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2 years ago

11

The degree of the polynomial function f(x) is 4.The roots of the equation f(x)=0 are −6, −2, 1, and 3.Which graph could be the g

raph of f(x)?

1 answer:

nalin [4]2 years ago

5 0

It’s a s 7.47 because of the five and six

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Evaluate this power with a base that is a negative fraction. (−1/4 )^2

Tomtit [17]

$\left(-\dfrac 1 4\right)^2 = (-1)^2 \cdot \dfrac{1}{4^2} = \dfrac{1}{16}$

Answer: 1/16

6 0

3 years ago

Read 2 more answers

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

J^2 over 2j times 2j over 3g

Serhud [2]

Answer:

D

Step-by-step explanation:

given $\frac{j^2}{2j}$ × $\frac{2j}{3g}$

the 2j on the denominator of the first fraction cancels with the 2j on the numerator of the second fraction, leaving the expression in simplified form as

= $\frac{j^2}{3g}$ → D

5 0

3 years ago

If AM = 7, MB = 6, and CM = 8, find CD.

geniusboy [140]

What kind of shape is it

3 0

3 years ago

Gregory’s age is 5 years greater than of Amanda’s age. Gregory is 17 years old. If Amanda’s age is denoted by x, which equation

Mariana [72]

Let Amanda's age = x.
Gregory's age = x + 5.

Since Gregory is 17 years old.
17 = x + 5
x = 17 - 5
x = 12

Amanda is 12 years old.

4 0

3 years ago