$p=2, q=-\frac{3}{2}, \gamma=-2$
(b) $p^2 \gamma^2+4 q^2$
Answer (2)
To calculate the expression p 2 γ 2 + 4 q 2 with the values p = 2 , q = − 2 3 , and γ = − 2 , we find that it equals 25 after evaluating the squares and performing the necessary operations. The final calculated value is 25 .
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Substitute the given values p = 2 , q = − 2 3 , and γ = − 2 into the expression p 2 γ 2 + 4 q 2 .
Calculate the squares: p 2 = 4 , γ 2 = 4 , and q 2 = 4 9 .
Multiply and add: 4 × 4 + 4 × 4 9 = 16 + 9 .
The final result 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 p 2 γ 2 + 4 q 2 .
Substituting the Values First, we substitute the given values into the expression: ( 2 ) 2 ( − 2 ) 2 + 4 ( − 2 3 ) 2
Calculating the Squares Next, we calculate the squares: 4 × 4 + 4 × 4 9
Performing the Multiplications Then, we perform the multiplications: 16 + 9
Adding the Results Finally, we add the results: 16 + 9 = 25 Therefore, the value of the expression is 25.
Examples
Understanding how to evaluate expressions with given variables is fundamental in many areas, such as physics and engineering. For example, in physics, you might use such calculations to determine the kinetic energy of an object, where the energy depends on the object's mass and velocity. If you have a formula that relates these variables, substituting the known values allows you to find the energy. Similarly, in engineering, you might calculate the stress on a material given certain forces and dimensions. These types of calculations are essential for designing safe and efficient structures and systems.
