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Airida [17]
3 years ago
7

Which expression is equivalent to (4^-3)^-6 a.) 4^3 b.) 4^-9 c.) 4^-18 d.) 4^18

Mathematics
1 answer:
mario62 [17]3 years ago
3 0

Answer:

Answer:

The answer is d.) 4^18

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 7x6, y
IgorC [24]

Answer:

The volume is \frac{490\pi}{39} cubic units.

Step-by-step explanation:

The given curve is

y=7x^6

The given line is

y=7x

Equate both the functions to find the intersection point of both line and curve.

7x^6=7x

7x^6-7x=0

7x^6-7x=0

7x(x^5-1)=0

7x=0\rightarrow x=0

x^5-1=0\rightarrow x=1

According to washer method:

V=\pi \int_{a}^{b}[f(x)^2-g(x)^2]dx

Using washer method, where a=0 and b=1, we get

V=\pi \int_{0}^{1}[(7x)^2-(7x^6)^2]dx

V=\pi \int_{0}^{1}[49x^2-49x^{12}]dx

V=49\pi \int_{0}^{1}[x^2-x^{12}]dx

V=49\pi [\frac{x^3}{3}-\frac{x^{13}}{13}]_0^1

V=49\pi [\frac{1^3}{3}-\frac{1^{13}}{13}-(0-0)]

V=49\pi [\frac{1}{3}-\frac{1}{13}]

V=49\pi (\frac{13-3}{39})

V=49\pi (\frac{10}{39})

V=\frac{490\pi}{39}

Therefore the volume is \frac{490\pi}{39} cubic units.

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3 years ago
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