Question

Can someone please help me with these 3 questions?

Answer 1

25) First, find the amount of minutes in 2 hours. Note that there are 60 minutes in one hour:

2 x 60 = 120 minutes per 2 hours.

Next, the bacteria doubles every 20 minutes. 120/20 = 6, which means that the bacteria will double 6 times:

1 x 2 = 2

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 2 = 32

32 x 2 = 64

64 bacteria will be your answer.

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26) The Area of a circle = πr²

Set the equation:

400π = π(r + 2)²

First, divide common factors from both sides, or π.

(400π)/π = (π(r + 2)²)/π

400 = (r + 2)²

√400 = √(r + 2)²

r + 2 = √400

r + 2 = √(20 x 20)

r + 2 = 20

r + 2 (-2) = 20 (-2)

r = 20 - 2

r = 18

18 is your final answer.

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27)

The volume of a box can be found by multiplying length x width x height:

`V (box) = l * w * h`

The volume given is 90, the height 3, and the width is 1 foot less then length:

First solve what you know:

`V(box) = 90\\h = 3\\l = l\\w = l - 1`

Plug in the corresponding terms with the corresponding variable. Isolate the variable, l. Divide 3 from both sides of the equation:

`90 = 3 * l (l - 1)\\(90)/(3) = (3 * l(l -1))/(3)\\30 = l(l - 1)\\`

Distribute l to both terms in the parenthesis:

`30 = l(l - 1)\\30 = l^2 - l`

Solve:

`30 = (6)^(2) -6\\30 = 36 - 6\\30 = 30`

∴
`l = 6`

Solve for width. Width is 1 less foot then length:

`l - 1 = w\\l = 6\\`

∴
`6 - 1 = w\\w = 5`

Equation:
`V (box) = l * w * h`

or

`l = (V(box))/(w * h)`

`V(box) = 90\\h = 3\\l = 6\\w = 5`