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2 years ago

assuming the growth rate stays constant at 1.2%, how many doublings would take place in a 500- year period?

Mathematics

1 answer:

Juliette [100K]2 years ago

3 0

9514 1404 393

Answer:

8.6

Step-by-step explanation:

The growth factor per year is 1.012, so in 500 years is ...

1.012^500

The number of doublings is the solution to ...

2^n = 1.012^500

Taking logarithms, we have ...

n·log(2) = 500·log(1.012)

n = 500·log(1.012)/log(2) ≈ 8.6046

About 8.6 doublings will take place in 500 years.

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It is given that 2^x = 5^y = 10^z , express z in terms of x and y

weqwewe [10]

9514 1404 393

Answer:

z = (xy)/(x+y)

Step-by-step explanation:

Taking logarithms base 10, we have ...

x·log(2) = y·log(5) = z·log(10)

z = x·log(2) = y·log(5) . . . . . . . . log(10) = 1

Then z/x = log(2), and z/y = log(5), so ...

z/x +z/y = log(2) +log(5) = log(2·5) = 1

z = 1/(1/x +1/y) = 1/((x+y)/(xy))

z = (xy)/(x+y)

4 0

3 years ago

Read 2 more answers

The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number

andreyandreev [35.5K]

Answer:

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed 2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

7 0

3 years ago

What’s the area of a rectangle measuring 13 inches times 12 inches ?

taurus [48]

Answer:

156 square inches

Step-by-step explanation:

We are given the two quantities

Let

length = l = 13 inches

and

Width = w = 12 inches

The formula for the area of rectangle is:

$Area=l*w$

where l is length and w is width

Putting the values of both that are given

$Area = 13*12\\=156$

so the area is 156 square inches ..

6 0

3 years ago

Which classification best represnts a triangle with side lengths 10in 12in and 15in

GarryVolchara [31]

Scalene Triangle - A triangle that has no sides of equal length

7 0

3 years ago

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A giraffe at the zoo is 5 meters tall. Name something else that is about 5 meters tall.

WITCHER [35]

Answer:

telephone pole

Step-by-step explanation:

5 0

3 years ago

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