Evaluate $-3 x^2-y^3$ when $x=1$ and $y=-4$
Answer (2)
Substitute x = 1 and y = − 4 into the expression − 3 x 2 − y 3 .
Calculate − 3 ( 1 ) 2 − ( − 4 ) 3 .
Simplify the expression: − 3 ( 1 ) − ( − 64 ) = − 3 + 64 = 61 .
The final answer is 61 .
Explanation
Understanding the Problem We are given the expression − 3 x 2 − y 3 and the values x = 1 and y = − 4 . Our goal is to evaluate the expression by substituting these values.
Substitution Substitute x = 1 and y = − 4 into the expression: − 3 x 2 − y 3 = − 3 ( 1 ) 2 − ( − 4 ) 3
Simplification Now, let's simplify the expression step by step: First, calculate 1 2 and ( − 4 ) 3 :
1 2 = 1 ( − 4 ) 3 = − 4 × − 4 × − 4 = 16 × − 4 = − 64 So, we have: − 3 ( 1 ) − ( − 64 ) = − 3 + 64 = 61
Final Answer Therefore, the value of the expression − 3 x 2 − y 3 when x = 1 and y = − 4 is 61.
Examples
Imagine you are calculating the energy of a system where the energy depends on two variables, x and y . The formula for the energy is given by E = − 3 x 2 − y 3 . If x represents the speed of a particle and y represents its position, you can plug in the values of x and y to find the energy E of the system. This type of calculation is common in physics and engineering to understand how different parameters affect the overall energy or state of a system.
To evaluate the expression − 3 x 2 − y 3 when x = 1 and y = − 4 , substitute the values and simplify the expression. This results in 61 .
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