Question

Find the area of the region bounded by y=−4x²+9

y=−1.25x+7, and both axes.
A) 54.4 square units
B) 41.6 square units
C) 31.2 square units
D) 23.8 square units

Answer 1

To find the area of the region bounded by two equations, we find the points of intersection and integrate between the x-values to calculate the area. The answer is option D) 23.8 square units.

Step-by-step explanation:

To find the area of the region bounded by the equations y = -4x² + 9 and y = -1.25x + 7, we need to find the points of intersection between the two curves.

Setting the equations equal to each other, we get -4x² + 9 = -1.25x + 7. Rearranging, we have -4x² + 1.25x + 2 = 0.

Using the quadratic formula, we can find the x-values of the points of intersection. Then, we can integrate the expression -4x² + 9 - (-1.25x + 7) with respect to x between the x-values to calculate the area.

The answer is option D) 23.8 square units.