Someone please help me I’ll give out brainliest please dont answer if you don’t know

Question

Kay [80]

Answer:

$f(x)=2(x-2)(x^2+64)$

Step-by-step explanation:

A standard polynomial in factored form is given by:

$f(x)=a(x-p)(x-q)...$

Where p and q are the zeros.

We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.

First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.

Therefore, we acquire:

$f(x)=a(x-(2))(x-(-8i))(x-(8i))$

Simplify:

$f(x)=a(x-2)(x+8i)(x-8i)$

Expand the second and third factors:

$=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64$

Hence, our function is now:

$f(x)=a(x-2)(x^2+64)$

It equals 320 when x = 4. Therefore:

$320=a(4-2)(4^2+64)$

Solve for a. Evaluate:

$320=(2)(80)a$

So:

$320=160a\Rightarrow a=2$

Our third-degree polynomial equation is:

$f(x)=2(x-2)(x^2+64)$

7 0

3 years ago

Find the indicated value f(x) - {3(x+1)+1.851 find f(0) >

Tpy6a [65]

Answer:

70

Step-by-step explanation:

6 0

3 years ago

A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, h

vova2212 [387]

Answer:

A sample size of 3 is required.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.96}{2} = 0.02$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.02 = 0.98$ , so Z = 2.054.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.

This means that $\sigma = 3.6$

He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.

The sample size needed is of n, and n is found when M = 5. So

$M = z\frac{\sigma}{\sqrt{n}}$

$5 = 2.054\frac{3.6}{\sqrt{n}}$

$5\sqrt{n} = 2.054*3.6$

$\sqrt{n} = \frac{2.054*3.6}{5}$

$(\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2$

$n = 2.19$

Rounding up:

A sample size of 3 is required.

4 0

3 years ago

The Whisky Rebellion:

Annette [7]

Answer:

Whiskey Rebellion, (1794), in American history, uprising that afforded the new U.S. government its first opportunity to establish federal authority by military means within state boundaries, as officials moved into western Pennsylvania to quell an uprising of settlers rebelling against the liquor tax.

The Whiskey Rebellion was a 1794 uprising of farmers and distillers in western Pennsylvania in protest of a whiskey tax enacted by the federal government. ... Opposition to the whiskey tax and the rebellion itself built support for the Republicans, which overtook Washington's Federalist Party for power in 1802.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Solid figure with a pentagon for a base and triangular faces

mafiozo [28]

It's a pentagonal pyramid.

6 0

4 years ago

Read 2 more answers