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Answer :
To solve for the value of [tex]\( c \)[/tex] given the equation [tex]\( f = c \cdot d^3 \)[/tex], with the values [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex], follow these steps:
1. Identify the Relationship: Start with the equation given:
[tex]\[
f = c \cdot d^3
\][/tex]
2. Substitute Known Values: Substitute [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex] into the equation. This will change the equation to:
[tex]\[
450 = c \cdot 10^3
\][/tex]
3. Calculate [tex]\( d^3 \)[/tex]: Compute [tex]\( 10^3 \)[/tex], which is [tex]\( 10 \times 10 \times 10 = 1000 \)[/tex].
4. Solve for [tex]\( c \)[/tex]: Rewrite the equation using the calculated cube of [tex]\( d \)[/tex]:
[tex]\[
450 = c \cdot 1000
\][/tex]
To solve for [tex]\( c \)[/tex], divide both sides of the equation by 1000:
[tex]\[
c = \frac{450}{1000}
\][/tex]
5. Simplify the Fraction: Simplify the fraction:
[tex]\[
c = 0.45
\][/tex]
Thus, the value of [tex]\( c \)[/tex] is [tex]\( 0.45 \)[/tex].
1. Identify the Relationship: Start with the equation given:
[tex]\[
f = c \cdot d^3
\][/tex]
2. Substitute Known Values: Substitute [tex]\( f = 450 \)[/tex] and [tex]\( d = 10 \)[/tex] into the equation. This will change the equation to:
[tex]\[
450 = c \cdot 10^3
\][/tex]
3. Calculate [tex]\( d^3 \)[/tex]: Compute [tex]\( 10^3 \)[/tex], which is [tex]\( 10 \times 10 \times 10 = 1000 \)[/tex].
4. Solve for [tex]\( c \)[/tex]: Rewrite the equation using the calculated cube of [tex]\( d \)[/tex]:
[tex]\[
450 = c \cdot 1000
\][/tex]
To solve for [tex]\( c \)[/tex], divide both sides of the equation by 1000:
[tex]\[
c = \frac{450}{1000}
\][/tex]
5. Simplify the Fraction: Simplify the fraction:
[tex]\[
c = 0.45
\][/tex]
Thus, the value of [tex]\( c \)[/tex] is [tex]\( 0.45 \)[/tex].
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