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 solve for [tex]\( c \)[/tex], we start with the formula given:

[tex]\[
f = c \cdot d^3
\][/tex]

We know the values:
- [tex]\( f = 450 \)[/tex]
- [tex]\( d = 10 \)[/tex]

We need to find [tex]\( c \)[/tex]. First, calculate [tex]\( d^3 \)[/tex]:

[tex]\[
d^3 = 10^3 = 1000
\][/tex]

Now, substituting the known values into the equation:

[tex]\[
450 = c \cdot 1000
\][/tex]

To isolate [tex]\( c \)[/tex], divide both sides of the equation by 1000:

[tex]\[
c = \frac{450}{1000}
\][/tex]

When we simplify this fraction:

[tex]\[
c = 0.45
\][/tex]

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