Find the linear approximation of the function g(x = 3 1 x at a = 0.

What are the surface area and volume of a spherical barrel cactus with a radius of 5 inches?

tino4ka555 [31]

$\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r = 5 \end{cases}\implies SA=4\pi (5)^2 \\\\\\ SA=100\pi\implies SA\approx 314.16 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad V=\cfrac{4\pi (5)^3}{3}\implies V=\cfrac{500\pi }{3}\implies V\approx 523.60$

7 0

3 years ago

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

wolverine [178]

Answer:

x^4 - 14x^2 - 40x - 75.

Step-by-step explanation:

As complex roots exist in conjugate pairs the other zero is -1 - 2i.

So in factor form we have the polynomial function:

(x - 5)(x + 3)(x - (-1 + 2i))(x - (-1 - 2i)

= (x - 5)(x + 3)( x + 1 - 2i)(x +1 + 2i)

The first 2 factors = x^2 - 2x - 15 and

( x + 1 - 2i)(x +1 + 2i) = x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i - 4 i^2

= x^2 + 2x + 1 + 4

= x^2 + 2x + 5.

So in standard form we have:

(x^2 - 2x - 15 )(x^2 + 2x + 5)

= x^4 + 2x^3 + 5x^2 - 2x^3 - 4x^2 - 10x - 15x^2 - 30x - 75

= x^4 - 14x^2 - 40x - 75.

7 0

3 years ago

The radius of a circle with area A can be approximated using the formula r = the square root of A/3 . Estimate the radius of a w

Arturiano [62]

Answer: 12

Step-by-step explanation:

Given:

A = 452

r = √A/3

Step 1: Substitute 452sqf for A

r = √452/3

Step 2: Solve

452 ÷ 3 = 150.66∞

√150.66∞ = 12.27∞

12.27∞ rounded to the nearest integer equal 12

3 0

2 years ago

Can someone help please

myrzilka [38]

<h3>Answer: 15x^(7/3) - 8x^(7/4) + x + 9000</h3>

=========================================================

Explanation:

If you know the cost function C(x), to find the marginal cost, we apply the derivative.

Marginal cost = derivative of cost function

Marginal cost = C ' (x)

Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.

$\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\$

$C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\$

D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).

To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.

Therefore, we go from this

$C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\$