Answer: 4.5
<u>Step-by-step explanation:</u>
First, find the points of intersection by solving the system.
y = x² + 2x + 4
y = x + 6
Solve by substitution:
x² + 2x + 4 = x + 6 ⇒ x² + x - 2 = 0 ⇒ (x + 2)(x - 1) = 0 ⇒ x = -2, x = 1
Now, integrate from x = -2 to x = 1
<em>the bottom of the integral is -2 </em>
=
=
=
=
=
=
= -3 + 1.5 + 6
= 4.5
Answer: Yes the ladder will reach the fire
Step-by-step explanation: Please refer to the attached diagram for details.
The fire is at point A, while the top of the truck is at point C. The fire is actually burning at 22 feet off the ground, but because the fire truck itself is already 6 feet off the ground, the point that would serve as the base of the building would be 16 feet from the third floor (which is 22 feet minus 6 feet). Hence, point A to point B is 16 feet. So we need to calculate if line AC (from the truck to the fire at the third floor, labeled as b) shall equal the length of the ladder which is 16-foot long.
The angle of the ladder with the top of the truck is 75 degrees. Therefore,
Sin 75 = opposite/hypotenuse
Sin 75 = 16/b
By cross multiplication we now have
b = 16/Sin 75
b = 16/0.9659
b = 16.56
If the distance from A to C is 16.56 feet, then the 16-foot long ladder would reach the fire.
