High School

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

F. 0.45
G. 4.5
H. 15
J. 45
K. 150

Answer :

Let's solve the question step-by-step:

1. Understand the given formula: We are given the equation [tex]\( f = c \cdot d^3 \)[/tex].

2. Identify known values:
- [tex]\( f = 450 \)[/tex]
- [tex]\( d = 10 \)[/tex]

3. Substitute the known values into the formula:
- Substitute [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex] into the equation [tex]\( f = c \cdot d^3 \)[/tex].

4. Rearrange the formula to find [tex]\( c \)[/tex]:
- The equation becomes [tex]\( 450 = c \cdot 10^3 \)[/tex].

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

6. Solve for [tex]\( c \)[/tex]:
- Now we have the equation [tex]\( 450 = c \cdot 1000 \)[/tex].
- To find [tex]\( c \)[/tex], divide both sides by 1000:
[tex]\[
c = \frac{450}{1000} = 0.45
\][/tex]

7. Identify the correct option:
- The value of [tex]\( c \)[/tex] is 0.45, which corresponds to option F.

Therefore, the correct answer is F. 0.45.