High School

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Given [tex]\( f = c d^3 \)[/tex], [tex]\( f = 450 \)[/tex], and [tex]\( d = 10 \)[/tex], what is [tex]\( c \)[/tex]?

A. 0.45
B. 4.5
C. 15
D. 45
E. 150

Answer :

To find the value of [tex]\(c\)[/tex], we start with the given equation [tex]\(f = c \cdot d^3\)[/tex]. We know from the problem that [tex]\(f = 450\)[/tex] and [tex]\(d = 10\)[/tex]. We need to rearrange the equation to solve for [tex]\(c\)[/tex].

Here’s how we do it step-by-step:

1. Start with the equation:
[tex]\[
f = c \cdot d^3
\][/tex]

2. Substitute the known values:
[tex]\[
450 = c \cdot 10^3
\][/tex]

3. Calculate [tex]\(10^3\)[/tex]:
[tex]\[
10^3 = 10 \times 10 \times 10 = 1000
\][/tex]

4. Substitute [tex]\(10^3 = 1000\)[/tex] back into the equation:
[tex]\[
450 = c \cdot 1000
\][/tex]

5. Solve for [tex]\(c\)[/tex] by dividing both sides by 1000:
[tex]\[
c = \frac{450}{1000}
\][/tex]

6. Calculate the division:
[tex]\[
c = 0.45
\][/tex]

Therefore, the value of [tex]\(c\)[/tex] is [tex]\(0.45\)[/tex].

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