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tatiyna
3 years ago
6

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y=e^x

, x=1, and y=1 is revolved around the line y=-2?

Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

The fourth option is correct.

See the attached image. The red cylinder represents a washer formed by the described revolution. Its volume is

\pi((\text{outer radius})^2-(\text{inner radius})^2)(\text{height})

so when we integrate, we take

\displaystyle\pi\int_0^1((e^x+2)^2-3^2)\,\mathrm dx

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Answer:

The answer is below

Step-by-step explanation:

We must first define the concepts a little:

We have that when the sides are congruent that is to say that they have the same direction and the same size and also the two opposite sides are parallel, the angles will be the same.

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Given:

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To find:

The measure of angle MFZ.

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In triangles MFZ and PFZ,

m\angle FMZ\cong \angle FPZ           (Right angle)

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FZ\cong FZ           (Common side)

\Delta MFZ\cong \Delta PFZ                  (HL congruent postulate)

\angle MFZ\cong \angle PFZ           (CPCTC)

m\angle MFZ=m\angle PFZ

x+9=2x-1

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The value of x is 10.

The measure of angle MFZ is:

m\angle MFZ=(x+9)^\circ

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399

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