Creating a Quadratic Model of the Form y = a ( x − h ) 2 + k Estimated time: 20 minutes Group Size: 3 In an earlier group activity, we modeled the path of a softball that was thrown from right field to third base. The data points are given in the table. The values of t represent the time in seconds after the ball was released, and y represents the height of the ball in feet. T i m e ( s e c ) t 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 H e i g h t ( f t ) y 5 11 16 19 21 22 21 19 16 12 6 Choose a different point ( t , y ) from the graph. Substitute these values into the equation in step 3 and then solve for a .
Creating a Quadratic Model of the Form y = a ( x − h ) 2 + k Estimated time: 20 minutes Group Size: 3 In an earlier group activity, we modeled the path of a softball that was thrown from right field to third base. The data points are given in the table. The values of t represent the time in seconds after the ball was released, and y represents the height of the ball in feet. T i m e ( s e c ) t 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 H e i g h t ( f t ) y 5 11 16 19 21 22 21 19 16 12 6 Choose a different point ( t , y ) from the graph. Substitute these values into the equation in step 3 and then solve for a .
Solution Summary: The author explains how to calculate the value of a by substituting the different point (t,y)2+k into the formula.
Creating a Quadratic Model of the Form
y
=
a
(
x
−
h
)
2
+
k
Estimated time: 20 minutes
Group Size: 3
In an earlier group activity, we modeled the path of a softball that was thrown from right field to third base. The data points are given in the table. The values of t represent the time in seconds after the ball was released, and y represents the height of the ball in feet.
T
i
m
e
(
s
e
c
)
t
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
H
e
i
g
h
t
(
f
t
)
y
5
11
16
19
21
22
21
19
16
12
6
Choose a different point
(
t
,
y
)
from the graph. Substitute these values into the equation in step 3 and then solve for a.
Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045.
2) Find Θ given sec Θ = 4.213.
3) Find Θ given cot Θ = 0.579. Solve the following three right triangles.
B
21.0
34.6° ca
52.5
4)c
26°
5)
A
b
6) B 84.0 a
42°
b
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
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