College

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 need to use the given equation [tex]\( f = c \cdot d^3 \)[/tex]. We're told that [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex].

Let's solve for [tex]\( c \)[/tex] step by step:

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

2. Substitute the given 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. Replace [tex]\( 10^3 \)[/tex] in the equation:
[tex]\[
450 = c \cdot 1000
\][/tex]

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

6. Simplify the fraction:
[tex]\[
c = 0.45
\][/tex]

Therefore, the value of [tex]\( c \)[/tex] is [tex]\( 0.45 \)[/tex]. The correct answer is option A) 0.45.