5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:
(a) Find a formula for the speed of the wagon in terms of q and the variable x in the figure.
(b) Find the speed of the wagon when x=0.6 if q=0.5 m/s.
Answers
The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.
[tex](a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.
Reasons:
(a) The distance from the cart to the pulley, r is given by Pythagoras's
theorem as follows;
r = √((3 - 0.6)² + x²) = √(2.4² + x²)
The speed of the wagon = [tex]\mathbf{\dfrac{dx}{dt}}[/tex]
The speed of the rope, q = [tex]\mathbf{\dfrac{dr}{dt}}[/tex]
By chain rule, we have;
[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}[/tex]
[tex]\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
Therefore;
[tex]\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}[/tex]
[tex]\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}[/tex]
(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;
[tex]\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243[/tex]
The speed of the wagon when x = 0.6 and q = 0.5 m/s, [tex]\dfrac{dx}{dt}[/tex] ≈ 0.243 m/s
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Answer:
4x+2
Step-by-step explanation:
(13x+x−53x)−(−43x+2)
Group all the same variables on each side.
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Step-by-step explanation:
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Answer:
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Let the faster train catches the slower one after x hours.
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Step-by-step explanation:
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Answers
Answer:
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ratio — 1:3
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1 — AC
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Answers
Answer:
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Step-by-step explanation:
The graph clearly shows that when x = -1, y = 2.
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Answers
Answer:
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Step-by-step explanation:
put 1 in for X
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Answer:
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Step-by-step explanation:
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Answer:
If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.
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Step-by-step explanation:
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Answer:
At most it can hold 18 bagels
Step-by-step explanation:
So we can make this an equation
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Answers
Answer:
3
Step-by-step explanation:
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Step-by-step explanation:
rebecca has 12 photos she wants to hang side by side on her wall.
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We want to find different ways of selecting and ordering elements. The answers are:
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If you want to learn more, you can read:
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Check the picture below.
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4.
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Answer:
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II and III only
Step-by-step explanation:
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I don't know how to represent it on a nomberline
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Hope this helps
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Step-by-step explanation:
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2910
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We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.
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Answers
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Step-by-step explanation:
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Answers
Answer:
10x=40
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Step-by-step explanation:
pls mark as brainliest
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Answer:
2/8 and 4/8
Step-by-step explanation:
Answer:
2/8,4/8 or 1/4,1/2
Step-by-step explanation:
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