A rock is thrown into the air. The height of the rock is modeled by s(t) = −16tଶ + 64t + 80 feet for t ≥ 0 seconds. The rock hits the ground at t = 5 seconds. Find the maximum height of the rock on the interval 0 ≤ t ≤ 5.

144 feets

Step-by-step explanation:

Look on s(t) like quadratic function. We need to find maximum of the function using 1st diferetioal:

s(t)=-16t^2+64t+80

s’(t)=-32t+64

S’(t)=0 if t=2

For t>2, s’(t)<0

For t<2, s’(t)>0. So the maximum od function is in the point 2.

S(2)=-16*4+64*2+80=-64+128+80=144

2 is the final ! : )

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x