How fast is the top of the ladder approaching the ground when the base is 9 from the fence? - ladder
A 25-foot ladder rests on a nearly 9 meters. The base of the ladder from the fence to 10 meters per minute. How fast is the top of the ladder, closer to the ground when the base is 9 of the fence? [Note: The scale is over the fence.]
The upper level is closer to the earth of_____ min m / min.
Monday, November 30, 2009
Ladder How Fast Is The Top Of The Ladder Approaching The Ground When The Base Is 9 From The Fence?
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Draw the triangle ABC. \\ \\ \\ \\ \\ \\ \\ \\ U0026lt, B = 90 degrees
AB is around and let y = AB
AC is straight and AC = 25
BC is the distance between the foot of the stairs and railings, is BC = x.
x ^ 2 + y ^ 2 = 25 ^ 2 ------------------( 1)
in a particular case when x = 9 (the base is 9 feet from the fence)
81 + y ^ 2 = 625
y ^ 2 = 544
y = 4 √ 34
Differentiating equation (1) with respect to t
2x dx / dt + 2y dt / dt = 0
x dx / dt + dy / dt = 0
where x = 9, y = 4 √ min 34, dx / dt = 10 m /
9 * (10) √ 34 + 4 dy / dt = 0
4 √ 34 dy / dt = -90
dy / dt = -90 / (4 √ 34)
= -22.5 / √ 34
= -3.86 (Negative because she slipped on the stairs)
The scale slides up to a height of 3.86 m / min
Draw the triangle ABC. \\ \\ \\ \\ \\ \\ \\ \\ U0026lt, B = 90 degrees
AB is around and let y = AB
AC is straight and AC = 25
BC is the distance between the foot of the stairs and railings, is BC = x.
x ^ 2 + y ^ 2 = 25 ^ 2 ------------------( 1)
in a particular case when x = 9 (the base is 9 feet from the fence)
81 + y ^ 2 = 625
y ^ 2 = 544
y = 4 √ 34
Differentiating equation (1) with respect to t
2x dx / dt + 2y dt / dt = 0
x dx / dt + dy / dt = 0
where x = 9, y = 4 √ min 34, dx / dt = 10 m /
9 * (10) √ 34 + 4 dy / dt = 0
4 √ 34 dy / dt = -90
dy / dt = -90 / (4 √ 34)
= -22.5 / √ 34
= -3.86 (Negative because she slipped on the stairs)
The scale slides up to a height of 3.86 m / min
Draw the triangle ABC. \\ \\ \\ \\ \\ \\ \\ \\ U0026lt, B = 90 degrees
AB is around and let y = AB
AC is straight and AC = 25
BC is the distance between the foot of the stairs and railings, is BC = x.
x ^ 2 + y ^ 2 = 25 ^ 2 ------------------( 1)
in a particular case when x = 9 (the base is 9 feet from the fence)
81 + y ^ 2 = 625
y ^ 2 = 544
y = 4 √ 34
Differentiating equation (1) with respect to t
2x dx / dt + 2y dt / dt = 0
x dx / dt + dy / dt = 0
where x = 9, y = 4 √ min 34, dx / dt = 10 m /
9 * (10) √ 34 + 4 dy / dt = 0
4 √ 34 dy / dt = -90
dy / dt = -90 / (4 √ 34)
= -22.5 / √ 34
= -3.86 (Negative because she slipped on the stairs)
The scale slides up to a height of 3.86 m / min
Using similar triangles, we get:
AB = hypotenuse of the triangle of 90 degrees from vertical and horizontal page with X, where 9 is the height of the fence.
small triangle is the triangle of 90 degrees in the major.
25 = hypotenuse of the larger triangle with the vertical part J.
(y / 9) = (25/AB), AB = (x ^ 2 + 9 ^ 2) ^ (1 / 2)
Y = 225 * (x ^ 2 +81) ^ (-1 / 2)
dy / dt = 225 *- 1 / 2 [(x ^ 2 +81) ^ (-3 / 2)] 2xdx/dt ...
Plug-in (dx / dt) = 10 x = 9 in the above equation.
The answer is: [-125 * (2) ^ (1 / 2)] / 18 ft / min
Using similar triangles, we get:
AB = hypotenuse of the triangle of 90 degrees from vertical and horizontal page with X, where 9 is the height of the fence.
small triangle is the triangle of 90 degrees in the major.
25 = hypotenuse of the larger triangle with the vertical part J.
(y / 9) = (25/AB), AB = (x ^ 2 + 9 ^ 2) ^ (1 / 2)
Y = 225 * (x ^ 2 +81) ^ (-1 / 2)
dy / dt = 225 *- 1 / 2 [(x ^ 2 +81) ^ (-3 / 2)] 2xdx/dt ...
Plug-in (dx / dt) = 10 x = 9 in the above equation.
The answer is: [-125 * (2) ^ (1 / 2)] / 18 ft / min
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