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Nataly [62]
3 years ago
12

Mr. Hardy built a fenced-in area for his children in the shape of a square with each side 75 feet in length. Find the distance o

f the diagonal path from one corner to the opposite corner.
Mathematics
1 answer:
8090 [49]3 years ago
3 0

Answer:

75 square root of 2

Step-by-step explanation:

if its a square using 45 45 90 triangle formula it'll be 75 to the the square root of 2

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If Jorge walks 1 mile in 1 hour. In 2 hours at the same place, How many yards can Jorge walk now
julsineya [31]

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3520 yards

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1 mile in 1 hour.

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For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th
alexira [117]

Answer:

The inner function is h(x)=4x^2 + 8 and the outer function is g(x)=3x^5.

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have 4x^2+8 inside parentheses. So h(x)=4x^2 + 8 is the inner function and the outer function is g(x)=3x^5.

The chain rule says:

\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)

It tells us how to differentiate composite functions.

The function f(x)=3(4x^2+8)^5 is the composition, g(h(x)), of

     outside function: g(x)=3x^5

     inside function: h(x)=4x^2 + 8

The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

3 0
3 years ago
Jaun's age, x, is 4 times his age 15 years ago
KIM [24]

The expression of the mathematical statement given as "Jaun's age, x, is 4 times his age 15 years ago" is x = 4 * (x - 15)

<h3>How to rewrite the statement as an expression?</h3>

The mathematical statement is given as

Jaun's age, x, is 4 times his age 15 years ago

From the statement, we have:

x represent Juan's current age

This means that his age 15 years ago is

15 years ago = x - 15

4 times his age 15 years ago is

4 * 15 years ago = 4 * (x - 15)

The above equation is equivalent to his current age

So, we have

x = 4 * (x - 15)

Hence, the expression of the mathematical statement given as "Jaun's age, x, is 4 times his age 15 years ago" is x = 4 * (x - 15)

Read more about expressions at

brainly.com/question/2972832

#SPJ1

7 0
1 year ago
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