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Alexxandr [17]
3 years ago
12

Use CALCULUS to find coordinates of the turning point on C.

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
3 0
Oi 

Just calculating the differential. Step by step:

y=12 \sqrt{x} -x \frac{3}{2}-10 \\  \\ y=12x^{ \frac{1}{2} } -x \frac{3}{2}-10 \ \ \ \boxed{transform \  \sqrt{x} =x^{ \frac{1}{2} }}  \\  \\  Differentiating \\  \\ y'=12. \frac{1}{2}.x^{ \frac{1}{2}-1 } -1.x^{1-1}. \frac{3}{2}-0 \\  \\  y'=6.x^{ -\frac{1}{2} } -x^{0}. \frac{3}{2} \\  \\  y'=6. \frac{1}{x^{ \frac{1}{2} }}  -1. \frac{3}{2}  \\  \\  \boxed{y'=\frac{6}{ \sqrt{x} }  -\frac{3}{2}}

If you want to know where the tangent has no slope:

\frac{6}{ \sqrt{x} } - \frac{3}{2} =0 \\  \\  \frac{6}{ \sqrt{x} } = \frac{3}{2}  \\  \\ 3 \sqrt{x} =12 \\  \\  \sqrt{x} = \frac{12}{3}  \\  \\  \sqrt{x} =4 \\  \\   (\sqrt{x})^2 =4^2 \\  \\ x=16
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How about the water in tank B?

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6 + 3 × [2x - 12x + 8]

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-30x + 24

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Two teams of movers are lowering a piano from the window of a 10 floor apartment building. The rope breaks when the piano is 30
GuDViN [60]

By solving the motion equations for the piano, we will see that they have 0.7 seconds to react.

<h3>How to find the motion equation for the piano.</h3>

So the piano is in a free fall from a height of 30m.

The motion equations will be given by:

  • The only force acting on the piano will be the gravitational one, thus the acceleration of the piano is the gravitational acceleration: a(t) = -9.8m/s^2 (Where the negative sign is because it is falling down).
  • To get the velocity we integrate over time, because the piano has no initial velocity, the constant of integration is zero: v(t) = (-9.8m/s^2)*t
  • To get the position equation we integrate again, here the initial position is 30 meters above the ground, so that will be our constant of integration: p(t) = (1/2)*(-9.8m/s^2)*t^2 + 30m

<h3>How long takes to fall?</h3>

We want to find the value of t such that the position is equal to zero, so we need to solve:

0 = (1/2)*(-9.8m/s^2)*t^2 + 30m

30m = (1/2)*(9.8m/s^2)*t^2

2*30m/(9.8m/s^2) = t^2

6.1 s^2 = t^2

√(6.1 s^2) = 2.5s = t

This means that the piano falls to the ground in 2.5 seconds.

But the workes notice it when the piano is 14 meters above the ground, it happens when:

p(t) = 14m =  (1/2)*(-9.8m/s^2)*t^2 + 30m

Solving that we get:

30m - 14m =  (1/2)*(9.8m/s^2)*t^2

2*16m/(9.8m/s^2) = t^2

3.27s^2 = t^2

√(3.27s^2) = t = 1.8s

So the piano falls in 2.5 seconds, and the works notice it 1.8 seconds after it starts falling, meaning that they have:

2.5 - 1.8 = 0.7 seconds to react.

If you want to learn more about motion equations, you can read:

brainly.com/question/2473092

4 0
2 years ago
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