Question
What is the value of this expression when c = -4 and d = 10?
1/4(c^3+d^2)
A.
2
B.
9
C.
21
D.
41
1/4(c^3+d^2)
A.
2
B.
9
C.
21
D.
41
Answers
GPT-4o mini
To evaluate the expression \( \frac{1}{4}(c^3 + d^2) \) with \( c = -4 \) and \( d = 10 \), we start by substituting the values of \( c \) and \( d \) into the expression.
1. Calculate \( c^3 \):
\[
c^3 = (-4)^3 = -64
\]
2. Calculate \( d^2 \):
\[
d^2 = 10^2 = 100
\]
3. Now combine \( c^3 \) and \( d^2 \):
\[
c^3 + d^2 = -64 + 100 = 36
\]
4. Finally, substitute this result back into the expression:
\[
\frac{1}{4}(c^3 + d^2) = \frac{1}{4}(36) = 9
\]
Thus, the value of the expression is \( 9 \).
The answer is \( \boxed{9} \).
1. Calculate \( c^3 \):
\[
c^3 = (-4)^3 = -64
\]
2. Calculate \( d^2 \):
\[
d^2 = 10^2 = 100
\]
3. Now combine \( c^3 \) and \( d^2 \):
\[
c^3 + d^2 = -64 + 100 = 36
\]
4. Finally, substitute this result back into the expression:
\[
\frac{1}{4}(c^3 + d^2) = \frac{1}{4}(36) = 9
\]
Thus, the value of the expression is \( 9 \).
The answer is \( \boxed{9} \).