Find the volume of the solid obtained by rotating the region enclosed by y=x^2,y=3x about the line y=9 using the method of disks or washers.
Answers
The volume of the solid obtained by rotating the region enclosed by y=x^2 and y=3x about the line y=9 using the method of washers is (27/2)π cubic units, obtained by integrating π(-x^4 + 15x^2 - 54x) over [0,3].
To find the volume of the solid obtained by rotating the region enclosed by y=x^2 and y=3x about the line y=9, we can use the method of washers.
Consider a vertical slice of the solid at an arbitrary value of x
The slice has width dx and thickness dy. The distance between the line y=9 and the curve y=x^2 is 9-x^2, and the distance between the line y=9 and the line y=3x is 9-3x. Therefore, the area of the washer at x with inner radius 9-3x and outer radius 9-x^2 is:
dA = π[(9-x^2)^2 - (9-3x)^2]dy
= π[(x^4 - 6x^2 + 81) - (9x^2 - 54x + 81)]dy
= π(-x^4 + 15x^2 - 54x)dy
Integrating this expression over the region of interest [0,3], we get:
V = ∫[0,3] π(-x^4 + 15x^2 - 54x)dy
= π[-(1/5)x^5 + 5x^3 - (27/2)x^2]_[0,3]
= π[(243/10) - (135/2) - (27/2)]
= (27/2)π
Therefore, the volume of the solid is (27/2)π cubic units.
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Related Questions
How mile does Zack walk in one month if he works 22 days that month
Answers
Answer:154 miles
Hi, to answer this question we simply have to multiply the distance that he walks every day (7 miles) by the number of days that he works in a month (22). Zack walks 154 miles in one month.
Step-by-step explanation:
HOPE THIS YOU GIVE A BRAINEST AM SMART AM HERE TO HELPPPP
help with homework asap pls. Rs. 100 are divided between Sangeeta and Manish in the ratio 4:1. Find theamount Sangeeta gets.
Answers
here is your answer
if you will not like then you will be ehsanfaramosh
the sales tax on a 30,000 purchese was $2.40. What was the sales tax rate for this purchese?
Answers
The sales tax on a $30,000 purchase was $2.40, so we can set up an equation:
$30,000 * r = $2.40
To find the sales tax rate, we can divide both sides of the equation by $30,000:
r = $2.40 / $30,000 = 0.008
So, the sales tax rate for this purchase was 0.008, or 0.8%.
If f(x) = 3x - 5, then f(2) =1.
Answers
step by step:
if its f(2) then u replace x with 2 so it would look like
f(2) = 3(2) - 5
3 times 2 is 6
6-5 is 1
thats how u solve it
Yes you are correct. It equals 1
The product of five and a number is equal to three times the difference of the number and six. Find the number. Answer 2 Points 0 0 0 0 None of these
Answers
Answer:
-9
Step-by-step explanation:
We can write an equation to solve this, using x as "the number":
(x·5)=3(x-6)
simplify
5x=3x-18
subtract 3x from both sides
2x=-18
divide both sides by 2
x=-9
Hope this helps! :)
The given number is -9.
Let's suppose the number be ‘x’.
According to the question, The product of five and a number is equal to three times the difference of the number and six.
Mathematically, it can be written as5x = 3(x - 6)
Solving this equation,5x = 3x - 185x - 3x = -18 (transferring 3x to LHS and -18 to RHS)2x = -18 (subtracting 3x from both the sides)
The value of x can be found out by dividing both the sides by 2.
Hence, x = -9
Thus, the value of the number is -9.
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The value of w???????
Answers
Answer:
Step-by-step explanation:
The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:
\(\frac{15}{18}=\frac{w}{30}\) and cross multiply.
18w = 450 so
w = 25
What is the area of the triangle in the diagram?
Answers
Answer:
l think the answer is =C for this area of triangle
A supermarket gives a special
offer to cus-
tomers who purchase at least a pack of
vests and a pack of T-shirts. The offer is
restricted to a total of 7 of these items.
a) Write down three inequalities which
must be satisfied.
(b) Draw the graphs of the above condi-
tions and shade the region that satis-
fies them.
(c) If the supermarket makes a gain of N5
on each vest and N8 on each T-shirt,
find the maximum gain made by the
supermarket.
Answers
A) the three inequalities that must be satisfied are:
The number of vests, represented by x, must be a non-negative integer: x ≥ 0.The number of T-shirts, represented by y, must also be a non-negative integer: y ≥ 0.The total number of vests and T-shirts must not exceed 7: x + y ≤ 7.B) Graph shaded and satisfying all conditions is attached.
What is an inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.
It is most commonly used to compare the sizes of two numbers on a number line.
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Which of the following is a direct proportion?
A. y=7x
B. y=x+7
C. y=7x−7
D. y=7
Answers
what is the answer for-4(2x+y)
Answers
Answer:
-8x-4y
Step-by-step explanation:
distrubutive property
Find the volume of radius 7 cm in diameter of 12 cm in 3.14
Answers
The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.
To find the volume of a sphere with a radius of 7 cm, we can use the formula:
V = (4/3) * π * r^3
where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.
The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:
V = (4/3) * π * (6 cm)^3
V = (4/3) * 3.14 * (6 cm)^3
V = (4/3) * 3.14 * 216 cm^3
V = 904.32 cm^3
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If you want to leave an 18% tip for a waiter on a $54.35 meal, what would the total bill be?
$64.13
$9.78
$44.57
$8.15
Answers
Answer:
$64.13
Step-by-step explanation:
the tip would be added to the meal cost
Answer:
54.35+$9.78=64.13
Step-by-step explanation:
54.35*.18=9.78
Hope this helps :)
What is one negative angle that is co-terminal to 150°? *
Answers
Answer:
-210 degrees.
Step-by-step explanation:
That is 150 - 360
= -210 degrees.
simplify the following radical expression
Answers
Answer:
\(2\sqrt{6} -13\sqrt{3} +4\sqrt{2}\)
Step-by-step explanation:
\(\sqrt{24} -5\sqrt{12} +4\sqrt{2} -3\sqrt{3}\)
\(=\sqrt{4\times 6} -5\sqrt{4\times 3} +4\sqrt{2} -3\sqrt{3}\)
\(=\sqrt{4} \times \sqrt{6} -5\times\sqrt{4} \times \sqrt{3} +4\sqrt{2} -3\sqrt{3}\)
\(=2\sqrt{6} -5\times2\sqrt{3} +4\sqrt{2} -3\sqrt{3}\)
\(=2\sqrt{6} -10\sqrt{3} +4\sqrt{2} -3\sqrt{3}\)
\(=2\sqrt{6} -13\sqrt{3} +4\sqrt{2}\)
Answer:
\( \boxed{ \tt 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} }\)
or
\( \boxed{ \tt \approx - 12.1}\)
Step-by-step explanation:
Simplify:
\( = \tt \sqrt{ {2}^{2} \times 6} −5 \sqrt{12} +4√2−3√3\)
\( = \tt \: 2 \sqrt{6} - 5 \sqrt{12} + 4 \sqrt{2 } - 3 \sqrt{3} \)
\( = \tt2 \sqrt{6} - \sqrt{ {2}^{2} \times 3} + 4 \sqrt{2} - 3 \sqrt{3} \)
\( = \tt \: 2√6−5(2√3)+4√2−3√3\)
\( \tt = 2√6−10√3+4√2−3√3\)
\( \tt = 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} \)
\( \tt \approx \: - 12.1\)
\( \rule{225pt}{2pt}\)
HELP ASAP IM GUNA FAIL!!!
Answers
Answer: -14
Step-by-step explanation: Use the given functions to set up and simplify g(−2)
-3•4-2
Multiply
-12-2
Add
Answer -14
May I get Brainly
abc is a right triangle with ab=ac. bisector of <a meets bc at d. prove that bc = 2ad.
Answers
Answer:
Let ac=ab=5
With this, bc= 5√2
Step-by-step explanation:
So to find ad, Let ad be x
5√2=(2)(x)
(5√2/2)= x
This proves that bc=2ad
6. What might be the opportunity cost of a large portion of your income going toward credit
card payments each month?
Answers
The geometric average of -10%, 20% and 40% is _________.
11.2%
14.8%
20.3%
21.4%
Answers
The geometric average of -10%, 20%, and 40% is approximately -20.2%.
To find the geometric average of a set of numbers, you need to multiply them together and then take the nth root, where n is the number of values.
In this case, we have three values: -10%, 20%, and 40%.
Step 1: Convert the percentages to decimal form by dividing by 100.
-10% becomes -0.10
20% becomes 0.20
40% becomes 0.40
Step 2: Multiply the decimal values together.
-0.10 * 0.20 * 0.40 = -0.008
Step 3: Take the cube root (since we have three values) of the result.
∛(-0.008) ≈ -0.202
Step 4: Convert the result back to a percentage by multiplying by 100.
-0.202 * 100 ≈ -20.2%
Therefore, the geometric average of -10%, 20%, and 40% is approximately -20.2%.
None of the given options (11.2%, 14.8%, 20.3%, and 21.4%) matches the calculated value.
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In the House of Commons, citizens elect their members. Of the 800 members, 530 are from England, 120 are from Wales, 100 are from Scotland and 50 are from Northern Ireland. What is the percentage of members from Wales?
Answers
Answer:
15%
I like your demon slayer profile picture
Answer:
The answer is 15%.
Step-by-step explanation:
If 100 is 10% it only makes since that 15% is the right answer.
Hope This Helps!
Need to find x?
3-x= -4
Answers
Answer:
x = 7
Step-by-step explanation:
First subtract 3 from both sides to get -x = -7. Now divide -1 from both sides to get x = 7.
Hope it helps!
You want to change your cell phone service. The new company charges $40 per
month for cell phone use. There is a one-time start-up fee of $25. Which equation
shows the total cost of your cell phone service over time?
Answers
Answer:
y=40x+25
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The expression 2 - x-1/x+2
is equivalent to
A. 1 - 3/x+2
B. 1 + 3/x+2
C. 1 - 1/x+2
D. 1 + 1/x+2
Answers
The expression \(2- \dfrac{x-1}{x+2}\) is equivalent to \(1 + \dfrac{3}{x+2}\).
We have to find, which equation is equivalent to the given expression.
The given expression is,
\(= 2- \dfrac{x-1}{x+2}\)
To determine the equivalent expression following all the steps given below.
Step1; Taking LCM in the equation,\(\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\\)
Step2; Solving the equation,\(= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\\)
Step3; rewrite the equation in the small factors,\(=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\\)
Step4; By using partial fraction rewrite the equation,\(= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}\)
Hence, The expression \(2- \dfrac{x-1}{x+2}\) is equivalent to \(1 + \dfrac{3}{x+2}\).
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What is y tan 0 when 0 = -45°? OA.-1 OB. 1 OC. 0 OD. undefined
Answers
The correct option is A. -1. To get the value of y tan 0, we first find the tangent of -45° which is -1
Given, 0 = -45°.
We are to find y tan 0.
Therefore, y tan 0 = y tan (-45°).
tan (-45°) = -1
We know that the value of tangent is negative in the 3rd quadrant, and therefore,
the value of y tan 0 = y (-1) = -y.
Hence, "y tan 0 = -y".
Calculation steps:
First, we find the value of the tangent of -45°, which is -1. As the value of y is unknown, we replace it with y.
So, y tan 0 = y tan (-45°)
tan (-45°) = -1 (as tangent is negative in the 3rd quadrant)
Therefore, y tan 0 = y (-1) = -y
Hence, y tan 0 = -y.
When we multiply a value with the tangent of an angle, we get the value of y tan 0. Here, we are given the angle 0 as -45°, and we have to find the value of y tan 0. To get the value of y tan 0, we first find the tangent of -45° which is -1.
As the angle is negative, it is in the third quadrant, where the value of tangent is negative. Now, we replace y with the calculated value and get -y as the answer. Hence, y tan 0 = -y.
Therefore, the correct answer is option A.
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what is -42=5(2c+9)-3(c+8)
MUST SHOW WORK!!!
Answers
Answer:
The variable c=9 is the answer the varibles
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
c = −15.8571428571
Step-by-step explanation:
-42 = 5(2c + 9) - 3(c + 8)
-42 = 10c + 45 - 3c + 24
-42 = 10c - 3c + 45 + 24
-42 = 7c + 69
-7c -7c
-------------------
-7c - 42 = 69
+42. +42
___________
-7c/-7 = 111/-7
c = −15.8571428571
200 students appeared in an examination. If 25% of student passed the examination, find the number of student who failed in the examination
a. 150
b. 100
c. 275
d. 175
Answers
Answer:
150 students failed
25% of 200 is 50 therefore 200-50 (50 being the amount of students passed) would be 150
Answer:
A 150student will fail the examination
The following system of linear equations is shown in the graph.
y=1/4x+5
x-4y=4
How many solutions does the system of linear equations have?
A. No solution
B. Infinitely many solutions
C. One solution at (4,0)
D. One solution at (0,-1)
Answers
Answer:
Step-by-step explanation:
The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.
A. No solution
y = 1/4x+5
x - 4y = 4
You can simplify the second equation into y = 1/4x - 1
Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.
Write all the properties for a kite
Answers
Answer:
Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles and (3) perpendicular diagonals. Other important polygon properties to be familiar with include trapezoid properties, parallelogram properties, rhombus properties, and rectangle and square properties.
Step-by-step explanation:
Answer: The diagonals cross at 90°.
Two pairs of sides are equal length.
One pair of diagonally opposite angel is equal.
Only one diagonal is bisected by the other.
The diagonals are perpendicular.
Step-by-step explanation:
hope this helps.❤❤ THANK YOU.
A triangle has a sides (x) feet, (x+3) feet, and (x+5) feet. The perimeter is 99.5 feet What is the measure for the largest side?
Answers
Answer:
35.5 feet
Step-by-step explanation:
x + x + 3 + x + 5 = 99.5
3x + 8 = 99.5
3x = 91.5
x = 30.5
Largest side = (x+5)
30.5 + 5 = 35.5 feet
!help!
what is the common factor for the two fractional terms 5/8x and 11/8xy?
The terms can be writen as (5) (1/8) (x) and (11) (1/8) (x) (y)
○ 5
○ 1/8x
○ 5/8
○ y
Answers
The common factor of given terms is x/8, which is given in option B.
What is factor?A factor is a number that divides another number, leaving no remainder.
Here, given terms are:
\(\frac{5}{8}x\) and \(\frac{11}{8} x\)
Now, factors of 5x/8 = 5 X 1/8 X (x)
factors of 11x/8 = 11 X 1/8 X (x)
So, common factors are 1/8 and x
Thus, the common factor of given terms is x/8, which is given in option B.
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In the manufacture of a certain article it is known that 1 out of 10 of the articles is defective. What is the probability that a random sample of 4 of the articles will contain
Answers
The probability that a random sample of 4 of the articles will contain a defective article is approximately 0.2916, or about 29.16%.
To find the probability that a random sample of 4 articles will contain a certain number of defective articles, we can use the binomial probability formula:
P(X = k) = (nCk) * (p^k) * (1-p)^(n-k)
where:
- n is the total number of articles in the sample (4 in this case)
- k is the number of defective articles we want to find the probability for
- p is the probability of an article being defective (1/10)
- 1-p is the probability of an article not being defective (9/10)
- nCk represents the number of combinations of n items taken k at a time
It appears that you haven't mentioned the specific number of defective articles you want in the sample of 4. However, you can use the formula above and plug in the values for k (0, 1, 2, 3, or 4) to find the probability for any desired number of defective articles in the sample.
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