1. For what value of b will 6 * 10 ^ 3 be 20 times larger than b * 10 ^ 2
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To find the value of b, we can set up the equation:
6 * 10^3 = 20 * (b * 10^2)
First, let's simplify the equation:
6 * 10^3 = 20 * b * 10^2
6 * 10^3 = 20 * 10^2 * b
Next, let's cancel out the common factor of 10^2:
6 * 10^3 = 20 * b
To find b, we can solve for it:
b = (6 * 10^3) / 20
b = 6000 / 20
b = 300
To find the value of b, we can set up the following equation:
6 * 10^3 = 20 * (b * 10^2)
Simplifying the equation:
6 * 10^3 = 20 * b * 10^2
Divide both sides of the equation by 20 * 10^2:
6 * 10^3 / (20 * 10^2) = b
Simplify the calculation:
6 * 10^3 / (20 * 10^2) = b
(6 * 10^3) / (20 * 10^2) = b
Multiply and divide:
6 * 10^3 / (20 * 10^2) = b
(6 / 20) * (10^3 / 10^2) = b
0.3 * 10^1 = b
0.3 * 10 = b
b = 3
Therefore, the value of b that makes 6 * 10^3 twenty times larger than b * 10^2 is 3.
To find the value of b, we can set up an equation based on the information given.
We are told that 6 * 10^3 is 20 times larger than b * 10^2.
Mathematically, we can express this as:
6 * 10^3 = 20 * (b * 10^2)
Next, we can simplify the equation by multiplying:
6000 = 20b * 100
To further simplify, we can divide both sides of the equation by 20:
6000 / 20 = 20b * 100 / 20
300 = b * 100
Finally, we can divide both sides by 100 to isolate b:
300 / 100 = b * 100 / 100
3 = b
Therefore, the value of b that makes 6 * 10^3 20 times larger than b * 10^2 is b = 3.