Question

The area of the region bounded by the two curves y=x² 2and y=4 is

O 4.00 square units
O 32 square units
O 2.67 square units
O 10.67 square units

Question 6
Not yet answered
Marked out of 1.00
Flag question

The points of intersection ( x values only) of the two curves
y=x²+2x and y=7x+14 are given by:
O x=−2 and x=7
O x=2 and x=7
O x=−2 and x=−7
O x=2 and x=−7

Answer 1

Explanation:

See the attached graph (ShadedArea). The area in question is the darker red in the center. An integration is required, but I chose to estimate an answer by breaking the shaded area into a square (4 x 4) and two triangles that cover the area that needs to be subtracted from the square. The answer options are quite different, so I'm hoping to find a quick answer that comes close to one of the options.

As the graph shows, a rough estimate of the shaded area is 9.6 units^2. !0.67 square units comes closest. The other options are significantly different.

6) y=x²+2x and y=7x+14

Lets find the value(s) of x when the y's are equal. Set the equations equal to each other:

x²+2x =7x+14

x² - 5x - 14 = 0

(x-7)(x+2)=0

x = 7 and x = -2

See the attached graph (Intersection)