The entrance to a tunnel is in the shape of a semiellipse over a 24 -ft by 8 -ft rectangular opening. The height at the center of the opening is 14 ft . a. Determine the height of the opening at a point 6 ft from the edge of the tunnel. Round to 1 decimal place. b. Can a 10 -ft high truck pass through the opening if the truck's outer wheel passes at a point 3 ft from the edge of the tunnel? c. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening h x (in ft) as a function of the horizontal distance x (in ft) from the center.
The entrance to a tunnel is in the shape of a semiellipse over a 24 -ft by 8 -ft rectangular opening. The height at the center of the opening is 14 ft . a. Determine the height of the opening at a point 6 ft from the edge of the tunnel. Round to 1 decimal place. b. Can a 10 -ft high truck pass through the opening if the truck's outer wheel passes at a point 3 ft from the edge of the tunnel? c. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening h x (in ft) as a function of the horizontal distance x (in ft) from the center.
The entrance to a tunnel is in the shape of a semiellipse over a
24
-ft
by
8
-ft
rectangular opening. The height at the center of the opening is
14
ft
.
a. Determine the height of the opening at a point
6
ft
from the edge of the tunnel. Round to
1
decimal place.
b. Can a
10
-ft
high truck pass through the opening if the truck's outer wheel passes at a point
3
ft
from the edge of the tunnel?
c. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening
h
x
(in ft) as a function of the horizontal distance
x
(in ft) from the center.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Is the function f(x) continuous at x = 1?
(z)
6
5
4
3.
2
1
0
-10
-9
-7
-5
-2
-1 0
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
○ The function f(x) is continuous at x = 1.
○ The right limit does not equal the left limit. Therefore, the function is not continuous.
○ The function f(x) is discontinuous at x = 1.
○ We cannot tell if the function is continuous or discontinuous.
Is the function f(x) shown in the graph below continuous at x = −5?
f(x)
7
6
5
4
2
1
0
-10
-9
-8 -7
-6
-5
-4
-3
-2
-1 0
1
2
3
4
5
6 7 8 9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
The function f(x) is continuous.
○ The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
○ We cannot tell if the function is continuous or discontinuous.
4. Evaluate the following integrals. Show your work.
a)
-x
b) f₁²x²/2 + x² dx
c) fe³xdx
d) [2 cos(5x) dx
e) √
35x6
3+5x7
dx
3
g) reve
√ dt
h) fx (x-5) 10 dx
dt
1+12
Elementary Statistics: Picturing the World (7th Edition)
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