*15 points

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 <u>Disc</u> <u>Method</u>, 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 = $\frac{64}{3}.\pi$

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2 years ago

Carly is constructing the inscribed circle for △MNP . She has already used her compass and straightedge to complete the part of

JulijaS [17]

Place the point of the compass on point J and draw an arc in the interior of the triangle.

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3 years ago

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(01.01) Kisha and Rae are asked to solve −5x − 14 = 2x + 7. Identify where one of them made an error.

lora16 [44]

It's A.
Rae made the error when she added 7.
the equation should be:
<span>-14 - 7 = 7x + 7 - 7 </span>

3 0

3 years ago

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Miss Williams asked her class if they prefer doing their homework before school or after school if the ratio of students who pre

fredd [130]

IT means that the students prefer doing homework after school more than before school!
<span>7 / 22 = 31.818181818182%
</span>
HOPE I HELPED!

~Tomas

6 0

3 years ago

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Determine if 0.59136363636363636... is rational or irrational and give a reason for<br> your answer

Reil [10]

The number 0.59136363636363636... is an irrational numbers

<h3>How to determine the number type?</h3>

The number is given as:

Number = 0.59136363636363636...

The three dots at the end of the number implies that the numbe is a non-terminating decimal

All non-terminating decimal are irrational numbers

Hence, the number 0.59136363636363636... is an irrational numbers

Read more about irrational numbers at

brainly.com/question/11919233

#SPJ1

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2 years ago