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3 years ago

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desceibe how to determine the average rate of change between x=4 and x=6 for the function f(x)=2x^3 +4

1 answer:

Ann [662]3 years ago

4 0

$slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= 2x^3+4\qquad \begin{cases} x_1=4\\ x_2=6 \end{cases}\implies \cfrac{f(6)-f(4)}{6-4} \\\\\\ \cfrac{[2(6)^3+4]~~ -~~[2(4)^3+4]}{2}\implies \cfrac{436~~ -~~132}{2}\implies \cfrac{304}{2}\implies 152$

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Step-by-step explanation:

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A rectangle with a perimeter of 19m^2+2m-10 and a width of m^2 write an expression for the lenght

never [62]

Answer: $\frac{17}{2}m^2+m-5$

Step-by-step explanation:

By definition, the perimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

If you solve for "l":

$P-2w=2l\\\\l=\frac{P-2w}{2}$

In this case, you know that the following expression represents the perimeter of the rectangle:

$19m^2+2m-10$

And the width of that rectanle is represented wih this expression:

$m^2$

Therefore, based on the explained above, you can conclude that the lenght of that rectangle is given by:

$\frac{19m^2+2m-10-2(m^2)}{2}$

Finally, simplifying the expression, you get:

$=\frac{17m^2+2m-10}{2}=\frac{17}{2}m^2+m-5$

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