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4 years ago

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Two circles are drawn in a 12-inch by 14-inch rectangle. Each circle has a diameter of 6 inches. If the circles do not extend be

yond the rectangular region, what is the greatest possible distance (in inches) between the centers of the two circles?

1 answer:

Dennis_Churaev [7]4 years ago

6 0

Answer:

d = 10 inch

Explanation:

The farthest distance between the centers, is along the diagonal of the rectangle. Therefore, we need to calculate the diagonal of the rectangle, but counting the fact that we have both circles.

So if, one side is 12 inch, and the other is 14 inch, we can use the Pitagoras theorem which is:

d = √(a²) + (b)²

Where a and b, are the lenght of the rectangle, but without the lenght of the diameter of both circles.

With this, the expression is this:

d = √(14 - 6)² + (12 - 6)²

d = √64+36

d = √100

d = 10 inches

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Answer:

$t_t=4.131\ s$

Explanation:

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$u_y=u.\sin\theta$

$u_y=40\times \sin30^{\circ}$

$u_y=20\ m.s^{-1}$

During the course of ascend in height of the ball when it reaches the maximum height then its vertical component of the velocity becomes zero.

So final vertical velocity during the course of ascend:

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Using eq. of motion:

$v_y^2=u_y^2-2g.h$ (-ve sign means that the direction of velocity is opposite to the direction of acceleration)

$0^2=20^2-2\times 9.8\times h$

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<u>Now we find the time taken to ascend to this height:</u>

$v_y=u_y-g.t$

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$t=2.041\ s$

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we've total height, $h'=h+y$ $=20.4082+1$

$h'=u_y'.t'+\frac{1}{2} g.t'^2$

during the course of descend its initial vertical velocity is zero because it is at the top height, so $u_y'=0\ m.s^{-1}$

$21.4082=0+4.9t'^2$

$t'=2.09\ s$

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3 years ago

42,43 and 44 please

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and the direction is in between the two original directions, therefore south-east. So, the correct answer is
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43) Since the light moves by uniform motion, we can calculate the distance corresponding to one light year by using the basic relationship between velocity, space and time. In fact, we know the velocity:
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$t=32,000,000 s=3.2 \cdot 10^7 s$
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Therefore, the correct answer is D.

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This question involves the concepts of the law of conservation of energy and kinetic energy.

The girl's fastest speed is "3.7 m/s".

According to the law of conservation of energy, the girl will have the fastest speed at mean position, which will be calculated as follows:

Loss in Potential Energy = Gain in Kinetic Energy

$mg\Delta h=\frac{1}{2}mv^2\\\\v=\sqrt{2g\Delta h}$

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Therefore,

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<u></u>

Learn more about the Law of Conservation of Energy here:

brainly.com/question/381281?referrer=searchResults

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2 years ago