Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
[tex]7 A^2=481[/tex]
Answer (2)
Divide both sides of the equation by 7: A 2 = 7 481 .
Take the square root of both sides: A = ± 7 481 .
Calculate the two possible values of A: A ≈ 8.2894 and A ≈ − 8.2894 .
Round both values of A to two decimal places: A ≈ 8.29 and A ≈ − 8.29 . The solutions are 8.29 , − 8.29 .
Explanation
Problem Analysis We are given the equation 7 A 2 = 481 and asked to solve for A , rounding the answer to two decimal places.
Isolating A^2 First, we need to isolate A 2 by dividing both sides of the equation by 7: A 2 = 7 481
Taking the Square Root Next, we take the square root of both sides to solve for A :
A = ± 7 481 This gives us two possible solutions for A .
Calculating the Values of A Now, we calculate the two values of A :
A = 7 481 ≈ 8.2894 A = − 7 481 ≈ − 8.2894
Rounding to Two Decimal Places Finally, we round both values to two decimal places: A ≈ 8.29 A ≈ − 8.29 So, the solutions are approximately 8.29 and − 8.29 .
Final Answer Therefore, the solutions to the equation 7 A 2 = 481 , rounded to two decimal places, are A ≈ 8.29 and A ≈ − 8.29 .
Examples
Imagine you are designing a square garden and need it to cover a specific area. If the area is related to the square of the side length by a constant factor, solving an equation like this helps you determine the exact side length needed. For instance, if the area of the garden with a special paving is given by 7 A 2 and you want the area to be 481 square feet, solving for A tells you the required side length of the garden. This ensures your garden fits perfectly within your planned space.
To solve 7 A 2 = 481 , divide both sides by 7 to get A 2 = 7 481 . Taking the square root gives A ≈ 8.29 and A ≈ − 8.29 after rounding both to two decimal places.
;
