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3 years ago

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Let f of x equals the integral from x to 1 of the square root of the quantity of 1 plus t squared . use your calculator to find

f'(1)

1 answer:

ollegr [7]3 years ago

8 0

Analytically, it will be

-√(1+1²) = -√2

The calculator shows it to be -1.41421356237

_____

= -√2 to 12 significant digits.

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The initial population of a town is 2600, and it grows with a doubling time of 10 years. Determine how long it will take for the

choli [55]

Answer:

It will take the 20 years for the population to quadruple.

Step-by-step explanation:

Exponential population growth:

An exponential model for population growth has the following model:

$P(t) = P(0)(1+r)^t$

In which P(0) is the initial population and r is the growth rate, as a decimal.

It grows with a doubling time of 10 years.

This means that $P(10) = 2P(0)$ . We use this to find r. So

$P(t) = P(0)(1+r)^t$

$2P(0) = P(0)(1+r)^10$

$(1+r)^10 = 2$

$\sqrt[10]{(1+r)^10} = \sqrt[10]{2}$

$1+r = 2^{\frac{1}{10}}$

$1 + r = 1.0718$

So

$P(t) = P(0)(1+r)^t$

$P(t) = P(0)(1.0718)^t$

Determine how long it will take for the population to quadruple.

This is t for which P(t) = 4P(0). So

$P(t) = P(0)(1.0718)^t$

$4P(0) = P(0)(1.0718)^t$

$(1.0718)^t = 4$

$\log{(1.0718)^t} = \log{4}$

$t\log{1.0718} = \log{4}$

$t = \frac{\log{4}}{\log{1.0718}}$

$t = 20$

It will take the 20 years for the population to quadruple.

5 0

2 years ago

Caroline wants to compare the expressions 15-9 and 9 (-15) to determine which result is greater. How can she do this without fin

Drupady [299]

Answer:

15-9 will be greater

Step-by-step explanation:

Caroline wants to compare the expressions 15-9 and 9 (-15)

For us to know the result that is greater, we will have to check if the first value is less than or greater than the other. For example

If for a-b

a-b is greater if a>b

a-b is lesser if a<b

Given 15 - 9

Since 15 > 9, this means that 15-9 will be greater compare to 9-15

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Murrr4er [49]

The mean would shift to the left because, simply, the average price of the car would go DOWN.

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DC↔ means “ _____ DC”<br><br> A. line DC<br> B. ray DC<br> C. line segment DC<br> D. angle DC

lidiya [134]

Your answer would be line DC or a have a nice day!

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2 years ago

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Michelle needs to rent storage space for some of her belongings. She paid a one-

Lerok [7]

Answer:

c

Step-by-step explanation:

she pays a one-time fee of 50, and 15$ per month

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2 years ago