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3 years ago

What is the simplified base of the function f(x) = One-fourth (Root Index 3 StartRoot 108 EndRoot) Superscript x?

Mathematics

1 answer:

Rainbow [258]3 years ago

4 0

Answer:

The base is: $3 \sqrt[3]{4}$

Step-by-step explanation:

Given

$f(x) = \frac{1}{4}(\sqrt[3]{108})^x$

Required

The base

Expand 108

$f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x$

Rewrite the exponent as:

$f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x$

Expand

$f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x$

$f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x$

Rewrite as:

$f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x$

An exponential function has the following form:

$f(x)=ab^x$

Where

$b \to base$

By comparison:

$b =3 \sqrt[3]{4}$

So, the base is: $3 \sqrt[3]{4}$

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Sergeeva-Olga [200]

Answer:

I think the answer is 92%.

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3 years ago

Please help me now plz I will mark you brainliest

PIT_PIT [208]

Answer:

On the circle

Step-by-step explanation:

Because all of the points on a circle are equidistant from the center, if a circle has a radius of 10 then all of the points are 10 units from the center. Using the Pythagorean Theorem, you know that the distance from (4,0) to (-2,8) is:

$\sqrt{(4-(-2))^2+(8-0)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10$ , meaning that it is on the circle. Hope this helps!

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3 years ago

Identify the expression with nonnegative limit values. More info on the pic. PLEASE HELP.

marshall27 [118]

Answer:

$\lim _{x\to 2}\:\frac{x-2}{x^2-2}\\\\ \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}\\\\ \lim _{x\to \frac{5}{2}}\left\frac{2x^2+x-15}{2x-5}\right$

Step-by-step explanation:

a) $\lim _{x\to 3}\:\frac{x^2-10x+21}{x^2+4x-21}=\lim \:_{x\to \:3}\:\frac{\left(x-7\right)\left(x-3\right)}{\left(x+7\right)\left(x-3\right)}=\lim \:_{x\to \:3}\:\frac{x-7}{x+7}=\frac{3-7}{3+7}=-\frac{4}{10}=-\frac{2}{5}$

b) $\lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=\lim \:_{x\to -\frac{3}{2}}\:\frac{\left(2x+3\right)\left(x-4\right)}{\left(2x+3\right)}=\lim \:\:_{x\to \:-\frac{3}{2}}\:\left(x-4\right)=-\frac{3}{2}-4\\ \\ \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=-\frac{11}{2}$

c) $\lim _{x\to 2}\:\frac{x-2}{x^2-2}=\frac{2-2}{\left(2\right)^2-2}=\frac{0}{4-2}=0$

d) $\lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}=\lim _{x\to 11}\:\frac{\left(x-11\right)\left(x+17\right)}{\left(x-11\right)\left(x+14\right)}=\lim _{x\to 11}\:\frac{\left(x+17\right)}{\left(x+14\right)}=\frac{11+17}{11+14}=\frac{28}{25}$

e) $\lim _{x\to 3}\:\frac{x^2-8x+15}{x-3}=\lim \:_{x\to \:3}\:\frac{\left(x-3\right)\left(x-5\right)}{x-3}=\lim _{x\to 3}\left(x-5\right)=3-5=-2$

f) $\lim _{x\to \frac{5}{2}}\left(\frac{2x^2+x-15}{2x-5}\right)=\lim \:_{x\to \:\frac{5}{2}}\frac{\left(2x-5\right)\left(x+3\right)}{2x-5}=\lim \:\:_{x\to \:\:\frac{5}{2}}\left(x+3\right)=\frac{5}{2}+3=\frac{11}{2}$

4 0

3 years ago

$27 for four large pizzas or $32 for five large pizzas

frez [133]

Answer: $27 for four large pizzas is cheaper than 32$ for five large pizzas

Step-by-step explanation:

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2 years ago

Read 2 more answers

Han has 10 cubes, each 5 inches on a side. A) Find the total volume of Han’s cubes. Express your answer as an expression using a

g100num [7]

Answer:

A) Vol_10_cubes = 2*(5^4) inch^3

B) Area_10_cubes = (2^2)*3*(5^3) inch^2

Step-by-step explanation:

A)The volume of a cube, as all sides are equal:

Vol_cube = (side)^3

side = 5 inches

Vol_cube = 5^3 inch^3

Since we have 10 cubes

10 = 2*5

Vol_10_cubes = 2*(5^4) inch^3

B) A cube has six faces, each with area equal to its squared side

Area_cube = 6*(side)^2

Area_cube = 6*(5)^2 inch^2

Area_10_cubes = 2*5*6*(5)^2 inch^2

Area_10_cubes = (2^2)*3*(5)^3 inch^2

8 0

3 years ago