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.
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
The correct answer is C,i know that we need to use stokes theorem and parametrize the equations then write the equation F with respect to the curve but i cant seem to find a way to do it, the integral should be from 0 to 2pi but i might be wrongcould you show me the steps to get to 18pi
Elementary Statistics: Picturing the World (7th Edition)
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