A long jumper leaves the ground at an angle of 20 o above the horizontal at a speed of11 m/sec. The height of the jumper can be modeled by h x = − 0.046 x 2 + 0.364 x , where h is the jumper’s height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c. What is the length of the jump? Round to 1 decimal place.
A long jumper leaves the ground at an angle of 20 o above the horizontal at a speed of11 m/sec. The height of the jumper can be modeled by h x = − 0.046 x 2 + 0.364 x , where h is the jumper’s height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c. What is the length of the jump? Round to 1 decimal place.
Solution Summary: The author calculates the horizontal distance from the point of launch at which the maximum height of the jumper occurs using f(x)=-0.046x2+0.364x.
A long jumper leaves the ground at an angle of
20
o
above the horizontal at a speed of11 m/sec. The height of the jumper can be modeled by
h
x
=
−
0.046
x
2
+
0.364
x
,
where h is the jumper’s height in meters and x is the horizontal distance from the point of launch.
a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places.
b. What is the maximum height of the long jumper? Round to 2 decimal places.
c. What is the length of the jump? Round to 1 decimal place.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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