2] about the... a) x-axis.
Answer:
[tex]v = \frac{32\pi}{3}[/tex]
or
[tex]v=33.52[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4x - x^2[/tex]
[tex]g(x) = x^2[/tex]
[tex][a,b] = [0,2][/tex]
Required
The volume of the solid formed
Rotating about the x-axis.
Using the washer method to calculate the volume, we have:
[tex]\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx[/tex]
Integrate
[tex]v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx[/tex]
[tex]v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx[/tex]
Substitute values for a, b, f(x) and g(x)
[tex]v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx[/tex]
Evaluate the exponents
[tex]v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx[/tex]
Simplify like terms
[tex]v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx[/tex]
Factor out 8
[tex]v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx[/tex]
Integrate
[tex]v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0[/tex]
[tex]v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0[/tex]
Substitute 2 and 0 for x, respectively
[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])[/tex]
[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])[/tex]
[tex]v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ][/tex]
[tex]v = 8\pi [ \frac{16}{3} - \frac{16}{4} ][/tex]
Take LCM
[tex]v = 8\pi [ \frac{16*4- 16 * 3}{12}][/tex]
[tex]v = 8\pi [ \frac{64- 48}{12}][/tex]
[tex]v = 8\pi * \frac{16}{12}[/tex]
Simplify
[tex]v = 8\pi * \frac{4}{3}[/tex]
[tex]v = \frac{32\pi}{3}[/tex]
or
[tex]v=\frac{32}{3} * \frac{22}{7}[/tex]
[tex]v=\frac{32*22}{3*7}[/tex]
[tex]v=\frac{704}{21}[/tex]
[tex]v=33.52[/tex]
What is the average of 86%, 100%, and 70%?
Answer:
87.3
Step-by-step explanation:
Answer:
85.3333333333
Step-by-step explanation:
add the number then divide them by the number u x them with
Part A what is the total number of cups of biscuit mix in one box Show your work or explain your answer.
Part B
What is the total number of biscuit that be made using one box of the biscuit mix Show you work or explain your answer.
Part C
What is the cost, in dollars and or cents, per biscuit Show your work or explain your.
5. Which one of the pairs of angles below is adjacent?
A. 23 and 21
B. 21 and 22
C. 22 and 24
D. 21 and 23
Which of the following is not a true statement about pi?
O the ratio of the circumference of a circle to its diameter
O approximated to be 3.14
O approximated to be 2217
O the ratio of the radius of a circle to its circumference
Answer:
the last one is incorrect
Step-by-step explanation:
the ratio of the circumference of a circle to its diameter Yes
O approximated to be 3.14 Yes
O approximated to be 2217 Yes
O the ratio of the radius of a circle to its circumference NO
-4t+ 14 = -9t+ 24
What value of 1 makes the equation true? Enter the answer in the box.
____
Answer:
cncjdkgkejgksjckwjnviekfkwkckkdk kdkf
Solve for x.
4x + 6
4x + 6
x = [?]
Entor
Answer:
4x+6+4x+6=180[straight line]
8x=180-12
x=168/8
x=21° is a required answer.
How many inches are in 4 1/2 feet ?
Answer:
54 in
Step-by-step explanation:
12 x 4= 48
1/2 ft= 6in
48 +6= 54
There are 54 inches in 4 1/2 feet.
We have,
To convert feet to inches, we know that 1 foot is equal to 12 inches.
To find the number of inches in 4 1/2 feet, we multiply the number of feet by 12 and add the number of inches.
4 feet multiplied by 12 inches/foot = 48 inches.
1/2 foot equals 1/2 multiplied by 12 inches/foot = 6 inches.
So,
4 1/2 feet is equal to 48 inches + 6 inches, which equals 54 inches.
Therefore,
There are 54 inches in 4 1/2 feet.
Learn more about unit conversion here:
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Which number on the number line the correct position of all lines showed
Answer:
D
Step-by-step explanation: i believe it is D
What is the image point of (-1,1) after a translation left 2 units and
down 2 units?
Answer:
The new point is (-3,-1)
Step-by-step explanation:
yessir
Paul is selling $2 raffle tickets for his baseball team. He needs to sell at least
$230 worth of tickets to earn a team jacket. If he has already sold $50 worth of tickets, how many more raffle tickets, x, does Paul need to sell to earn a team jacket?
Answer: 90 more tickets
Step-by-step explanation:
230 - 50 = 180
180 divided by 2 = 90 tickets
2965
-9654what the answer
Choose the function whose graph is given by:
O A. y = tan(2(x + 7)) - 1
O B. y =tan(x - 2) + 1
O C. y=tan(x + 1) - 76
O D. y = tan(x - ) - 1
Help ASAP I’ll mark branliest
Answer:
C - 129
Step-by-step explanation:
180-51=129
36) The speed of a boat in still water is 5km/hr. If the speed of the boat against the stream is 3
km/hr, what is the speed of the stream?
1. 1.5 km/hr
2. 2 km/hr
3. 2.5 km/hr
4. 1 km/hr
Answer:
2km/hr
Step-by-step explanation:
Given the following
Speed of boat in water = 5km/hr
Speed of boat against stream = 3km/hr
Since the speed of boat is going against that of the stream, hence, the speed of the stream will be the difference between the speed of boat and that when the boat is against the stream
Speed of stream = 5km/hr - 3km/hr
Speed of stream = 2km/hr
hence the required speed of stream is 2km/hr
saras bookshelf is 40cm long 50 cm wide and 900 mm high she wants to paint it and calculated its volume as 180000cm3 check if theres something wrong if yes show your working for correction
ill mark u
Answer:
The volume of the bookshelf is 180000 cm³.
Step-by-step explanation:
The dimensions of the bookshelf are 40 cm, 50 cm and 900 mm.
We know that,
1 mm = 0.1 cm
900 mm = 90 cm
Now the dimensions become 40 cm, 50 cm and 90 cm.
The volume of the bookshelf can be calculated as :
V = lbh
Substitute all the values,
V = 40 cm × 50 cm × 90 cm
V = 180000 cm³
So, the volume of the bookshelf is 180000 cm³.
You're playing a fantasy game that allows you to create your own character. There are 5 options for the
race of the character, and there are 3 options for the character's main tool.
If you randomly choose the race and the tool, which of these diagrams can be used to find all of the
possible outcomes?
Answer:
A i think
Step-by-step explanation:
Name the property that justifies the statement 17=17
Answer:
the property that justifies the statement 17=17 is equality
Step-by-step explanation:
because it shows that it is equal
500% of what number is 1,450?
Answer:
34.48 maybe
Step-by-step explanation:
Answer:
Step-by-step explanation:
1450÷500%
1450÷5.0 = 290
Pls helppppp!! Brainlyest answerrrr
Which situation can be represented by the expression below 12x + 10 A. A person drives 12 miles each day for 10 days. B. A person runs x miles at a Rate of 12 minutes per mile then walks fro 10 minutes. C. A person drives 12 miles plus 10 miles for each addition hour they drive. D. A person runs 12 miles the first day , x miles the second day. And 10 miles the next day
Answer:
b, i think.
Step-by-step explanation:
please help will mark you brainliest. ( all links will be reported)
Answer:
$6.22
Step-by-step explanation:
25.20
would be your answer!
In the diagram m ∠ = 102 what is m ∠ G?
A. 51
B. 58
C.78
D. 102
Answer:
it's C
and that is because it's 1313
The measure of angle G is 78 degree. for better understanding check the calculation here
Calculation
From the given diagram the measure of angle I is 102 degrees.
In a cyclic quadrilateral, the sum of opposite angles are supplementary .
The sum of opposite angles are equal to 180 degrees.
[tex]m < I +m < G = 180\\[/tex]
Substitute the value of angle I and solve for angle G
[tex]m < I +m < G = 180\\\\m < I=102\\102+m < G=180\\[/tex]
subtract 102 on both sides
[tex]102-102+m < G=180-102\\m < G=78[/tex]
The measure of angle G is 78 degrees.
Option C is correct
Learn more information about 'Cyclic quadrilateral ' here
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please help. math homework. only three questions.
Step-by-step explanation:
1). 1
2). 36
3). 16
sorry I can't explain it properly, all you have to do is to dive the coefficient of x by 2 and square the result
What is the product of 16(cos(47)+isin(47)) and 4(cos(12)+isin(12))?
Write both complex numbers in polar form: (exp(x) is the same as e ˣ)
z = 16 (cos(47°) + i sin(47°)) = 16 exp(i 47°)
w = 4 (cos(12°) + i sin(12°)) = 4 exp(i 12°)
→ zw = 64 exp(i (47° + 12°)) = 64 exp(i 59°)
→ zw = 64 (cos(59°) + i sin(59°))
Select the correct answer.
The number of books checked out at two different libraries each day this week are shown below. (at bottom)
How do the median number of books checked out each day compare?
A.
The median number of books checked out at Ryder is equal to the median number of books checked out at Williams.
B.
The median number of books checked out at Ryder is 23 more than the median number of books checked out at Williams.
C.
The median number of books checked out at Williams is 25 more than the median number of books checked out at Ryder.
D.
The median number of books checked out at Ryder is 18 more than the median number of books checked out at Williams.
Answer:
the answer is B.
Step-by-step explanation:
W= median is 58
R= median is 81
81-58=23
The median number of books checked out at Ryder is 23 more than the median number of books checked out at Williams.
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
Let the data of Williams be represented as W
Now , W = { 63 , 56 , 60 , 55 , 62 , 55 }
And , the data of Ryder be R
where R = { 80 , 75 , 82 , 84 , 82 , 79 }
And , the median of Williams = (56 + 60) / 2 = 58
And , the median of Ryder is = 81
So , the difference of medians = 81 - 58 = 23
Hence , median number of books checked out at Ryder is 23 more than Williams
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Numbers 1, and 3 please
Answer:
1. shifts the graph right 2 units
2. y = -2(x -3)² +7
Step-by-step explanation:
1) Replacing x with x-h in any function shifts the graph h units to the right. Here, you have replaced x with (x-2), so the graph will be shifted 2 units to the right.
__
3) The vertex form of the equation of a parabola is ...
y = a(x -h)² +k . . . . . . . . for vertex (h, k) and vertical scale factor 'a'
Here, the vertex is (h, k) = (3, 7), and the parabola opens downward. This tells us the sign of 'a' is negative.
The graph is not so clear that it is easy to read the value of 'a' directly from it, but there are several clues.
The zeros of the above function are found at h±√(k/a). This graph shows the zeros to be located such that √(7/a) is slightly less than 2. This means the magnitude of 'a' will be slightly more than 7/2² = 1.75. The y-intercept of the function is 7-9a. It is less than -7, but probably more than -14. This puts bounds on 'a':
-14 < 7-9a < -7
-21/9 < -a < -14/9 ⇒ -2.33 < -a < -1.56
If we assume that 'a' is an integer value, we have bounded its magnitude as being between 1.75 and 2.33, so a=-2 is a reasonable choice.
The equation of the graph may be ...
y = -2(x -3)² +7
5m - 12 - 2m + 6 + 3m
Answer:
6(m-1)
Step-by-step explanation:
See Image Below:)
At the store, 8 oz of Brand A glue costs $2.08, while 6 oz of Brand B glue costs $1.62. Which is the better buy
Answer:
Brand AStep-by-step explanation:
Unit rates are:
Brand A glue = $2.08/8 = $0.26 per ozBrand B glue = $1.62/6 = $0.27 per ozBrand A glue is cheaper, so is the better buy
Answer:
8 oz of Brand A glue costs $2.08
1 oz of Brand A glue costs $2.08×1/8=$0.26
6 oz of Brand B glue costs $1.62
1 oz of Brand B glue costs $1.62/6=$0.27
so..A is cheap.
8 oz of Brand A glue costs $2.08 is needed to buy.