A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance d ( t ) ( in ft ) that the car travels t seconds after the brakes are applied is given by d ( t ) = − 4.84 t 2 + 88 t , where 0 ≤ t ≤ 9.09 . ( See Example 5 ) a. Find the difference quotient d ( t + h ) − d ( t ) h . Use the difference quotient to determine the average rate of speed on the following intervals for t . b. [ 0 , 2 ] ( Hint : t = 0 and h = 2 ) c. [ 2 , 4 ] ( Hint : t = 2 and h = 2 ) d. [ 4 , 6 ] ( Hint : t = 4 and h = 2 ) e. [ 6 , 8 ] ( Hint : t = 6 and h = 2 )
A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance d ( t ) ( in ft ) that the car travels t seconds after the brakes are applied is given by d ( t ) = − 4.84 t 2 + 88 t , where 0 ≤ t ≤ 9.09 . ( See Example 5 ) a. Find the difference quotient d ( t + h ) − d ( t ) h . Use the difference quotient to determine the average rate of speed on the following intervals for t . b. [ 0 , 2 ] ( Hint : t = 0 and h = 2 ) c. [ 2 , 4 ] ( Hint : t = 2 and h = 2 ) d. [ 4 , 6 ] ( Hint : t = 4 and h = 2 ) e. [ 6 , 8 ] ( Hint : t = 6 and h = 2 )
Solution Summary: The author calculates the difference quotient of the distance function d(t)=-4.84t
A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance
d
(
t
)
(
in ft
)
that the car travels t seconds after the brakes are applied is given by
d
(
t
)
=
−
4.84
t
2
+
88
t
, where
0
≤
t
≤
9.09
. (See Example 5 )
a. Find the difference quotient
d
(
t
+
h
)
−
d
(
t
)
h
.
Use the difference quotient to determine the average rate of speed on the following intervals for t.
You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
Plane II is spanned by the vectors:
- (2) · P² - (4)
P1=2
P21
3
Subspace W is spanned by the vectors:
2
W1
- (9) ·
1
W2
1
= (³)
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Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License