High School

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 :

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

We are given the equation [tex]\( f = c \cdot d^3 \)[/tex], with [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex]. We need to find the value of [tex]\( c \)[/tex].

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

Since [tex]\( d = 10 \)[/tex], we need to calculate [tex]\( 10^3 \)[/tex].

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

2. Solve for [tex]\( c \)[/tex]:

We know that [tex]\( f = c \cdot d^3 \)[/tex]. We can solve for [tex]\( c \)[/tex] by rearranging the equation:

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

Substitute the known values into the equation:

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

3. Calculate the value of [tex]\( c \)[/tex]:

Divide 450 by 1000 to find [tex]\( c \)[/tex].

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

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