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Sliva [168]
3 years ago
5

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating

rectangle.
x = 28 − 7y2,
x = 7y2 − 28

Mathematics
1 answer:
natulia [17]3 years ago
8 0

Answer:

V=25088π vu

Step-by-step explanation:

Because the curves are a function of "y" it is decided to take the axis of rotation as y

, according to the graph 1 the cutoff points of f(y)₁ and f(y)₂ are ±2

f(y)₁ = 7y²-28;  f(y)₂=28-7y²

y=0;   x=28-0 ⇒ x=28

x=0;   0 = 7y²-28 ⇒ 7y²=28 ⇒ y²= 28/7 =4 ⇒ y=√4 =±2

Knowing that the volume of a solid of revolution  V=πR²h, where R²=(r₁-r₂) and h=dy then:

dV=π(7y²-28-(28-7y²))²dy ⇒dV=π(7y²-28-28+7y²)²dy = 4π(7y²-28)²dy

dV=4π(49y⁴-392y²+784)dy integrating on both sides

∫dV=4π∫(49y⁴-392y²+784)dy ⇒ solving  ∫(49y⁴-392y²+784)dy

49∫y⁴dy-392∫y²dy+784∫dy =

V=4π( 49\frac{y^{5} }{5}-392\frac{y^{3}}{3}+784y ) evaluated -2≤y≤2, or 2(0≤y≤2), also

V=8\pi(49\frac{2^{5} }{5}-392\frac{2^{3} }{3}+784.2)  ⇒ V=25088π vu

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Answer:

Step-by-step explanation:

(5,4) ;  (-3, -2)

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(5,4) & m = (3/4)

y -y1 = m(x-x1)

y - 4 = (3/4)(x - 5)

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7 0
3 years ago
The histogram below shows information about the number of books students read in a month:
max2010maxim [7]

Answer:

Option C is true - The number of students who read 4 books or fewer

Step-by-step explanation:

Here, to find the mean and median, we do not have proper information or specific values. We just have the ranges, so both the mean and median cannot be determined.  So, options A and B are not correct.

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6 0
3 years ago
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Step-by-step explanation:

5 0
3 years ago
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Ne4ueva [31]

Answer:

29 and 35

Step-by-step explanation:

x+y=64

x-y=6

Solve by substitution.

x=6+y

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7 0
3 years ago
Add: 7/8 + 5/6 .......
Rashid [163]

Answer:

1 17/24

Step-by-step explanation:

To add fractions, find the LCD and then combine.

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Mixed Number Form:

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6 0
3 years ago
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