Answers
It's not clear whether you're talking about the bounded region to the left or right of the y-axis, but due to symmetry it doesn't really matter.
The two curves y = 8 and y = 8x ² intersect for
8 = 8x ² → x ² = 1 → x = -1, x = 1
but we only care about one of these; take the positive solution, so the region of interest lies to the right of the y-axis.
Each washer has an outer radius (distance from the "top" curve to the axis of revolution) of 8 and an inner radius (distance from the "bottom" curve) of 8x ². Take the heights to be some small length ∆x . Then each has a volume of π (outer radius)² - π (inner radius)², or
π (64 - 64x ⁴) ∆x
Now take n such washers, take their sum, and let n → ∞ and ∆x → 0. This amounts to computing the integral,
∫₀¹ π (64 - 64x ⁴) dx = π (64x - 64/5 x ⁵) |₀¹
… = π (64 - 64/5)
… = 256π/5
The two curves y = 8 and y = 8x ² intersect for
8 = 8x ² → x ² = 1 → x = -1, x = 1
but we only care about one of these; take the positive solution, so the region of interest lies to the right of the y-axis.
Each washer has an outer radius (distance from the "top" curve to the axis of revolution) of 8 and an inner radius (distance from the "bottom" curve) of 8x ². Take the heights to be some small length ∆x . Then each has a volume of π (outer radius)² - π (inner radius)², or
π (64 - 64x ⁴) ∆x
Now take n such washers, take their sum, and let n → ∞ and ∆x → 0. This amounts to computing the integral,
∫₀¹ π (64 - 64x ⁴) dx = π (64x - 64/5 x ⁵) |₀¹
… = π (64 - 64/5)
… = 256π/5
THANKS
Related Questions
Last year, Lien earned $1,600 more than her husband. Together they earned $51,000. How much did each of them earn?
Answers
Answer:
Lien: $26300 Her husband: $24700
Step-by-step explanation:
x+(x+1600)=51000
2x+1600=51000
2x=49400
x=24700
Her husband earned 24700
24700+1600=26300
Lien earned 26300
Is the point (-4, 1/2) on the graph of y= 1\2 x-4 ? How do you know? Show your work/thinking.
Answers
9514 1404 393
Answer:
no, when x is even, y will be an integer, not a fraction
Step-by-step explanation:
We observe that the coefficient of x is 1/2, so the x-term will be an integer only if x is a multiple of 2 (even). If the x-term is an integer, y will be an integer.
The given point has x even (-4), so we expect y to be an integer. The given point has y=1/2, not an integer, so the point will NOT be on the graph.
If $18 is 45% what is 100%
Answers
Answer:
$40Step-by-step explanation:
45% = 45/100 = 0.45
0.45x = 18x = 18/0.45x = 40100% is $40
Answer:
solution given;
let total be X
45% of X=$18
X=$18×100/45=$40
So.100% is $40.
HELP ME PLS I NEED HELP ALSO I NEED A SHOW YOUR WORK BUT PLS HELP
Answers
Step-by-step explanation:
6 y = mx + b
7. m
8. b
9a m = 4 (slope), b = 12(yintercept)
9b -1. 4
9c 8. 21
9d 12. 9
is this a function? please help
Answers
What is the volume of this prism?
Answers
Answer:
The answer is 42ft ^3 (42 ft units cubed)
Step-by-step explanation:
To find the volume for a rectangular prism, first of all you need to know the formula. The formula is V=lwh (volume= length x width x height)
The formmula for this problem is V= 7ft x 2ft x 3ft= 42ft
There were 650 fruit in a fruit stall. 62% of the fruit were sold. How many fruit were left?
Answers
Answer:
62/100 multiplied by 650 which is 403 fruits left
Kelly jarred 30 liters of jam after 8 days. What is the unit rate? Pleasee help
Answers
Answer:
3.75 liters a day
Step-by-step explanation:
GIVING OUT BRAINLIEST TO WHOEVER CAN PROVIDE THE CORRECT ANSWER !! Asap
Answers
A circular mirror has a diameter of 12 inches. And a circular frame that is 3 inches wide surrounds the mirror. What is the combined area, in square inches, of the circular mirror and the frame? *
Answers
Answer:
254.5 in.^2
Step-by-step explanation:
diameter of mirror = 12 in.
radius of mirror = diameter/2 = 13 in. / 2 = 6 in.
frame width = 3 in.
radius if combined mirror and frame = 6 in. + 3 in. = 9 in.
A = (pi)(r^2)
A = 3.14159 * (9 in.)^2
A = 3.14159 * 81 in.^2
A = 254.5 in.^2
Find the x- and y-intercepts of the graph of x + 3y = 33. State your answers as
whole numbers or as improper fractions in simplest form.
Answers
Answer:
x intercept is (33,0)
y intercept is (0, 11)
Step-by-step explanation:
x-intercepts are found when y=0
x + 3(0)=33,,, x=33
y-intercepts are found when x=0
0 + 3y= 33,,, y=11
David averaged 12 points per game during his 7th grade basketball season. As a result of practicing all summer, he averaged 20 points per game during his 8th-grade season. By what percent did his average change?
Answers
Answer:
20-12=8 the answer is 8 I did the math
Answer:
8 is right
Step-by-step explanation:
because 20-12=8
The table below shows the number of people, y, who ride a roller coaster at a theme park over a certain number of hours, x, during a day. Write an equation that represents the relationship between the number of people that ride a roller coaster in terms of the time, in hours, as shown in the table. Use the on-screen keyboard to type the correct equation in the box.
Answers
Answer:
y = 350x
Step-by-step explanation:
To find the equation of the chart, we simply find the slope and then follow the slope-intercept equation.
Points on the chart: (0, 0) and (1.5, 525)
Slope:
m=(y2-y1)/(x2-x1)
m=(525-0)/(1.5-0)
m=525/1.5
m = 350
Slope-intercept:
y - y1 = m(x - x1)
y - 0 = 350(x - 0)
y - 0 = 350x
y = 350x
Please help anybody due in LESS THAN 1 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
distance was 35 units and the average speed was 5 units per minute
Step-by-step explanation:
-47--12=-35
the absolute value of -35 is 35
35 units took 7 minutes
so 1 unit takes 35/7 minutes= 5 minutes
An expression is shown below:
f(x) = 2x^2 − x − 10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answers
A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
Answers
Pls help asapppppp!!!!!
Answers
explanation :
f(4)=4^2 - 6
4f=4^2 - 6
4f=16 - 6
4f=10
Which of the following points( X,Y) lies on the graph of 8X + 2Y = 24
Answers
Step-by-step explanation:
don't see any points to pick from however the following would lie on the graph
(0,12)
(1,8)
(2,4)
(3,0)
(4,-4)
Kelly purchased a t-shirt
for 9.99 and a pair of
jeans for $21.50. The
sales tax rate is 8.25%.
What was the total cost
of Kelly's purchase
(including sales tax)?
PLEASE HELP
Answers
Answer:
34.09
Step-by-step explanation:
Answer: $34.09
Step-by-step explanation:
Answers please and explain
Answers
To get the answer you have to fill in the 14 for r because that is the radius. Then multiply 14 by it self to get 196 then multiply that by pie to get your answer of 615.75216.
So the answer is 615.75216
Sam has $560 in his savings account.
He earns 2.5% interest every 3 years.
How much TOTAL savings will he have in his account?
Answers
I will mark you brainlist!
The circle graph shows how Tremaine divided his time on the computer last week.
Tremaine used the computer a total of 30 hours last week. How many more hours did Tremaine use the computer to play video games than to do research?
Group of answer choices
6 hours
20 hours
7.5 hours
1.5 hours
Please explain the answer to me
Answers
Answer: 6
Step-by-step explanation:
So he spends 25% of his 30 hours on games so 30x0.25=7.5 since 25% is equal to 0.25. He also spends 5% of the 30 hours on research. 30x0.05=1.5. 7.5-1.5=6
Solve each inequality. Then check each number that is a solution
I Don't know how to solve this. as nothing has helped so far.
Answers
Answer:
3, 6, 4, 5
Step-by-step explanation:
First of all we have to multiply 2 by 2x and -9 and we obtain
4x -18 ≤ 6
now we have to move -18 on the right side of the minor or equal and change its sign
4x ≤ 6 + 18
now we have to added up 6 and 18
4x ≤ 24
At least we have to divide the the two members by 4
x ≤ 6
We have to find the numbers ≤ 6
so the answer is : 3, 6, 4, 5
Answer:
click on 3,6,4,5 are less than or equal to 6
Step-by-step explanation:
2(2×3-9)= -6
2(2×6-9)= 6
2(2×4-9)= -2
2(2×5-9)= 2
2(2×7-9)= 10
5 rubber stamps cost $9.70.
Which equation would help determine the cost of 11 rubber stamps?
A: x/11 = 5/9.70
B: 11\$9.70 = x/5
C: 5/11 = x/9.70
D: 11/5 = 9.70/x
E: None of the above
Answers
What is the measure of ZBAC?
Answers
Step-by-step explanation:
50°+50°+θ=180°
θ=180°-100°
θ=80°
Answer:
80 or b....................................
Mrs Tay baked 45 cookies.
She gave of them to her friends.
How many cookies did she give her friends?
45
Answers
Answer:
15cookies
Step-by-step explanation:
Complete question:
Mrs Tay baked 45 cookies. She gave 1/3 of them to her friends. How many cookies did she give her friends?
Given the following
Total cookies = 45 cookies
Fraction of cookies given = 1/3
Amount she gave her friends= 1/3 * 45
Amount she gave her friends= 45/3
Amount she gave her friends= 15cookies
Hence she gave 15cookies to her friends
here's the question
Answers
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 10% of scores B: Scores below the top 10% and above the bottom 58% C: Scores below the top 42% and above the bottom 20% D: Scores below the top 80% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answers
Answer:
The numerical limits for a D grade are 58(lower limit) and 61(upper limit).
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3.
This means that [tex]\mu = 67.3, \sigma = 7.3[/tex]
D: Scores below the top 80% and above the bottom 9%
This means that lower bound is the 9th percentile and the upper bound is the 100 - 80 = 20th percentile.
9th percentile:
This is X when Z has a pvalue of 0.09. So X when Z = -1.34.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.34 = \frac{X - 67.3}{7.3}[/tex]
[tex]X - 67.3 = -1.34*7.3[/tex]
[tex]X = 57.52[/tex]
Rounding to the nearest whole number, 58.
20th percentile:
This is X when Z has a pvalue of 0.2. So X when Z = -0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 67.3}{7.3}[/tex]
[tex]X - 67.3 = -0.84*7.3[/tex]
[tex]X = 61.17[/tex]
Rounding to the nearest whole number, 61.
The numerical limits for a D grade are 58(lower limit) and 61(upper limit).
5 = w + 1.5
whats the answer
Answers
Answer:
w = 3.5
Step-by-step explanation:
5 = w + 1.5
5- 1.5 = 3.5
quick mathz
Need help fast please
Answers
Answer:
1. 53 97 159
2 6 and 6.1
3. 1 1/3
