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aniked [119]
2 years ago
11

Given the function, f(x) = x2 - 3, calculate the average rate of change of the function from x = 1 to x = 3.

Mathematics
2 answers:
Crank2 years ago
7 0

\bf slope = m = \cfrac{rise}{run} \implies  \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby  \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= x^2-3  \qquad  \begin{cases} x_1=1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(1)}{3-1} \\\\\\ \cfrac{[3^2-3]-[1^2-3]}{2}\implies \cfrac{6 - (-2)}{2}\implies \cfrac{6+2}{2}\implies \cfrac{8}{2}\implies 4

Valentin [98]2 years ago
3 0

Answer: 4

Step-by-step explanation:

The given function : f(x) = x^2 - 3

The average rate of change in a function g(x) from x=a to x=b is given by :-

k=\dfrac{g(b)-g(a)}{b-a}

Then, the average rate of change of the given function from x = 1 to x = 3 will be :-

k=\dfrac{f(3)-f(1)}{3-1}\\\\=\dfrac{(3)^2-3-(1^2-3)}{2}=\dfrac{9-3-1+3}{2}\\\\=\dfrac{8}{2}=4

Hence, the average rate of change of the function from x = 1 to x = 3 is 4.

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Write a function describing the relationship of the given variables.
Oliga [24]

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

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  variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

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* Now lets solve the problem

# V is varies directly with the square  of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

 by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

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3 years ago
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Answer: Oliver is correct

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6 0
3 years ago
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Aneli [31]

Answer:

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The differences are

1) The difference between E and F is that the parallel lines used for the construction of E are all one block higher than that of F

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Step-by-step explanation:

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Answer:

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