Let Upper C left-parenthesis q right-parenthesis represent the cost, Upper R left-parenthesis q right-parenthesis the revenue, and pi left-parenthesis q right-parenthesis the total profit, in dollars, of producing q items.(a) If Upper C prime left-parenthesis 50 right-parenthesis equals 75 and Upper R prime left-parenthesis 50 right-parenthesis equals 88, approximately how much profit is earned by the 51 Superscript st item?The profit earned from the 51 Superscript st item will be approximately_______ dollar-sign.(b) If Upper C prime left-parenthesis 90 right-parenthesis equals 71 and Upper R prime left-parenthesis 90 right-parenthesis equals 67, approximately how much profit is earned by the 91 Superscript st item?The profit earned from the 91 Superscript st item will be approximately______ dollar-sign

Answers

Answer 1
Answer:

Answer:

(a)$13

(b) Loss of $4

Step-by-step explanation:

C(q) represents Cost of producing q units.

R(q) represents Revenue generated from q units.

P(q) represents Total Profit made from producing q units.

Marginal analysis is concerned with estimating the effect on quantities such as cost, revenue, and profit when the level of production is changed by a unit amount. For example, if C(q) is the cost of producing q units of a certain commodity, then the marginal cost, MC(q), is the additional cost of producing one more unit and is given by the difference

MC(q) = C(q + 1) − C(q).

Using the estimation

C'(q)≈[TeX]\frac{C(q+1)-C(q)}{(q+1)-q}[/TeX]=C(q+1)-C(q)

We find out that MC(q)=C'(q)

We can therefore compute the marginal cost by the derivative C'(q).

This also holds for Revenue, R(q) and Profit, P(q).

(a) If C'(50)=75 and R'(50)=88

51st item.

P'(50)=R'(50)-C'(50)

=88-75=$13

The profit earned from the 51st item will be approximately $13.

(b) If C'(90)=71 and R'(90)=67, approximately how much profit is earned by the 91st item.

P'(90)=R'(90)-C'(90)

=67-71= -$4

The profit earned from the 91 st item will be approximately -$4.

There was a loss of $4.


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A kite flier wondered how high her kite was flying. She used a protractor to measure an angle of 33° from level ground to the kite string. If she used a full 90 yard spool of string, how high, in feet, was the kite? Round your answer to 3 decimal places. (Disregard the string sag and the height of the string reel above the ground.)
Use the graphs shown in the figure below. All have the form f(x) = abx Which graph has the smallest value for b? A B C D E F

25% of 56.
We are practicing finding the percent of each number

Answers

25% is 1/4. Do 56 divided by 4, you get 14
You would divide 56 by 4 to get 14. 25% of 56 =14.

The constant in the expression 8x 3 + 4x 2 – 9 is

Answers

Answer : 9

Step-by-step explanation:

The answer is 9 because a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

This Venn diagram represents the science subjects studied by students what is the probability chosen at random that that child does not study chemistry

Answers

Answer:

Step-by-step explanation:

Looking at the Venn diagram,

The total number of students surveyed is 7 + 5 + 8 + 6 + 2 + 4 + 3 + 6 = 41

The number of children that studies none of the subjects is 6

The number of children that study only biology is 7

The number of children that study only physics is 5

The number of children that study only physics and biology is 2

Therefore, the number of students that do not study chemistry is 6 + 7 + 2 + 5 = 20

Probability = number of favorable outcomes/total number of outcomes

Therefore, the probability that a child chosen at random does not study chemistry is 20/41 = 0.49

The temperature, H, in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation. H = 70 + 120(1/4)t (a) What is the coffee's temperature initially (that is, at time t = 0)? 190 °F What is the coffee's temperature after 1 hour? 100 °F What is the coffee's temperature after 2 hours? (Round your answer to one decimal place.) 2 °F (b) How long does it take the coffee to cool down to 85°F? (Round your answer to three decimal places.) 5 hr How long does it take the coffee to cool down to 75°F? (Round your answer to three decimal places.) 5 hr

Answers

Answer:

The temperature a t = 0 is 190 °F

The temperature a t = 1 is 100 °F

The temperature a t = 2 is 77.5 °F

It takes 1.5 hours to take the coffee to cool down to 85°F

It takes 2.293 hours to take the coffee to cool down to 75°F

Step-by-step explanation:

We know that the temperature in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation:

H(t)=70+120((1)/(4))^t

a) To find the temperature a t = 0 you need to replace the time in the equation:

H(0)=70+120((1)/(4))^0\nH(0)=70+120\cdot 1\nH(0) = 70+120\nH(0)=190 \:\°F

b) To find the temperature after 1 hour you need to:

H(1)=70+120((1)/(4))^1\nH(1)=70+120((1)/(4))\nH(1) = 70+30\nH(1)=100 \:\°F

c) To find the temperature after 2 hours you need to:

H(2)=70+120((1)/(4))^2\nH(2)=70+120((1)/(16))\nH(2) = 70+(15)/(2) \nH(2)=77.5 \:\°F

d) To find the time to take the coffee to cool down 85 \:\°F, you need to:

85 = 70+120((1)/(4))^t\n70+120\left((1)/(4)\right)^t=85\n70+120\left((1)/(4)\right)^t-70=85-70\n120\left((1)/(4)\right)^t=15\n(120\left((1)/(4)\right)^t)/(120)=(15)/(120)\n\left((1)/(4)\right)^t=(1)/(8)

\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)

\ln \left(\left((1)/(4)\right)^t\right)=\ln \left((1)/(8)\right)

\mathrm{Apply\:log\:rule}=\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)

t\ln \left((1)/(4)\right)=\ln \left((1)/(8)\right)

t=(\ln \left((1)/(8)\right))/(\ln \left((1)/(4)\right))\nt=(3)/(2) = 1.5 \:hours

e) To find the time to take the coffee to cool down 75 \:\°F, you need to:

75=70+120\left((1)/(4)\right)^t\n70+120\left((1)/(4)\right)^t=75\n70+120\left((1)/(4)\right)^t-70=75-70\n120\left((1)/(4)\right)^t=5\n\left((1)/(4)\right)^t=(1)/(24)

\ln \left(\left((1)/(4)\right)^t\right)=\ln \left((1)/(24)\right)\nt\ln \left((1)/(4)\right)=\ln \left((1)/(24)\right)\nt=(\ln \left(24\right))/(2\ln \left(2\right)) \approx = 2.293 \:hours

A quadrilateral has angles that measure 60°, 95°, and 150°. What is the measure of the fourth angle?

A.
25°

B.
55°

C.
85°

D.
125°

Answers

The sum of angles in a quadrilateral = 360 degrees.

Let the fourth angle be x:

Therefore:  60 + 95 + 150 + x = 360

305 + x = 360

x = 360 - 305

x = 55

Option B. I hope this helps.

If x2 = 40, what is the value of x?

Answers

if you mean 2x=40 x=20 
but if you mean x^2=40 i think its x=80

You have to divided by 2 on both sides and you get x=20. Checking your answer you multiply 20 by 2 which is 40.