The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.
A function is defined as a expression containing one or more variables.
Technically speaking, a function is a means of linking a set of inputs to a set of outputs.
The height of the ball at any time t is given by the function:
![h(t)=-16t^2+38t+2](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%2B38t%2B2)
Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.
Let us substitute the values:
![\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0](https://tex.z-dn.net/?f=%5Cimplies%20h%28t%29%3D-16t%5E2%2B38t%2B2%5C%5C%5Cimplies%2016%3D-16t%5E2%2B38t%2B2%5C%5C%5Cimplies%2016t%5E2-38t%2B14%3D0%5C%5C%5Cimplies%208t%5E2-19t%2B7%3D0)
This is in the form of a quadratic equation in t.
Solving by using the quadratic formula:
We know that for a quadratic equation ![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
![x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Therefore for the above quadratic equation:
![t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-%28-19%29%5Cpm%20%5Csqrt%7B%28-19%29%5E2-4%288%29%287%29%7D%7D%7B2%288%29%7D%5C%5Ct%3D%5Cfrac%7B19%2B%5Csqrt%7B137%7D%7D%7B8%7D%2Ct%3D%5Cfrac%7B19-%5Csqrt%7B137%7D%7D%7B8%7D%5C%5Ct%3D1.919...%2Ct%3D0.455...)
Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.
To learn more about functions:
brainly.com/question/12431044
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Answer:
For the first one:
y = 2/3x + 1
For the second one:
y = -5x + 4
Step-by-step explanation:
As you may already know, in the y=mx+b equation format:
m = slope
b = y-intercept
On the graph, it already shows the y-intercept, so you can automatically find your b in the equation.
And, the easiest, most quick way to find the slope by using a graph is to calculate using rise/run. So, by doing that you can calculate the equation.
Then, you can just leave the variables y and x alone.
Hope this helped!!
Answer:
3 24/100
Step-by-step explanation:
and then you make it small to 12/50 then 6/25 then your finally answer is 3 6/25
The relationship between fractions and decimals is that with a fraction you are dividing whereas a decimal is treated like a number.
i.e. 1/4=0.25
Think of decimals as 100 being the whole or 1 so split 100 into 4 and you get 25 or 0.25