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3 years ago

Rewrite the expression using rational exponents.

Mathematics

2 answers:

Vedmedyk [2.9K]3 years ago

4 0

Answer:

$x^{8/3}$

Step-by-step explanation:

when taking the radical of a number its really just a fractioned exponent for example $\sqrt{x}$ = $x^{1/2}$

This is because in the radical the x has an exponent of 1 and since its the square root the radical is to the 2nd so you take the exponent of the X and put that of the what ever kind of radial you have such as a square root third root fourth root and so on...

in your case you would take X's exponent of 8 and since your taking the cube root would put the 8 over the 3.

hope that helped

vichka [17]3 years ago

3 0

X/8 3 that’s the answer

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Answer:

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3 years ago

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3 years ago

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Satellite dishes are shaped like parabolas to optimally revive signals. The cross section of a satellite dish can be modeled by

Anna11 [10]

The cross section of the satellite dish is an illustration of a quadratic function

The quadratic function that models the cross-section is y = 1/6(x^2 - 9)

<h3>How to determie the equation of the cross-section?</h3>

The given parameters are:

Width = 6 feet

Depth = 1.5 feet

Express the width the sum of two equal numbers

Width = 3 + 3

The above means that, the equation of the cross section passes through the x-axis at:

x = -3 and 3

So, we have:

y = a(x - 3) * (x + 3)

Express as the difference of two squares

y = a(x^2 - 9)

The depth is 1.5.

This is represented as: (x,y) =(0,-1.5)

So, we have:

-1.5 = a(0^2 - 9)

Evaluate the exponent

-1.5 = -9a

Divide both sides by -9

a = 1/6

Substitute 1/6 for a in y = a(x^2 - 9)

y = 1/6(x^2 - 9)

Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)

Read more about quadratic functions at:

brainly.com/question/1497716

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2 years ago

Alice's grandmothers age is a composite number between 70 and 80 and has a factor of 11 what is it

pshichka [43]

The factor of 11 is going to be 77 because you have to stay in between 70 to 80

and 7 times 11 is 77. It also has to be a number in the 11 timetables. It can't be 88 because we can't cross 80 so the factor is going to be 77.

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3 years ago

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Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is