$\begin{array}{l}p=2, q=-\frac{3}{2} \gamma=-2 \\ p q-4 p \gamma^2+10\end{array}$
Answer (2)
To find the value of the expression pq − 4 p γ 2 + 10 with the given variables, first substitute the values for p , q , and γ . After substituting and performing the calculations, the final result is − 25 .
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Substitute the given values: p = 2 , q = − 2 3 , and γ = − 2 into the expression pq − 4 p γ 2 + 10 .
Calculate pq = 2 × ( − 2 3 ) = − 3 .
Calculate 4 p γ 2 = 4 × 2 × ( − 2 ) 2 = 32 .
Evaluate the expression: − 3 − 32 + 10 = − 25 . The final answer is − 25 .
Explanation
Understanding the Problem We are given the values p = 2 , q = − 2 3 , and γ = − 2 . We need to evaluate the expression pq − 4 p γ 2 + 10 .
Substituting the Values First, let's substitute the given values into the expression: pq − 4 p γ 2 + 10 = ( 2 ) ( − 2 3 ) − 4 ( 2 ) ( − 2 ) 2 + 10
Calculating pq Now, let's calculate the product pq : pq = ( 2 ) ( − 2 3 ) = − 3
Calculating gamma squared Next, let's calculate γ 2 : γ 2 = ( − 2 ) 2 = 4
Calculating 4p*gamma^2 Now, let's calculate 4 p γ 2 : 4 p γ 2 = 4 ( 2 ) ( 4 ) = 32
Calculating pq - 4p*gamma^2 Now, let's calculate pq − 4 p γ 2 : pq − 4 p γ 2 = − 3 − 32 = − 35
Adding 10 Finally, let's add 10 to the result: pq − 4 p γ 2 + 10 = − 35 + 10 = − 25
Examples
This type of algebraic expression evaluation is fundamental in many areas of science and engineering. For instance, in physics, you might use such an expression to calculate the potential energy of a system, where p, q, and γ represent physical parameters like charge, distance, and angle. By substituting specific values, you can determine the energy level, which is crucial for understanding the system's behavior. Similarly, in finance, these expressions can model investment returns, where the variables represent initial investment, growth rate, and risk factors.
