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2 years ago

Write In (4/9) in terms of In 2 and In 3.

1 answer:

7 0

Answer

A) 2 ln 2 - 2 ln 3

Explanation

Using the laws of logarithms:

ln (x/y) = ln (x) - ln (y)

ln (4/9) = ln (4) - ln (9)

This can be written as

ln (2^2) - ln (3^2)

Another law is:

ln (n^m) = m ln(n)

So finally:

2ln (2) - 2ln 3

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Water is pumped into a tank at a rate of r (t)=30(1−e− 0.16t) gallons per minute, where t is the number of minutes since the pum

Vlad1618 [11]

Answer:

The total volume of the water in the tank after 20 minutes = 1220 gallons

Step-by-step explanation:

Rate of water pumped into the tank r (t) = 30 (1 - $e^{-0.16 t}$ )

Initial volume of water in the tank = 800 gallons

The water in the tank after 20 minutes = Initial volume of water in the tank + Volume of water being pumped in the tank

$V_{total} = V_{i} + V_{pump}$

$V_{pump}$ = $\int\limits^a_b {r(t)} \, dt$

Where a = 0 , b = 20

Put the value of r (t) in above equation we get

$V_{pump}$ = $\int\limits^a_b {30 (1 - e^{-0.16t} )} \, dt$

$V_{pump}$ = $30 [ t + \frac{e^{-0.16t} }{0.16} ]$

$V_{pump}$ = $30[ (20- 0) + \frac{1}{0.16}(e^{-0.16 (20)}- e^{0} )$

$V_{pump}$ = 420 gallon

Now, total volume in the tank

$V_{total} = V_{i} + V_{pump}$

$V_{total} = 800 + 420$

$V_{total} = 1220 \ gallon$

Therefore the total volume of the water in the tank after 20 minutes = 1220 gallons

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3 years ago

Jeff writes comic strips for a local newspaper. The number of comic strips he creates is represented by the function f(x) = 3x,

Andrei [34K]

If he does three hours, its 9 strips, for four, its 12, six is 18, seven is 21, and nine is 27

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3 years ago

Explain how numbers with a 5 in the ones place are not prime numbers

aleksandrvk [35]

Because they will always be divisible by 5

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3 years ago

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Using Definition of at a point find the derivative of the following function <br>f(x)= 5x +4 ,x=-1

marishachu [46]

Answer:

Step-by-step explanation:

here

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2 years ago

Please help please help

Romashka [77]

Step-by-step explanation:

$\frac{-x^{2}+9}{x+3} \\ \\ \frac{-(x^{2}-9)}{x+3} \\ \\ \frac{-(x-3)(x+3)}{x+3} \\ \\ -x(x-3)$

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2 years ago