Ask question

Ask question

All categories

3 years ago

10

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $420 to drive 500 mi

and in June it cost her $444 to drive 620 mi. (a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. C(d)

1 answer:

djyliett [7]3 years ago

6 0

Answer:

$C(d) = \frac{1}{5}d + 320$

Step-by-step explanation:

Given

$d \to miles$

$C \to cost$

So:

$(d_1,C_1) = (500,420)$ --- May

$(d_2,C_2) = (620,444)$ --- June

Required

Express as a function

Start by calculating the slope (m)

$m = \frac{\triangle C}{\triangle d}$

$m = \frac{444-420}{620-500}$

$m = \frac{24}{120}$

Simplify

$m = \frac{1}{5}$

The equation is:

$C(d) = m(d - d_1) +C_1$

$C(d) = \frac{1}{5}(d - 500) +420$

$C(d) = \frac{1}{5}d - 100 +420$

Take LCM

$C(d) = \frac{1}{5}d + 320$

You might be interested in

What is the partial derivative of a given function

Marizza181 [45]

Partial differentiation of a function with more than one variables refers to its derivative being taken with respect to one of those variables, while the rest being held as a constant.

An example is the volume of a cylinder given by:
$V(h, r) = \pi r^{2}h$

The volume requires two variables in order to work out the volume, namely the radius and the height.

Using partial differentiation, its partial derivative can become:
$\frac{\partial V}{\partial r} = 2\pi rh$

This symbol is used in place of the derivative symbol, in order to distinguish total derivatives and partial derivatives.

7 0

3 years ago

If c varies directly as the square root of d, and c=14, when d = 64, find c when d= 324

zubka84 [21]

Answer:

c = 31.5

Step-by-step explanation:

Given c varies directly as $\sqrt{d}$ then the equation relating them is

c = k $\sqrt{d}$ ← k is the constant of variation

To find k use the condition c = 14 when d = 64, then

14 = k × $\sqrt{64}$ = 8k ( divide both sides by 8 )

1.75 = k

c = 1.75 $\sqrt{d}$ ← equation of variation

When d = 324 , then

c = 1.75 × $\sqrt{324}$ = 1.75 × 18 = 31.5

5 0

3 years ago

Question 5: prove that it’s =0

mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that $\cos(\frac{2}{x})$ is a variable number between -1 and 1 (inclusive).

This means that $-1 \le \cos(\frac{2}{x}) \le 1$ .

$x^4 \ge 0$ for all value $x$ . So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

$-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

By squeeze theorem, if $-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

and $\lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L$ , then we can also conclude that $\im_{x \rightarrow} x^4\cos(\frac{2}{x})=L$ .

So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at $x=0$ .

$\lim_{x \rightarrow 0}x^4=0^4=0$

$\lim_{x \rightarrow 0}-x^4=-0^4=-0=0$ .

We can finally conclude that $\lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0$ by squeeze theorem.

Some people call this sandwich theorem.

6 0

3 years ago

Mei tapes two pieces of paper together that each measure 30.45

ikadub [295]

Answer: 50.48

Step-by-step explanation: 30.45 x 2 (cuz theres 2 pieces of paper) = 60.9

60.9 - 10.42 = 50.48

6 0

3 years ago

Question 10 of 24

skad [1K]

The answer would be: B

4 0

3 years ago