1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kotykmax [81]
3 years ago
6

99 POINT QUESTION, PLUS BRAINLIEST!!!

Mathematics
1 answer:
Elden [556K]3 years ago
6 0
We draw region ABC. Lines that connect y = 0 and y = x³ are vertical so:
(i) prependicular to the axis x - disc method;
(ii) parallel to the axis y - shell method;
(iii) parallel to the line x = 18 - shell method.

Limits of integration for x are easy x₁ = 0 and x₂ = 9.
Now, we have all information, so we could calculate volume.

(i)

V=\pi\cdot\int\limits_a^bf^2(x)\, dx\qquad\implies \qquad a=0\qquad b=9\qquad f(x)=x^3


V=\pi\cdot\int\limits_0^9(x^3)^2\, dx=\pi\cdot\int\limits_0^9x^6\, dx=\pi\cdot\left[\dfrac{x^7}{7}\right]_0^9=\pi\cdot\left(\dfrac{9^7}{7}-\dfrac{0^7}{7}\right)=\dfrac{9^7}{7}\pi=\\\\\\=\boxed{\dfrac{4782969}{7}\pi}

Answer B. or D.

(ii)

V=2\pi\cdot\int\limits_a^bx\cdot f(x)\, dx


V=2\pi\cdot\int\limits_0^{9}(x\cdot x^3)\, dx=2\pi\cdot\int\limits_0^{9}x^4\, dx=
2\pi\cdot\left[\dfrac{x^5}{5}\right]_0^9=2\pi\cdot\left(\dfrac{9^5}{5}-\dfrac{0^5}{5}\right)=\\\\\\=2\pi\cdot\dfrac{9^5}{5}=\boxed{\dfrac{118098}{5}\pi}

So we know that the correct answer is D.

(iii)
Line x = h

V=2\pi\cdot\int\limits_a^b(h-x)\cdot f(x)\, dx\qquad\implies\qquad h=18


V=2\pi\cdot\int\limits_0^9\big((18-x)\cdot x^3\big)\, dx=2\pi\cdot\int\limits_0^9(18x^3-x^4)\, dx=\\\\\\=2\pi\cdot\left(\int\limits_0^918x^3\, dx-\int\limits_0^9x^4\, dx\right)=2\pi\cdot\left(18\int\limits_0^9x^3\, dx-\int\limits_0^9x^4\, dx\right)=\\\\\\=2\pi\cdot\left(18\left[\dfrac{x^4}{4}\right]_0^9-\left[\dfrac{x^5}{5}\right]_0^9\right)=2\pi\cdot\Biggl(18\biggl(\dfrac{9^4}{4}-\dfrac{0^4}{4}\biggr)-\biggl(\dfrac{9^5}{5}-\dfrac{0^5}{5}\biggr)\Biggr)=\\\\\\

=2\pi\cdot\left(18\cdot\dfrac{9^4}{4}-\dfrac{9^5}{5}\right)=2\pi\cdot\dfrac{177147}{10}=\boxed{\dfrac{177147\pi}{5}}

Answer D. just as before.

You might be interested in
Which Step should be performed to isolate X
hichkok12 [17]
If you're talking x in particular, it can't be isolated. See, if we have this equation, x=5, we divide the Answer by the Answer, so 5/5=1. We divide the Answer by x, so x would appear x/5. So, x/5=1
7 0
3 years ago
X + (-4) = -2 <br> What does X repesents??? Please help
Nonamiya [84]

Answer:

x=2

Step-by-step explanation:

x+(-4) is the same as x-4

First you have to get X alone so you add 4 to both sides because when you add 4 to both sides it will take away the 4 on the x side.

x-4=-2

+4    +4

x= -2+4                or you can see this as 4-2 which is 2

x=2

8 0
3 years ago
Read 2 more answers
If measurement angle L = 58 then measurement angle LKJ = _________ degrees.
Montano1993 [528]

because the sides are the same and angle L = 58, that means that angle J is also 58, so LKJ would be 180-58-58 = 64 degrees


if JKM = 48, M = 90

 so J = 180 -90 -48 = 42 degrees

4 0
3 years ago
The table below represents a function. Which of the following equations could be its function rule?
cricket20 [7]

Answer:

it's the 3rd choice, Y= -3x

4 0
3 years ago
Karan and Preeti are sharing a packet of sweets in the ratio of 2:3 .If the total sweets is 50,how many sweets will Preeti get
Viktor [21]

Answer:

30 sweets

Step-by-step explanation:

From the above question

The ratio is given as:

Karan : Preeti

2:3

The sum of the proportion = 2 + 3 = 5

Total number of sweets = 50 sweets

The number of sweets Preeti will get is calculated as:

3/5 × 50 sweets

= 30 Sweets

Therefore, the number of sweets Preeti will get is 30 sweets

8 0
3 years ago
Other questions:
  • 2c/15=8.8 Solve The Equation. What Is The Value Of "C"
    5·2 answers
  • What is the numerator of the simplified sum?<br> x/x^2 +3x+2 + 3/x+1
    15·1 answer
  • Need help ASAP
    15·1 answer
  • Let () = 2 - 7 and () = -6 - 3. Find () + () and state its domain.
    8·1 answer
  • How do you factor 0 = 4x2 + 2x – 30?
    6·2 answers
  • What is the slope of (-7,5) and (5,-1)
    10·1 answer
  • What is the difference of <br> 5<br> 6<br> −<br> 5<br> 12<br> ? Use the fraction strip to help.
    9·1 answer
  • 15 POINTS FOR THE BRAINLIEST
    15·2 answers
  • Which of the following polynomials are quadratic
    14·1 answer
  • Each cheerleading uniform includes a shirt and a skirt. Shirts cost $17 each and skirts cost $19 each. The expression 17u + 19u
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!