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4 years ago

I really need help!!!!!! 25 points!!

Mathematics

1 answer:

SCORPION-xisa [38]4 years ago

5 0

Answer:

1. 9/25 units^2

2. s = 1/4 unit

3. = 8/27 units^3

4. s = 3/4 unit

Step-by-step explanation:

1. The area of a square is A=s^2

A = (3/5)^2

= (3/5) *(3/5)

= 9/25 units^2

2. The area of a square is A=s^2

1/16 = s^2

Take the square root of each side

sqrt(1/16) = sqrt(s^2)

1/4 = s

s = 1/4 unit

3. The volume of a cube is V = s^3

V = (2/3)^3

= (2/3) (2/3) (2/3)

= 8/27 units^3

4.The volume of a cube is V = s^3

27/64 = s^3

Take the cube root of each side

(27/64)^(1/3) = (s^3)^(1/3)

3/4 = s

s = 3/4 unit

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

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

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The derivative of this is computed as

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

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