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valkas [14]
3 years ago
9

Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the regi

on bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Mathematics
1 answer:
vredina [299]3 years ago
3 0

Answer:

The answer is "\frac{5\pi}{6}"

Step-by-step explanation:

Please find the graph file.

h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\

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If ΔOPQ is dilated from point Q by a scale factor of 3, which of the following equations is true about segment R prime S prime?
Sergio [31]

Answer:

\overline {R'S'}  = 3 {\overline {RS} }

Step-by-step explanation:

The scale factor of dilation of triangle ΔOPQ, S.F. = 3

The center of dilation = Point <em>Q</em>

Therefore;

The length of the segment, {\overline {S'Q'} } = 3 × The length of the segment, {\overline {SQ} }

Similarly;

The length of the segment, {\overline {R'Q'} } = 3 × The length of the segment, {\overline {RQ} }

By Pythagoras theorem, we have;

{\overline {R'Q'} }^2 = {\overline {R'S'} }^2 + {\overline {S'Q'} }^2

Therefore;

{\overline {R'S'} }^2  = {\overline {R'Q'} }^2  - {\overline {S'Q'} }^2 = \left ({3 \times \overline {RQ} } \right) ^2  - \left (3 \times {\overline {SQ} } \right) ^2 = 9 \times \left (\overline {RQ} }  ^2  -  {\overline {SQ} } ^2 \right) = 9 \times  {\overline {RS} }^2

\therefore \sqrt{  {\overline {R'S'} }^2} =  \sqrt{ 9 \times  {\overline {RS} }^2}= 3 \times  {\overline {RS} }

\overline {R'S'}  = 3 \times  {\overline {RS} }.

6 0
3 years ago
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max2010maxim [7]

Answer:

\frac{\pi }{6}

Step-by-step explanation:

\frac{7\pi }{6} is in the third quadrant

To find the reference angle subtract π from it, that is

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8 0
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Answer:the term of the loan is approximately 4 months

Step-by-step explanation:

The term of the loan means the period for which the loan was given.

We would apply the formula for simple interest which is expressed as

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P represents the principal

R represents interest rate

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I = interest after t years

From the information given

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R = 6.5%

I = total amount paid - principal

I = 17,873.97 - 17,500.00 = 373.97

Therefore

373.97 = (17500 × 6.5 × T)/100

373.97 = 1137.5T

T = 373.97/1137.5

T = 0.32 years

Converting to months, it becomes

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3 0
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charle [14.2K]

Answer:

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Step-by-step explanation:

7 0
3 years ago
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Answer:

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substitute 5 for x

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4 0
3 years ago
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