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pishuonlain [190]
3 years ago
13

Y=x, y=0, y=4, x=6 : find the volume of the solid generated revolving around line x=6

Mathematics
1 answer:
Vilka [71]3 years ago
5 0
Using shells, the volume is

\displaystyle2\pi\int_0^6(6-x)x\,\mathrm dx

where 6-x is the distance from any point in the region along the x-axis to the axis of revolution x=6, which makes up the radius of each shell; and x is the height of each shell, which is determined by the line y=x.

So the volume is

\displaystyle2\pi\int_0^6(6x-x^2)\,\mathrm dx=2\pi\left(3x^2-\frac{x^3}3\right)\bigg|_{x=0}^{x=6}=72\pi
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Answer:

Width of border = 1 ft

Step-by-step explanation:

Total Area = 99 ft²

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3 years ago
Classify the following triangle as acute, obtuse, or right.
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2 years ago
Write an equation of the line through (6,-5) having slope 0. Give the answer in standard form.
allsm [11]

0x + 1y = -5 is the standard form of equation

<em><u>Solution:</u></em>

Given that we have to write the equation of line passing thorugh (6, -5) and has slope 0

<em><u>The equation of line in slope intercept form is given as:</u></em>

y = mx + c ---------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given that, m = 0

Given point is (6, -5)

<em><u>To find the y - intercept:</u></em>

<em><u>Substitute (x, y) = (6, -5) and m = 0 in eqn 1</u></em>

-5 = 0(6) + c

c = -5

<em><u>Substitute c = -5 and m = 0 in eqn 1</u></em>

y = 0x + (-5)

y = -5

<em><u>The standard form of equation is given as:</u></em>

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

y = -5

0x + 1y = -5 is the standard form of equation

8 0
2 years ago
Pls help me i need help with he answer i been on this question for hours it keeps saying my answer is wrong sooo at this point i
Nikitich [7]

Answer:

-100 + x = 40

Step-by-step explanation:

According to the question:

Tyler's original height = -100 feet

Tyler's final height = 40

X to represent change in elevation

As initial + change = final, the equation would be:  

-100 + x = 40  

Please mark it as brainliest if it helps you!

I wasn't sure about my answer, so used the gauthmath app.

5 0
3 years ago
Read 2 more answers
What is the area of a circle?<br><br> The answer is A=πr2, but I want you to show the work.
Cerrena [4.2K]

Answer:

the area of a circle is A= πr²

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2 years ago
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