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State the given in the question
Given that the sum of a number and 3 is subtracted from, the result is 5
State what is to be found in the question
We are to find the number. In other to achieve this, we would follow the steps below:
Step 1: Represent the number with an unknown
Let x represent the number
Step 2: Interpret the given statement mathematically
If x is the number, then the sum of the number and 3 would be
Then the sum of a number and 3 subtracted from 10 would be
Finally, when the sum of a number and 3 subtracted from 10, the result is 5, would be
Step 3: Solve for x in the mathematical interpretation of the given statement
The value of x is as calculated as shown below:
Hence, the number is 5
Answer:
a) No. t < 0 is not part of the useful domain of the function
b) 2.0 seconds
Step-by-step explanation:
a) A graph of the function is shown below. It shows t-intercepts at t=-0.25 and t=2.0. We presume that t is measured forward from some event such as the ball being thrown or hit. The model's predicted ball location has no meaning prior to that event, when values of t are negative.
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b) It is convenient to use a graphing calculator to find the t-intercepts. Or, the equation can be solved for h=0 any of several ways algebraically. One is by factoring.
h = 0 = -16t² +28t +8 . . . . . . . . . . . . the ball hits the ground when h = 0
0 = -4(4t² -7t -2) = -4(4t +1)(t -2)
This has t-intercepts where the factors are zero, at t=-1/4 and t=2.
The ball will hit the ground after 2 seconds.
