Question

.A toy rocket is launched from a 4.9 m high platform in such a way that its​ height, h​ (in meters), after t seconds is given by the equation h=−4.9t2+33.6t+4.9. How long will it take for the rocket to hit the​ ground?

he toy rocket will hit the ground after approximately enter your response here seconds.

2.The length of a rectangle is 7 centimeters less than five times its width. Its area is 24 square centimeters. Find the dimensions of the rectangle.
The width is enter your response here cm.
Part 2
The length is enter your response here cm.

3.Jeff and Kirk can build a​ 75-ft retaining wall together in 10 hours. Because Jeff has more​ experience, he could build the wall by himself 1 hour quicker than Kirk. How long would it take Kirk​ (to the nearest​ minute) to build the wall by​ himself?
It will take Kirk approximately enter your response here hours enter your response here min to build the wall himself.
​(Round to the nearest minute as​ needed.)


4.On the last three physics exams a student scored 87​, 85​, and 91. What score must the student earn on the next exam to have an average of at least​ 90?

The student must score at least enter your response here​%.

Answer 1

1- To find the time it takes for the rocket to hit the ground, we need to solve the equation h = 0. Substituting 0 for h and solving for t, we get:

0 = -4.9t^2 + 33.6t + 4.9

-4.9t^2 + 33.6t + 4.9 = 0

Using the quadratic formula, we get:

t = (-33.6 +/- sqrt(33.6^2 - 4(-4.9)(4.9))) / (2(-4.9))

t = (-33.6 +/- sqrt(1124.96)) / -9.8

t = (-33.6 +/- sqrt(1132.56)) / -9.8

t = (-33.6 +/- 33.6) / -9.8

t = (-67.2) / -9.8

t = 6.939

The rocket will hit the ground after approximately 6.939 seconds.

2- Let w be the width of the rectangle and l be the length. We are given that l = 5w - 7 and that the area of the rectangle is 24. We can set up the equation lw = 24 and substitute the expression for l:

(5w - 7)w = 24

5w^2 - 7w = 24

5w^2 - 7w - 24 = 0

Using the quadratic formula, we get:

w = (7 +/- sqrt(49 - 4(5)(-24))) / (2(5))

w = (7 +/- sqrt(49 - -120)) / 10

w = (7 +/- sqrt(169)) / 10

w = (7 +/- 13) / 10

w = 20/10 or w = -6/10

w = 2 or w = -0.6

Since the width cannot be negative, the width of the rectangle is 2 cm. The length is then 5w - 7 = 5(2) - 7 = 3 cm.

3- Jeff can build the wall in 10 - 1 = 9 hours. Kirk can build the wall in 10 hours. The combined time it takes for Jeff and Kirk to build the wall is 9 + 10 = 19 hours. The total time it takes for Kirk to build the wall is 75 / (1/10) = 750 minutes. 750 minutes is equivalent to 750/60 = 12.5 hours. Kirk builds the wall in 12.5 - 10 = 2.5 hours. Kirk builds the wall in 2.5 hours, or 2.5 * 60 = 150 minutes. Kirk will take approximately 150 minutes to build the wall by himself.

4- The student's average score so far is (87 + 85 + 91) / 3 = 263 / 3 = 87.67. To have an average of at least 90, the student needs to score at least 90 * 4 - 263 = 360 - 263 = 97. The student must score at least 97% on the next exam.