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3 years ago

Easy question - giving brainly is correct and work is shown!

Mathematics

1 answer:

Ymorist [56]3 years ago

4 0

Answer:

the answer is 102 pls mark brainlest

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Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like.

stepladder [879]

The length of the curve $y = \frac{1}{27}(9x^2 + 6)^\frac 32$ from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

$y = \frac{1}{27}(9x^2 + 6)^\frac 32$ from x = 3 to x = 6

Start by differentiating the curve function

$y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x$

Evaluate

$y' = x(9x^2 + 6)^\frac 12$

The length of the curve is calculated using:

$L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx$

This gives

$L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx$

Expand

$L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx$

This gives

$L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx$

Express as a perfect square

$L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx$

Evaluate the exponent

$L =\int\limits^6_3 {3x^2 + 1} \ dx$

Differentiate

$L = x^3 + x|\limits^6_3$

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units

Read more about curve lengths at:

brainly.com/question/14015568

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7 0

2 years ago

I needddddd helpppp itsss dueeeeeeeeeee TODAY

Nimfa-mama [501]

Answer:

Term and Coefficcent

Step-by-step explanation:

5 0

3 years ago

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Complete the equation of the graphed linear function in point-slope form. y – (–2) = (x – ) The graph of the function goes throu

sammy [17]

Answer:

$y-(-2) = 4(x-1)$

Step-by-step explanation:

Point-slope form of the equation of a straight line is:

$y-y_0 = m(x-x_0)$ (1)

The two points given in the problem are:

$(x_0,y_0)=(1,-2)\\(x_1,y_1)=(2,2)$

So, the slope of the line is given by:

$m=\frac{y_1 -y_0}{x_1 -x_0}=\frac{2-(-2)}{2-1}=\frac{4}{1}=4$

And substituting into eq.(1), we find:

$y-(-2) = 4(x-1)$

4 0

4 years ago

If f(x) = 25 -x^2 and g(x) = x + 5, what is (f/g)(x)? <br>Write your answer in the simplest form.

nikdorinn [45]

Answer:

Step-by-step explanation:

We are asked to divide the first equation f(x) by the second equation g(x) and then multiply the division by x

We will be using the difference of two squares to solve this question somewhere in the process

(f/g) * x

(25-x^2) / (x+5) * x

Check the attachment for detailed solution

4 0

4 years ago

a fruit basket contains 12 red apples 6 green apples pineapple and oranges .in simplest form write the ratio of green apples to

Doss [256]

1:1 bc there is 6 green apple and 6 pineapples

7 0

3 years ago

Read 2 more answers