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3 years ago

What is the average rate of change of the function over the interval x = 0 to x = 8?

Mathematics

1 answer:

serious [3.7K]3 years ago

7 0

Answer:

The average rate of change is:

$\frac{13}{161}$

Step-by-step explanation:

The rational function given to us is;

$f(x)=\frac{3x+4}{2x+7}$

$f(0)=\frac{3(0)+4}{2(0)+7}$

$f(0)=\frac{4}{7}$

$f(8)=\frac{3(8)+4}{2(8)+7}$

$f(0)=\frac{28}{23}=1$

The average rate of change of this function from x=0 to x=8 is the slope of the secant line connecting:

(0,f(0)) and (8,f(8))

Average rate of change = $=\frac{f(8)-f(0)}{8-0}$

$=\frac{\frac{28}{23}-\frac{4}{7} }{8}$

$=\frac{13}{161}$

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Taylor buys nail polish from a shop that cost $3.95 each. She has a maximum of $30 to spend on nail polish purchases. The total

kati45 [8]

Answer:

$C_t=3.95x,\ 0\leq x\leq 7$

Step-by-step explanation:

<u>Modeling With Functions</u>

It's a common practice to try to mathematically represent the relation between two or more variables. It allows us to better understand the behavior of the phenomena being observed and, more importantly, to be able to predict future values.

The specific situation stated in the question relates how Taylor buys nail polish for $3.95 each, with a maximum of $30 to spend. If x is the number of nail polish purchased, then the total cost will be

$C_t=3.95x$

But we know Taylor has a limited budget of $30, so the total cost cannot exceed that amount

$3.95x\leq 30$

Solving the inequality for x

$x\leq 30/3.95$

$x\leq 7.6$

We round down to

$x\leq 7$

Of course, the lower limit of x is 0, because Taylor cannot purchase negative quantities of nail polish

Our model is now complete if the state the limits of x, or its domain

$\boxed{C_t=3.95x,\ 0\leq x\leq 7}$

3 0

3 years ago

Yesterday Mike bought 2 gallons of regular gasoline and 3 gallons of premium gasoline at a gas station for $13.60 today he bough

larisa [96]

Answer:

Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.

Step-by-step explanation:

Let the Cost of Regular gasoline be 'x'.

Let the Cost of Premium gasoline be 'y'.

Given:

Amount of regular gasoline bought yesterday = 2 gallons

Amount of premium gasoline bought yesterday = 3 gallons

Total Cost of yesterday = $13.60

Now we know that Total Cost of yesterday is equal to sum of Amount of regular gasoline bought yesterday multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought yesterday multiplied by Cost of premium gasoline.

Framing in equation form we get;

$2x+3y=13.60 \ \ \ \ equation\ 1$

Also Given:

Amount of regular gasoline bought today = 3 gallons

Amount of premium gasoline bought Today = 4 gallons

Total Cost of Today = $18.95

Now we know that Total Cost of Today is equal to sum of Amount of regular gasoline bought Today multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought Today multiplied by Cost of premium gasoline.

Framing in equation form we get;

$3x+4y=18.95 \ \ \ \ equation\ 2$