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3 years ago

What is the average rate of change of the function f(x)=2x+4 over the interval -4 ≤ x ≤ 1? Table

Mathematics

1 answer:

Tom [10]3 years ago

7 0

Answer:

Step-by-step explanation:

the rate of change is measured as

$\frac{f(b) - f(a)}{b-a}$ in the closed interval [ a, b ]

here [a, b ] = [- 4, 1 ]

f(b) = f(1) = 2 + 4 = 6

f(a) = f(- 4) = - 8 + 4 = - 4

average rate of change = $\frac{6-(-4)}{1-(-4)}$ = $\frac{10}{5}$ = 2

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3 years ago

Solving Rational Inequalities and use sign diagram to sketch the graph. Image attached for better understanding.

Digiron [165]

Answer:

x ∈ (-∞, -1) ∪ (1, ∞)

Step-by-step explanation:

To solve this problem we must factor the expression that is shown in the denominator of the inequality.

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So the roots are:

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Therefore we can write the expression in the following way:

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Now the expression is as follows:

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Now we use the study of signs to solve this inequality.

We have 3 roots for the polynomials that make up the expression:

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We know that the first two are not allowed because they make the denominator zero.

Observe the attached image.

Note that:

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3 years ago

A pile of coal is stored in a barrel-shaped bin whose base has a radius of 3 meters. the height of the pile measures 1.5 meters.

Aleksandr-060686 [28]

42.41 cubic meters
The volume of a cylinder is bh where b is the area of the base and h is the height of the cylinder. And since the area of a circle is pi r^2, we have this equation for the volume of a cylinder
V = pi*r^2*h
Now substitute, the known values for r and h, then calculate the result:
V = pi*r^2*h
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V = 3.14159*9*1.5
V = 42.411465
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So the volume of the coal pile is 42.41 cubic meters.

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