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3 years ago

What is the value of the expression below? (27^2/3)^1/2A. 9 B. 81 C. 27 D. 3

Mathematics

1 answer:

navik [9.2K]3 years ago

7 0

I think it might be A

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

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3 years ago

This is a sketch of the curve with equation y = f(x).

Katen [24]

Answer:

We have to use the formule to calculate the vertex which is: V(-b/2a;4ac-b^2/4a)

A) y=x+7 where a=1 b=0 and c=7

By replacing we have: V(0;28/4) V(0;7)

B) y=-x where a=-1 b and c=0 so V(0,0)

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3 years ago

What is the value of the expression below? (27^2/3)^1/2A. 9 B. 81 C. 27 D. 3​

What is the value of the expression below? (27^2/3)^1/2A. 9 B. 81 C. 27 D. 3