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3 years ago

Line r is parallel to the graph of 2x – 3y = –18. The y-intercept of line ris

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

4 0

Answer:

3 or (3,0)

Step-by-step explanation:

prisoha [69]3 years ago

4 0

Answer:

(-3,0)

Step-by-step explanation:

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In science class, Sarah calculates the mass of a planet to be 918,000,000,000,000,000,000 kg. What is the mass of the planet in

Alexeev081 [22]

Answer:

Step-by-step explanation:

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7 0

3 years ago

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive

Ivan

Answer:

(a) The average cost function is $\bar{C}(x)=95+\frac{230000}{x}$

(b) The marginal average cost function is $\bar{C}'(x)=-\frac{230000}{x^2}$

(c) The average cost approaches to 95 if the production level is very high.

Step-by-step explanation:

(a) Suppose $C(x)$ is a total cost function. Then the average cost function, denoted by $\bar{C}(x)$ , is

$\frac{C(x)}{x}$

We know that the total cost for making x units of their Senior Executive model is given by the function

$C(x) = 95x + 230000$

The average cost function is

$\bar{C}(x)=\frac{C(x)}{x}=\frac{95x + 230000}{x} \\\bar{C}(x)=95+\frac{230000}{x}$

(b) The derivative $\bar{C}'(x)$ of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.

The marginal average cost function is

$\bar{C}'(x)=\frac{d}{dx}\left(95+\frac{230000}{x}\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g\\\\\frac{d}{dx}\left(95\right)+\frac{d}{dx}\left(\frac{230000}{x}\right)\\\\\bar{C}'(x)=-\frac{230000}{x^2}$

(c) The average cost approaches to 95 if the production level is very high.

$\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})\\\\\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\\\=\lim _{x\to \infty \:}\left(95\right)+\lim _{x\to \infty \:}\left(\frac{230000}{x}\right)\\\\\lim _{x\to a}c=c\\\lim _{x\to \infty \:}\left(95\right)=95\\\\\mathrm{Apply\:Infinity\:Property:}\:\lim _{x\to \infty }\left(\frac{c}{x^a}\right)=0\\\lim_{x \to \infty} (\frac{230000}{x} )=0$

$\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})= 95$

6 0

3 years ago

Question 4 plz show ALL STEPS

scoray [572]

Part (a)

Locate x = -1 on the x axis. Draw a vertical line through this x value until you reach the f(x) curve. Then move horizontally until you reach the y axis. You should arrive at y = 4. Check out the diagram below to see what I mean.

Since f(-1) = 4, this means we can then say

g( f(-1) ) = g( 4 ) = 4

To evaluate g(4), we'll follow the same idea as what we did with f(x). However, we'll start at x = 4 and draw a vertical line until we reach the g(x) curve this time.

<h3>Answer: 4</h3>

==========================================================

Part (b)

We use the same idea as part (a)

f(-2) = 5

g( f(-2) ) = g(5) = 6

<h3>Answer: 6</h3>

==========================================================

Part (c)

Same idea as the last two parts. We start on the inside and work toward the outside. Keep in mind that g(x) is now the inner function for this part and for part (d) as well.

g(1) = -2

f( g(1) ) = f(-2) = 5

<h3>Answer: 5</h3>

==========================================================

Part (d)

Same idea as part (c)

g(2) = 0

f( g(2) ) = f( 0 ) = 3

<h3>Answer: 3</h3>

6 0

3 years ago

Please help thanks❗

Fynjy0 [20]

Answer:

U, V

Step-by-step explanation:

4 0

3 years ago

Need help with math problems

mrs_skeptik [129]

Ok like what kind of math problems

3 0

3 years ago