What are the coordinates of A,B,C ?

The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit

wolverine [178]

Answer:

(a) $\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

(b)P'(5)=-($4.54) Thousand

(c)P'(11)=-($2.10) Thousand

(d)The fifth Month

Step-by-step explanation:

Given the monthly profit model:

$P(t)=\frac{240t-40t^2}{t^2+20}$

(a)We want to derive a model that gives the Marginal Profit, P' of the book.

We differentiate

$P(t)=\frac{240t-40t^2}{t^2+20}$ using quotient rule.

$\frac{dP}{dt}=\frac{(t^2+20)(240-80t)-(240t-40t^2)(2t)}{(t^2+20)^2}$

Simplifying

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

We have derived a model for the marginal profit.

(b) After 5 months, at t=5

Marginal Profit=P'(5)

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

$P^{'}(5)=\frac{4800-1600(5)-240(5)^2}{(5^2+20)^2}$

=-($4.54) Thousand of dollars

(c)Marginal Profit 11 Months after book release

$P^{'}(11)=\frac{4800-1600(11)-240(11)^2}{(11^2+20)^2}$

=-($2.10) Thousand of dollars

(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.

6 0

2 years ago

Angle of the Sun A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun

scoray [572]

Answer:

The angle of elevation of the sun is 39⁰

Step-by-step explanation:

Given;

height of the tree, h = 96 ft

length of the shadow, L = 120 ft

|

| 96ft

|

θ------------------------------------

120ft

Completing this triangle to cut across the top of the tree gives you a right angled triangle with θ as the angle of elevation of the sun.

Apply trig-ratio to determine the angle of elevation of the sun;

tanθ = opposite side / adjacent side

tanθ = 96 / 120

tanθ = 0.8

θ = tan⁻¹(0.8)

θ = 38.7⁰

θ = 39⁰

Therefore, the angle of elevation of the sun is 39⁰

4 0

2 years ago

3. Complete the sentence by choosing the proper option from the given choices.

DanielleElmas [232]

Answer:

B. is exactly 1 triangle

Step-by-step explanation:

For any given triangle, the sum of the internal angles is $180^{o}$ . Thus from the given question, adding the given angles;

30° + 70° + 80° = $180^{o}$

Therefore, only one triangle can be produced with the given measure of angles. This implies that there is exactly one triangle. So that the correct option is B.

3 0

2 years ago

Train A and train B leave the station at 2 pm. The graph below shows the distance covered by the two trains. Compare the two spe

jarptica [38.1K]

Both trains travel for 7 time units.

Train A travels 385 distance units, so its speed is

$\dfrac{385}{7}=55$

Train B travels 577.5 distance units, so its speed is

$\dfrac{577.5}{7}=82.5$

Note that the units are not specified, but considering that we're talking about trains, the graph is likely to be showing distance in km (or miles) and time in hours.

Also, the distance traveled by train B is not perfectly aligned with the grid, so I assumed that it was the average between the two ticks of 550 and 605.

7 0

2 years ago

James earned $39,600 last year. He paid $11,250 towards rent and $1,422 in car payments. What percent of his earnings did Jon pa

tester [92]

Step 1:
Add rent & car payments

=11,250+1422
=$12,672

Step 2:
to determine %, set up a proportion
12,672 is to his total of 39,600 as x is to 100

12,672/39,600 = x/100
cross multiply
(12,672)(100) = (39,600)(x)
1,267,200= 39,600x
divide both sides by 39,600
32%= x

OR

Alternative Step 2:
12,672 ÷ 39,600= 0.32
Alternative Step 3:
0.32 x 100 = 32%
or move decimal to the right 2 places

His rent and car payments are 32% of his earnings.

Hope this helps! :)

5 0

2 years ago

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