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The latest questions and answers, from members following Math at eNotes.Wed, 4 Mar 2015 05:59:01 PSTen-usA ball is thrown into the air with an initial velocity of 40 ft/s...
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A ball is thrown into the air with an initial velocity of 40 ft/s vertically upwards. t seconds after it has been thrown up, the height of the ball is given by the function `f(t) = 40t - 16t^2` . The average velocity of the ball for a time period between `t_0` and `t_1` is given by: v = `(f(t_1) - f(t_0))/(t_1 - t_0)` To measure the average velocity for the time period beginning t = 2, `t_0` = 2. If it lasts 0.5 s, `t_1` = 2.5: average...http://www.enotes.com/homework-help/ball-thrown-into-air-with-velocity-40-ft-s-its-475141Wed, 4 Mar 2015 05:59:01 PSTIf a ball is thrown into the air with a velocity of 40 ft/s, its height...
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If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet seconds later is given by y = 40t -16t^2.Find the average velocity for the time period beginning when t = 2 and lasting ,0.5 second ,0.1 second, 0.05 second and 0.01 second. What is the instantaneous velocity when t = 2.http://www.enotes.com/homework-help/ball-thrown-into-air-with-velocity-40-ft-s-its-475141#1March 4, 2015, 5:38 am PSTTake note that the work done by the force F(x) in moving an object from...
http://www.enotes.com/homework-help/1600-lb-elevator-suspended-by-200-ft-cable-that-475123
Take note that the work done by the force F(x) in moving an object from x=a to x=b is given by: `W= int_a^b F(x) dx` To apply this to the problem above, let x be the amount of cable that has been pulled up. So at the basement, the amount of cable that has been pulled up is x=0. And at the third floor , it is x = 30. And the forces acting in moving object are the weight of the elevator (which is constant) and the weight of the cable at a...http://www.enotes.com/homework-help/1600-lb-elevator-suspended-by-200-ft-cable-that-475123Wed, 4 Mar 2015 01:31:47 PSTWe will apply the foil method here first before integrating it. Kindly...
http://www.enotes.com/homework-help/this-integral-represents-volume-solid-find-volume-475112
We will apply the foil method here first before integrating it. Kindly recall that we can rewrite `(1 - y^2)^2` as `(1 - y^2)(1 - y^2)` . FOIL means first terms, outer terms, inner terms, last terms.So, we will have: First terms `= 1 * 1 = 1` . Outer terms `= 1 * - y^2 = -y^2` . Inner terms `= -y^2 * 1 = -y^2` . Last terms` = -y^2 * -y^2 = y^4` . `(1 - y^2)(1 - y^2) = 1 - y^2 - y^2 + y^4` Combine like terms. `(1 - y^2)(1 - y^2) = 1 - y^2 -...http://www.enotes.com/homework-help/this-integral-represents-volume-solid-find-volume-475112Wed, 4 Mar 2015 00:33:57 PSTThe average value of an integrable function on an interval [a,b] is...
http://www.enotes.com/homework-help/find-average-value-function-f-t-t-sin-t-2-interval-475121
The average value of an integrable function on an interval [a,b] is defined as: `"Avg"= 1/(b-a) int_(a)^(b) f(x)dx ` Find the average value of `f(t)= t sin(t^2) dt ` on [0,10]: `"Avg"= 1/10 int_0^10 t sin(t^2) dt ` Let `u=t^2, du=2tdt ==> tdt=du/2 ` ; also x=0 ==> u=0 and x=10 ==> u=100 so we can rewrite as: ` =1/10 int_0^100 sin(u) 1/2 du ` or factoring out the constant: `=1/20 int_0^100 sin(u)du ` `=1/20[ -cos(u) |_0^100 ] `...http://www.enotes.com/homework-help/find-average-value-function-f-t-t-sin-t-2-interval-475121Tue, 3 Mar 2015 22:03:44 PSTFind the average value of `f(t)=t cos(t^2) ` on the interval [0,10]: The...
http://www.enotes.com/homework-help/find-average-value-function-f-t-t-cos-t-2-interval-475122
Find the average value of `f(t)=t cos(t^2) ` on the interval [0,10]: The average value of an integrable function on an interval [a,b] is defined as : `1/(b-a) int_(a)^(b) f(x)dx ` So we find: `1/10 int_0^10 t cos(t^2) dt ` Let `u=t^2, du=2tdt ==> tdt=1/2du ` Also, t=0 ==> u=0 and t=10 ==> u=100. So we can rewrite as `1/10 int_0^(100) cos(u)1/2 du ` or `=1/20 int_0^(100) cos(u) du ` `=1/20[ sin(u) |_0^(100) ] `...http://www.enotes.com/homework-help/find-average-value-function-f-t-t-cos-t-2-interval-475122Tue, 3 Mar 2015 21:55:06 PSTThe force required to maintain a spring stretched by the length `Delta...
http://www.enotes.com/homework-help/force-30-n-required-maintain-spring-stretched-475120
The force required to maintain a spring stretched by the length `Delta x` is determined by the formula `F = 1/2 k(Deltax)` , where k is a constant depending on the properties of the spring and `Delta x = x_1 - x_0` . `x_1 = 15 cm = 0.15 m` - the length of the streched spring `x_2 = 12cm = 0.12 m` - the natural length of the spring. Since the force is given, the constant k can be determined: `Delta x = 0.15 - 0.12 = 0.03 m` `30 N = 1/2 k...http://www.enotes.com/homework-help/force-30-n-required-maintain-spring-stretched-475120Tue, 3 Mar 2015 21:17:08 PSTThe last part in bold should be If f(x) = 3 - 2x this implies that...
http://www.enotes.com/homework-help/f-2-x-f-x-3-2x-475115
The last part in bold should be If f(x) = 3 - 2x this implies that f(2-x) = 2x - 1. We can work this through by considering a new variable y where we define y = 2-xhttp://www.enotes.com/homework-help/f-2-x-f-x-3-2x-475115Tue, 3 Mar 2015 21:10:54 PSTWe have the function `f(x) = 3 -2x ` This is a function of the variable...
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We have the function `f(x) = 3 -2x ` This is a function of the variable `x ` where `x ` can take the value of any number - a small number, a large number, a small negative number or a large negative number. To be formal we might say that the domain of `x ` ranges from negative infinity to positive infinity. That is the domain of `x ` is `(-infty,infty) `. This unlimited domain is called the real line and is what you would normally think of as...http://www.enotes.com/homework-help/f-2-x-f-x-3-2x-475115#2Tue, 3 Mar 2015 21:08:06 PSTA 1600 lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft....
http://www.enotes.com/homework-help/1600-lb-elevator-suspended-by-200-ft-cable-that-475123
A 1600 lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30ft?http://www.enotes.com/homework-help/1600-lb-elevator-suspended-by-200-ft-cable-that-475123#3March 3, 2015, 8:34 pm PSTFind the average value of the function `f(t) = t cos(t^2)` on the...
http://www.enotes.com/homework-help/find-average-value-function-f-t-t-cos-t-2-interval-475122
Find the average value of the function `f(t) = t cos(t^2)` on the interval [0, 10]http://www.enotes.com/homework-help/find-average-value-function-f-t-t-cos-t-2-interval-475122#4March 3, 2015, 8:30 pm PSTFind the average value of the function f(t) = t sin(t^2) on the interval...
http://www.enotes.com/homework-help/find-average-value-function-f-t-t-sin-t-2-interval-475121
Find the average value of the function f(t) = t sin(t^2) on the interval [0, 10]http://www.enotes.com/homework-help/find-average-value-function-f-t-t-sin-t-2-interval-475121#5March 3, 2015, 8:25 pm PSTA force of 30 N is required to maintain a spring stretched from its...
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A force of 30 N is required to maintain a spring stretched from its natural length of 12 c to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?http://www.enotes.com/homework-help/force-30-n-required-maintain-spring-stretched-475120#6March 3, 2015, 8:22 pm PSTf(2-x)=? if f(x)=3-2x
http://www.enotes.com/homework-help/f-2-x-f-x-3-2x-475115
f(2-x)=? if f(x)=3-2xhttp://www.enotes.com/homework-help/f-2-x-f-x-3-2x-475115#7March 3, 2015, 7:57 pm PSTThis integral represents the volume of a solid. Find the volume, and...
http://www.enotes.com/homework-help/this-integral-represents-volume-solid-find-volume-475112
This integral represents the volume of a solid. Find the volume, and describe the solid. `pi int_-1^1 (1-y^2)^2 dy`http://www.enotes.com/homework-help/this-integral-represents-volume-solid-find-volume-475112#8March 3, 2015, 7:26 pm PST