A given polynomial has a root of $x = 3$ , an zero of $x = - 2$ , and an x-intercept of $x = - 1$ .
The equation of this polynomial in factored form would be $f (x) =$
The equation of this polynomial in standard form would be $f (x) =$

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asked 2022-05-06

x^6-28

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asked 2021-08-21

Use the properties of logarithms to write expression as a sum, difference, or product of simpler logarithms.
$\ln \frac{2 \sqrt{5}}{\sqrt[2]{7}}$

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asked 2021-11-05

\log_{a} (x) = 1.5

and

\log_{a} (y) = 4.7

find the following using the properties of logarithms.

\log_{a} (\frac{x}{y})

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New questions

Characteristic function of logarithm of random variable
If I know the characteristic function

ϕ_{X} (t)

of a random variable

X > 0

, how can I write the characteristic function

ϕ_{Y} (t)

Y = \log (X)

?
I know that

ϕ_{X} (t) = E [e^{i t X}]

and

ϕ_{Y} (t) = E [e^{i t \log (X)}]

. But I can't derive one from the other. Any idea? I would like to use

ϕ_{X} (t)

to calculate the second moments

X

Olympic athletes compete in a 3000 meter event, but not in two miles event. Which race is longer 3000 meters or 2.00 miles? (Given: 1 mi-1.61 km)
1. 3000 meters
2. 2.00 miles

The square root of 49 is how much less than four squared

Use the difference quotient to calculate the average rate of change across the following intervals.
Difference quotient of

d (t) : 3 t^{2} + 5 t h - 2

The interval 2 to 3:
The interval 2 to 2.5:
The interval 2 to 2.1:

Integer solutions to fraction equation
I am having trouble finding all solutions (or at least proving I have all the solutions already).
The equation is

\frac{1}{a} + \frac{1}{b} + \frac{2}{c} = 1

*a,b,c are positive I tried to base it on the solutions of a similar equation with the last term a 1 instead of a 2.

Finding unknown in log equation
I was given a log equation:

D = 10 \log (I / I_{0})

I

is the unknown in this case,

I_{0} = 10^{- 12}

and

D = 89.3

I did the following steps:

\begin{aligned} 89.3 & = 10 \log (\frac{I}{10^{- 12}}) \\ \frac{89.3}{10} & = \log (\frac{I}{10^{- 12}}) \\ 8.93 & = \log (\frac{I}{10^{- 12}}) \end{aligned}

I'm not quite sure how to isolate I after step 3, and I'm also unsure if dividing

89.3 / 10

is correct as well. So how can I find the unknown (

I

Express the given decimal as a percentage and a reduced fraction. 0.75
What is the percentage form of 0.75?

u = ⟨ 2, - 4 ⟩ and v = ⟨ 5, - 3 ⟩

. Find the angle between them to the nearest tenth of a degree

Why does the same inequality give different answers?

(\log_{2} (x) - 2) (\log_{2} (x) + 1) < 0

has a solution

\frac{1}{2} < x < 4

But when we take the second part alone that is

(\log_{2} (x) + 1) < 0

it gives a solution

0 < x < \frac{1}{2}

why is

x > \frac{1}{2}

in the first case but

x < \frac{1}{2}

in the second case?

The limit of a sequence
Given

x_{n} = \frac{1}{n^{2} + 1} + \frac{1}{n^{2} + 2} + \frac{1}{n^{2} + 3} + \dots + \frac{1}{n^{2} + n}

Verify if there is or no a limit. Find it if affirmative.
Let

a_{n} = \frac{n}{n^{2} + 1}

(The biggest portion of the sum

n

times) and

b_{n} = \frac{n}{n^{2} + n}

(the smallest portion of the sum

n

times) then

b_{n} \leq x_{n} \leq a_{n}

b_{n} \leq x_{n} \leq a_{n}

since

lim \frac{n}{n^{2} + 1} = lim \frac{n}{n^{2} + n} = 0,

we have that

lim x_{n} = 0.

Is this wrong? why? If it is, any tips on how to find

lim x_{n}

? Grateful for any help.

Solve 19-?=5.

Want to know more about Polynomial arithmetic?

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