Answer:
t=3.5 seconds
Step-by-step explanation:
Given
h(t) = −16t^2 + 111t + 0
h'(t)= -32t + 111
Maximum height occurs when h(t) = 0 and the ball begins to fall
h(t)= -32t + 111=0
-32t + 111=0
-32t=-111
Divide both sides by -32
t=3.46872
Approximately, t=3.5 seconds
Recall,
Maximum height occurs when h(t) = 0
h(t)= -32t + 111=0
= -32(3.46872)+111
= -110.99904+111
= 0.00096 ft
28 men are needed to paint the room in 3 hours
<h3><u>Solution:</u></h3>
Given that it takes 12 hours for 7 men to paint a room
We are asked to find number of men required to paint the room in 3 hours
Recognize, "paint the room" is 1 task. One job.
7 men -------- 12 hours ------ 1 job
(7/7) = 1 men ------- 12 x 7 (84) ------- same 1 job
The one men is rate is 84 hours to do the job
We can express this as 1/84 jobs per hour, the one-person rate
Now lets find how many men needed to paint the room in 3 hours
Let the required number of men for 3 hours be "a"
The rates of each person is simply additive.
corresponds to rate x hours = jobs and "a" is a variable for how many men
Thus 28 men are needed to paint the room in 3 hours
The legs are 12 cm each, so the hypotenuse is√(144+144)=12√2☺☺☺☺
Let's solve this system of equations through substitution.
We have these two equations.
-7x-2y=14
6x+6y=18
Now let divide the second equation by 6.
6x+6y=18 ----> x+y=3
Next, let us move y to the right side of the equation.
x+y=3 -------> x=3-y (x equals 3-y)
Because we found out that what x is in terms of y, we can input that in for every instance of x in this equation below.
-7x-2y=14 becomes -7(3-y)-2y=14 (Why? Because x equals 3-y!)
We have a one variable equation now and can solve for y.
-7(3-y)-2y=14
-21+7y-2y=14
5y=35
y=7
Plug in 7 for y in any equation to find x.
x+y=3
x+7=3
x=-4
answer: x=-4, y=7
