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3 years ago

Write a division sentence; (fraction divide by a fraction) and the quotient is 3/8. *

Mathematics

2 answers:

madam [21]3 years ago

8 0

Answer:

3/1 ÷ 8/1 = 3/8

Step2247 [10]3 years ago

6 0

9514 1404 393

Answer:

(1/4)/(2/3) = 3/8

Step-by-step explanation:

(1/4)/(2/3) = 3/8

This can be confirmed by a couple of different methods of dividing fractions.

1) express using a common denominator and take the ratio of numerators.

(1/4)/(2/3) = (3/12)/(8/12) = 3/8

2) invert the denominator and multiply

(1/4)/(2/3) = (1/4)(3/2) = (1·3)/(4·2) = 3/8

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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.

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