The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit can be approximated with the model P(t) 240t - 40t t2 +20 where P is in thousands of dollars and t is in months from the time of release. a. Derive a model that gives the marginal profit of the book. P'(t) Preview b. Specify the expected marginal profit 5 months after release. Round to 2 decimal places thousands of dollars per month c. Specify the expected marginal profit 11 months after release. Round to 2 decimal places. thousands of dollars per month d. After which month is the monthly profit start to decrease steadily?

(a)

(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:

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

We differentiate

using quotient rule.

Simplifying

We have derived a model for the marginal profit.

(b) After 5 months, at t=5

Marginal Profit=P'(5)

=-($4.54) Thousand of dollars

(c)Marginal Profit 11 Months after book release

=-($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.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .