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3 years ago

In a square, x represents the length of its side. Which value of x illustrates that the area and the

Mathematics

1 answer:

weeeeeb [17]3 years ago

4 0

Area of square is given by , $A=x^2$ .

Perimeter of square is , P = 4x .

We need to find value of x when area and perimeter are equal :

So ,

$x^2=4x\\\\x(x-4)=0\\\\x=4$

For x = 4 units area is equal to the perimeter of square.

Hence, this is the required solution.

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A small business owner borrowed $4,200 at an annual simple interest rate of 12%. What is the total amount that must be repaid in

zavuch27 [327]

It’s is a total of 123 borrowed and repaired in a total of 3 months I just took this test sweets

3 0

4 years ago

Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs

JulsSmile [24]

Answer:

1) V = 12 π ㏑ 3

2) $\mathbf{V = \dfrac{328 \pi}{9}}$

Step-by-step explanation:

Given that:

the graphs of the equations about each given line is:

$y = \dfrac{6}{x^2}, y =0 , x=1 , x=3$

Using Shell method to determine the required volume,

where;

shell radius = x; &

height of the shell = $\dfrac{6}{x^2}$

∴

Volume V = $\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx$

$V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx$

$V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx$

$V = 12 \pi ( In \ x ) ^3_{x-1}$

V = 12 π ( ㏑ 3 - ㏑ 1)

V = 12 π ( ㏑ 3 - 0)

V = 12 π ㏑ 3

2) Find the line y=6

Using the disk method here;

where,

Inner radius $r(x) = 6 - \dfrac{6}{x^2}$

outer radius R(x) = 6

Thus, the volume of the solid is as follows:

$V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx$

$V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx$

Recall that:

$\int x^n dx = \dfrac{x^n +1}{n+1}$

Then:

$V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}$

$V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}$

$V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}$

$V = 36 \pi (\dfrac{82}{81})$

$\mathbf{V = \dfrac{328 \pi}{9}}$

The graph of equation for 1 and 2 is also attached in the file below.

5 0

4 years ago

The mean is defined as the

Tema [17]

Is the average<span> of the numbers: a calculated "central" value of a set of numbers. To calculate: Just add up all the numbers, then divide by how many numbers there are.</span>

7 0

3 years ago

15. Jackson builds legos at a rate of 3 projects per hour. Write

deff fn [24]

Answer:

f(x)=3x

Step-by-step explanation:

This is pretty much slope-intercept form (y=mx+b) but b is not present in this situation. 3 projects per hour (3x).

f(x)=3x and its y-intercept will be (0,0).

6 0

4 years ago

In Exercise, use the properties of exponents to simplify the expression.<br> (e1/2)(e4)

iogann1982 [59]

Answer:

$e^{9/2}$

Step-by-step explanation:

Let's consider the following expression.

$(e^{1/2})(e^{4} )$

We will use the Product of Powers Property. This property states that to multiply powers having the same base, we have to add the exponents.

$(e^{1/2})(e^{4} )=e^{1/2+4} =e^{1/2+8/2}=e^{9/2}$

The simplified expression is $e^{9/2}$ .

7 0

3 years ago