Answer :
To solve the problem of finding the value of [tex]\( c \)[/tex] when given the equation [tex]\( f = c \cdot d^3 \)[/tex], along with the values [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex], follow these steps:
1. Substitute the known values: Start by plugging the given values into the equation. You have [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex].
2. Write the equation with substituted 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. Substitute [tex]\( 10^3 \)[/tex] with 1000 in the equation:
[tex]\[
450 = c \cdot 1000
\][/tex]
5. Solve for [tex]\( c \)[/tex]: To find [tex]\( c \)[/tex], divide both sides of the equation by 1000.
[tex]\[
c = \frac{450}{1000}
\][/tex]
6. Calculate the division:
[tex]\[
c = 0.45
\][/tex]
Therefore, the value of [tex]\( c \)[/tex] is 0.45.
1. Substitute the known values: Start by plugging the given values into the equation. You have [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex].
2. Write the equation with substituted 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. Substitute [tex]\( 10^3 \)[/tex] with 1000 in the equation:
[tex]\[
450 = c \cdot 1000
\][/tex]
5. Solve for [tex]\( c \)[/tex]: To find [tex]\( c \)[/tex], divide both sides of the equation by 1000.
[tex]\[
c = \frac{450}{1000}
\][/tex]
6. Calculate the division:
[tex]\[
c = 0.45
\][/tex]
Therefore, the value of [tex]\( c \)[/tex] is 0.45.
