Question

The table shows the approximate height of an object x seconds after the object was dropped. the function h(x) = –16x2 100 models the data in the table. a 2-column table with 5 rows. the first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2. the second column is labeled height (feet) with entries 100, 96, 84, 65, 37. for which value of x would this model make the least sense to use? –2.75 0.25 1.75 2.25

Answer 1

The value of x for which this model will make the least sense to use is at x=-2.75 seconds.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The function that is given to us is h(x) = –16x²+100 where x is the time in seconds.

Now, use the function to know the height of the object, therefore, the height of the object can be written as,

Time, t₁=0

Now, the height can be written as,

$h(x) = -16x^2+100\\\\h(0)=0+100\\\\h_1=100$

Thus, the height of the object when the time is 0 seconds is 100.

Time, t₂=0.5

Now, the height can be written as,

$h(x) = -16x^2+100\\\\h(0.5)=-4+100\\\\h_2=96$

Thus, the height of the object when the time is 0.5 seconds is 96.

Time, t₃=1

Now, the height can be written as,

$h(x) = -16x^2+100\\\\h(1)=-16+100\\\\h_1=84$

Thus, the height of the object when the time is 1 second is 84.

Time, t₄=1.5

Now, the height can be written as,

$h(x) = -16x^2+100\\\\h(1.5)=-36+100\\\\h_4=64$

Thus, the height of the object when the time is 1.5 seconds is 64.

Time, t₅=2

Now, the height can be written as,

$h(x) = -16x^2+100\\\\h(2)=0+100\\\\h_5=36$

Thus, the height of the object when the time is 2 seconds is 36.

Now as we can see that the error in the height of the object can be a maximum of 1, therefore, for different values of x, the change in height will be,

Time, t₆= -2.75

Now, the height can be written as,

$h(x) = -16x^2+100\\\\h(-2.75)=-121+100\\\\h_6= -21$

Thus, the height of the object when the time is -2.75 seconds is -21.

Hence, the value of x for which this model will make the least sense to use is at x=-2.75 seconds.

Learn more about Function:

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Answer 2

Answer:

-2.75

Step-by-step explanation:

A