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3 years ago

What is the input value for the following function if the output value is 5?

Mathematics

1 answer:

Zina [86]3 years ago

8 0

The answer to the problem is d

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Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis

guapka [62]

Answer: V = $\frac{64}{3}\pi$

Step-by-step explanation: A solid formed by revolving the region about the x-axis can be considered to have a thin vertical strip with thickness Δx and height y = f(x). The strip creates a circular disk with volume:

V = $\pi. y^{2}.$ Δx

Using the Disc Method, it is possible to calculate all the volume of these strips, giving the volume of the revolved solid:

V = $\int\limits^a_b {\pi. y^{2} } \, dx$

Then, for the region generated by y = - x + 4:

V = $\int\limits^4_0 {\pi.(-x+4)^{2} } \, dx$

V = $\pi.\int\limits^4_0 {(x^{2}-8x+16)} \, dx$

V = $\pi.(\frac{x^{3}}{3}-4x^{2}+16x )$

V = $\pi.(\frac{4^{3}}{3}-4.4^{2}+16.4 - 0 )$

V = $\frac{64}{3}.\pi$

The volume of the revolved region is V = $\frac{64}{3}.\pi$

8 0

2 years ago

Pluto is approximately 2.7 miles from the Sun.

4vir4ik [10]

Answer:

40 times greater

Step-by-step explanation:

5 0

2 years ago

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Which rate is faster:a bird traveling at a constant rate of 2 kilometer per hour or an insect travelinf at a constant rate of 1,

Alla [95]

The bird since 1 kilometer is 1000 meters

6 0

3 years ago

7x + 5y = -10 solve for y

katen-ka-za [31]

The y intercept is (0,-2)

5 0

2 years ago

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Solve using substitution. 4x – 7y = -18 x = 6

levacccp [35]

Answer:

Step-by-step explanation:

4(6) - 7y = -18

24 - 7y = -18

-7y= -42

y= 6

3 0

2 years ago

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