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m_a_m_a [10]
3 years ago
14

Find the volume of the solid obtained by rotating the region bounded by y = 8 x 2 , x = 1 , and y = 0 , about the x -axis.

Mathematics
1 answer:
pashok25 [27]3 years ago
6 0
A cross-section is a disc with radius 8x^2

V = \int_0^1 A(x)\, dx = \int_0^1 \pi\left(8x^2\right)^2 dx = \int_0^1 64 \pi x^4 = \left[\frac{64\pi}{5} x^5\right]_0^1 \\
\\
= \frac{64\pi}{5}
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Which of the following statements regarding the expansion of (x + y)^n are correct?
kompoz [17]

Answer:

A, B and D are true statements.

Step-by-step explanation:

We are given a binomial expansion

(x+y)^n=^nC_0x^ny^0+^nC_1x^{n-1}y^1+^nC_2x^{n-2}y^2+...........+^nC_nx^0y^n

(x+y)^n=x^n+nx^{n-1}y+^nC_2x^{n-2}y^2+...........nxy^{n-1}+y^n

Now we will check each option

Option A: The coefficients of x^n and y^n both equal 1.

If we see first and last term of the expansion, This statement is true.

Option B: For any term x^ay^b in the expansion, a + b = n.

Let we take 3rd term of expansion ^nC_2x^{n-2}y^2

Here, a=n-2 and b=2

If we do  a+b = n-2+2=n

a+b=n is true statement.

Option C: For any term x^ay^b in the expansion, a - b = n.

Let we take 3rd term of expansion ^nC_2x^{n-2}y^2

Here, a=n-2 and b=2

If we do  a-b = n-2-2=n-4≠n

a-b=n is false statement.

Option D: The coefficients of x^ay^b and x^by^a are equal.

If we take second term from beginning and last of the expansion.

\text{Coefficient From beginning } nx^{n-1}y=n

\text{From last } nxy^{n-1}=n

This statement true.

8 0
3 years ago
going against the current a boat takes 6 hours to make a 120 mile trip when the boat travels with the current on the return trip
Irina18 [472]
Speed against current = 120 miles / 6 hours = 20 miles / hour
Speed with current = 120 miles /5 hours = 24 miles / hour.

Speed of boat in still water = (20+24)/2 = 22 miles / hour
6 0
2 years ago
What is 0.45 as a fraction how do I show my work
g100num [7]
45/100 = 9/20

Work: divide by 5
7 0
3 years ago
Read 2 more answers
Find the area and perimeter of the rectangle Length = 5cm Breadth =2cm
avanturin [10]

Answer:

perimeter: 14

Area: 10

Step-by-step explanation:

PERIMETER

2x(L+B) = 2x(5+2) = 2x(7) = 14

AREA

LxB = 5x2 = 10

PLEASE MARK ME BRAINLIEST

5 0
3 years ago
Can anyone help me plz ?? Lakita has 66 water bottles for the 5K race participants. In addition, she is planning to buy boxes of
Ivanshal [37]

Answer:

65,81,97,113,129


Step-by-step explanation:


she has 65 water bottles and she is buying boxes of water bottles (x) that hold 16 water bottles each. She can only buy up to 5 water bottles.



f(x) = 16x + 65...where f(x) = total water bottles and x = number of boxes


x < = 5 here is ur restriction



the range is ur f(x) values which represent the total number of water bottles...keep in mind, she can only buy 5. Therefore, the numbers that can be subbing in for x are 0 thru 5.



So when subbing in 0 thru 5 for x, the results for f(x) are :


{ 65,81,97,113,129 }

8 0
2 years ago
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