College

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

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

Answer :

To find the value of [tex]\( c \)[/tex], we start with the equation given in the problem:

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

We are given that [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex]. Our goal is to solve for [tex]\( c \)[/tex].

Step 1: Calculate [tex]\( d^3 \)[/tex].

Since [tex]\( d = 10 \)[/tex], we have:

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

Step 2: Rearrange the equation to solve for [tex]\( c \)[/tex].

By rearranging the equation [tex]\( f = c \times d^3 \)[/tex], we get:

[tex]\[ c = \frac{f}{d^3} \][/tex]

Step 3: Substitute the known values into the equation.

Now we substitute [tex]\( f = 450 \)[/tex] and [tex]\( d^3 = 1000 \)[/tex] into the equation for [tex]\( c \)[/tex]:

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

Step 4: Simplify the fraction to find [tex]\( c \)[/tex].

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

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