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3 years ago

What is the true solution to 2 In e in5x = 2 In 15?

Mathematics

2 answers:

just olya [345]3 years ago

5 0

Answer:

x = 3

Step-by-step explanation:

Using the rules of logarithms

ln x = ln y ⇒ x = y

ln e = 1

Given

2 ln e ln 5x = 2 ln 15 ( divide both sides by 2 )

ln e ln 5x = ln 15

ln 5x = ln 15, hence

5x = 15 ( divide both sides by 5 )

x = 3

Oduvanchick [21]3 years ago

5 0

Answer:

B. x=3

Step-by-step explanation:

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The number of pens sold at the school bookstore on Monday, p, increased 45% on Tuesday. The expression p+0.45p represents the nu

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Answer:

p + (45/100) p or 1.45 p

Step-by-step explanation:

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2 years ago

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.

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2 years ago

13 - 4x = 1 - x<br><br>Step by step please

Virty [35]

Answer:

13 - 4x = 1 - x

Subtract 13 from both sides.

-4x = -12 - x

Add x to both sides.

-3x = -12

Divide both sides by -3.

x=4

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2 years ago

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satela [25.4K]

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3 years ago

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Calculate the mean and variance of the sample data set provided below. show and explain your steps. round to the nearest tenth.

eimsori [14]

Mean = (14 + 16 + 7 + 9 + 11 + 13 + 8 + 10) ÷ 8 = 11

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3 years ago