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3 years ago

Find the average rate of change over the given interval: f(x) = 3^x, [1, 4]

Mathematics

1 answer:

GREYUIT [131]3 years ago

3 0

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= 3^x \qquad 
\stackrel{[1,4]}{\begin{cases}
x_1=1\\
x_2=4
\end{cases}}\implies \cfrac{f(4)-f(1)}{4-1}\implies \cfrac{3^4~-~3^1}{3}
\\\\\\
\cfrac{81-3}{3}\implies \cfrac{78}{3}\implies 26$

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2 years ago

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2 years ago

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3 years ago

2x = 4y + 8, x - 2y = 4

Evgen [1.6K]

Answer: x = 8, y = 2, coordinates (8,2)

Step-by-step explanation:

2x = 4y + 8 (divide by 2 to get value of x)

x = 2y + 4

(now substitute x into the second equation to find value of y)

2y + 4 - 2y = 4

2y - 2y = 4 - 4 (divide by 2 to get value of y)

y - y = 2 - 2

y = 2

Now plug in value of "y" to get value of "x".

x - 2(2) = 4

x - 4 = 4

x = 8

Coordinates (8,2)

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3 years ago

Michael gets test grades of 73, 77, 82, and 86. He gets a 93 on his final exam. Find the weighted mean if the tests each count f

leonid [27]

Answer:

84.9

Step-by-step explanation:

The weighted mean is given by the sum of the products of each grade by its respective weight. If the first four grades correspond to 15% of the final grade each, and the final exam is equivalent to 40% of the final grade, Michael's final grade is:

$G= (73+77+82+86)*0.15+(93*0.4)\\G= 84.9$

Michael's final weighted mean is 84.9.

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3 years ago