44. Here is a table showing values for the function H(t, h). a. Estimate the val

Question

44. Here is a table showing values for the function H(t, h). a. Estimate the value of - at (3, 150). b. Estimate the value of at (3, 150). c. Use your answers to parts a and b to estimate the value of H(2.6,156). d. The values in the table came from H(t, h)= h + 15t - 4.9t^2, which gives the height in meters above the ground after t seconds of an object that is thrown upward from an initial height of h meters with an initial velocity of 15 meters per second. How close are your estimates from parts a, b, and c

Explanation / Answer

a) To find Ht at (3 , 150)
Here height, h = 150 ---> constant
Since we are finding Ht, what i shall do is find the slope between (2 , 160.4) and (3 , 150.9) first
Slope = (150.9 - 160.4) / (3 - 2)
Slope = -9.5

Now, i shall find the slope between (3 , 150.9) and (4 , 131.6)
Slope = (131.6 - 150.9) / (4 - 3)
Slope = -19.3

Now, to find the value Ht, i shall average out the above two slopes found

Ht = (-19.3 + -9.5) / 2
Ht = -14.4 ---> ANSWER

b)
In this case, time, t = 3 ---> constant
I shall first find the slope between (100 , 100.9) and (150 , 150.9)
(150.9 - 100.9) / (150 - 100)
50/50
Slope = 1

Now, i shall find the slope between (150,150.9) and (200,200.9)
Slope = (200.9 - 150.9) / (200 - 150)
Slope = 50/50
Slope = 1

Now, i shall average out the aboive found slopes

Hh = (1 + 1) / 2
Hh = 1 -----> ANSWER

d)

H(t,h) = h + 15t - 4.9t^2

Ht = partial derivative with respect to time, t
Ht = 0 + 15 - 4.9(2t)
Ht = 15 - 9.8*t
Ht = 15 - 9.8*3
Ht = -14.4
So, the answer to A is an exact match

Hh = partial derivative with respect to h
H = h + 15t - 4.9t^2
Hh = 1 + 0 - 0
Hh = 1
So, the answer to B is also an exact match

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.