Let f (x) = 10/x-4

Mathematics

1 answer:

SashulF [63]3 years ago

5 0

Answer:

1.875

Step-by-step explanation:

The rate of change is the derivative of the function.

$f(x) = \frac{10}{x-4}\\\\f'(x)=10\times \frac {d}{dx}\frac{1}{x-4}\\\\f'(x)=\frac{-10}{(x-4)^{2}}\\\\f'(2) = \frac{-10}{(2-4)^{2}} =-2.5\\\\f'(8)= \frac{-10}{(8-4)^{2}} =-0.625\\$

So, the rate of change is

f'(8) - f'(2) = - 0.625 + 2.5 = 1.875

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Write the standard form of the equation of each line given the slope and y-intereept.

Elena-2011 [213]

Answer:

5y + 15x = 25, 9x - y = -4

Step-by-step explanation:

The standard form is Ax + By = C. We can make this simple by first creating the slope intercept equations of both questions:

1. y = (-3/5)x + 5

2. y = 9x + 4

For the first one, we must first get rid of the denominator by multiplying everything by 5, so we get 5y = -15x + 25, and then you can add 3x to both sides to arrive at your first standard eqn, 5y + 15x = 25.

For the second, all you need to do is swap the y and the 4, subtracting both y and 4 from each side, arriving at 9x - y = -4

6 0

3 years ago

A pole that is 3.5m tall casts a shadow that is 1.47m long. At the same time, a nearby tower casts a shadow that is 42.75m long.

Stells [14]

<u>Answer:</u>

The height of the tower nearby the pole is 102 m.

<u>Solution:</u>

Given,

Height of the pole = 3.5 m

Length of the shadow of the pole = 1.47 m

Length of the shadow of the tower nearby = 42.75 m