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:
[tex]V (box) = l * w * h[/tex]
The volume given is 90, the height 3, and the width is 1 foot less then length:
First solve what you know:
[tex]V(box) = 90\\h = 3\\l = l\\w = l - 1[/tex]
Plug in the corresponding terms with the corresponding variable. Isolate the variable, l. Divide 3 from both sides of the equation:
[tex]90 = 3 * l (l - 1)\\\frac{90}{3} = \frac{3 * l(l -1)}{3}\\30 = l(l - 1)\\[/tex]
Distribute l to both terms in the parenthesis:
[tex]30 = l(l - 1)\\30 = l^2 - l[/tex]
Solve:
[tex]30 = (6)^{2} -6\\30 = 36 - 6\\30 = 30[/tex]
∴ [tex]l = 6[/tex]
Solve for width. Width is 1 less foot then length:
[tex]l - 1 = w\\l = 6\\[/tex]
∴ [tex]6 - 1 = w\\w = 5[/tex]
Equation: [tex]V (box) = l * w * h[/tex]
or
[tex]l = \frac{V(box)}{w * h}[/tex]
[tex]V(box) = 90\\h = 3\\l = 6\\w = 5[/tex]
