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3 years ago

HELP WILL GIVE 15 POINTS what is the range of this function and pls explain

Mathematics

1 answer:

Nataly [62]3 years ago

4 0

Answer:

$f(x)\geq -2$

Step-by-step explanation:

Range corresponds to the values of y on the y-axis. If we see the graph the minimum value of the y-coordinate is -2 and then it tends to increase from it. We do not know till where the y values will increase in the figure it shows 6 but it's still actually increasing we keep on tracing the graph but the minimum value will always remain the same which is -2 . So we can say that the range of the function is

$f(x)\geq -2\\$

Where f(x) is the function and since the values of y on the y-axis increase from -2 we can say that the function has the range of values greater than or equal to -2

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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

Help!!!!!! <br><br>complete the problem involving the linear equation.

Arisa [49]

Answer:

<h2>8. slope = 2</h2><h2>9. y-intercept = -3</h2><h2>10. in the attachment</h2>

Step-by-step explanation:

The slope-intercept form y = mx + b

m - slope

b - y-intercept → (0, b)

We have the equation

y - 2x = -3 <em>add 2x to both sides</em>

y = 2x - 3

slope m = 2

y-intercept b = -3

We need two points to draw a graph of this linear function.

One is y-intercept (0, -3). The second one is calculated by choosing any value of x and put it to the equation:

for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1).

8 0

3 years ago

When x = 2, what is the value of the expression 5x^2 - 4?

Ivenika [448]

The value of the expression, 5x^2 - 4, when x = 2 is: 16.

<h3>What is the the Value of an Expression?</h3>

To find the value of an expression, plug in the given value of the variable and solve by simplifying.

Given the expression, 5x^2 - 4, when x = 2, we would have:

5(2)^2 - 4

5(4) - 4

20 - 4

= 16

Therefore, the value of the expression, 5x^2 - 4, when x = 2 is: 16.

Learn more about value of expression on:

brainly.com/question/625174

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3 years ago

Read 2 more answers

Raúl is mixing a cleaning spray. The instructions say to combine 2 cups vinegar with 1 cup water. Raúl wants to make 15 cups of

-BARSIC- [3]

So 15/3 = 5 then
vinegar = 5x2 = 10 cups
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3 0

3 years ago

Colton wrote a ratio comparing the number of sports video games that he owns to the number of driving video games that he owns a

AveGali [126]

Answer:

4 to 3

Step-by-step explanation:

Since in the question it is mentioned that the ratio is written by comparing the number of video games with respect to sports to the number of video games with respect to the driving is 4: 3

Also the ratio defines a relationship between the two variables

So, the ratio that is equal to cotton ratio is 4 to 3 and the same is to be considered

7 0

3 years ago

HELP WILL GIVE 15 POINTS what is the range of this function and pls explain​

HELP WILL GIVE 15 POINTS what is the range of this function and pls explain