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Lisa [10]
3 years ago
6

Let r be the region in the first quadrant bounded by the graph y=8- x^ (3/2) Find the area of the region R . Find the volume of

the solid generated when R is revolved about the x-axis
Mathematics
1 answer:
Vanyuwa [196]3 years ago
8 0
The boundaries:
x = 0,  y = 8;  y = 0,  √x³ = = 8,  x = 4
A= \int\limits^4_0 {(8- x^{3/2}) } \, dx = \\ =8 x - 2 \sqrt{ x^{5} }/5= \\ 8*4-64/5 =19.2
V =  \int\limits^4_0 { \pi (8 -  x^{3/2}) } \, dx = \\ = \pi  \int\limits^0_4 {(64 - 16 * 2 \sqrt{ x^{5} /5} +  x^{4}/4)  \, dx =
= π ( 64 x - 16 * 2 *√x^5  + x^4 / 4 ) =
= π ( 320 - 1024/5 + 64 ) = 179.2 π

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Divide f(x) by d(x), and write a summary statement in the form indicated.
Mandarinka [93]

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The correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

Step-by-step explanation:

Consider the provided function.

f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5 and d(x) = x^2+1

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor:\frac{x^4}{x^2}=x^2

Write the calculated result in upper part of the table.

Multiply it by the divisor: x^2(x^2+1)=x^4+x^2

Now Subtract the dividend from the obtained result:

(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5

Again divide the leading term of the obtained remainder by the leading term of the divisor: \frac{4x^3}{x^2}=4x

Write the calculated result in upper part of the table.

Multiply it by the divisor: 4x(x^2+1)=4x^3+4x

Subtract the dividend:

(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5

Divide the leading term of the obtained remainder by the leading term of the divisor: \frac{5x^2}{x^2}=5

Multiply it by the divisor: 5(x^2+1)=5x^2+5

Subtract the dividend:

(5x^2+5)-(5x^2+5)=0

Therefore,

Dividend = x^4 + 4x^3 + 6x^2 + 4x + 5

Divisor = x^2+1

Quotient = x^2+4x+5

Remainder = 0

Dividend = Divisor × Quotient + Remainder

f(x) = (x^2+1)(x^2+4x+5)

Hence, the correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

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3 years ago
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Answer:

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Step-by-step explanation:

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Step 2: Isolate x by subtracting 6 on both sides

9x = 36

Step 3: Isolate x by dividing by 9 on both sides

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