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velikii [3]
3 years ago
10

What is the arc measure of DBC in degrees?

Mathematics
1 answer:
Arisa [49]3 years ago
8 0
<h2>Answer:</h2><h2 />

In this context:

\boxed{\angle DBC=x=60^{\circ}}

<h2>Explanation:</h2>

Hello! Remember to write complete questions in order to get good and exact answers. Here the figure is missing so I'll assume the arc measure of DBC is given in radian and you want it in degrees. By definition, an arc's measure is <em>the measure of its central angle </em>being a central angle an <em>angle between two radii in a circle</em>. Suppose that angle measures:

\angle DBC=\frac{\pi}{3}\ radian \\ \\ \\ So, \ by \ rule \ of \ three: \\\\ \\ \pi \ radian \rightarrow 180 \ degrees \\ \\ \pi/3 \ radian \rightarrow x \ degrees \\ \\ \\ x =\frac{180\pi}{3\pi}=60^{\circ} \\ \\ \\ Finally: \\ \\ \boxed{\angle DBC=x=60^{\circ}}

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A man hits a baseball when it is 4 ft above the ground with an initial velocity of 120 ft/sec. The ball leaves the bat at a 30 d
Sauron [17]
<span>et us assume that the origin is the floor right below the 30 ft. fence

To work this one out, we'll start with acceleration and integrate our way up to position.

At the time that the player hits the ball, the only force in action is gravity where: a = g (vector)
ax = 0
ay = -g (let's assume that g = 32.8 ft/s^2. If you use a different value for gravity, change the numbers.

To get the velocity of the ball, we integrate the acceleration
vx = v0x = v0cos30 = 103.92
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To get the positioning, we integrate the speed.
x = v0cos30t + x0 = 103.92t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + 60t + 4

If the ball clears the fence, it means x = 0, y > 30

x = 0 -> 103.92 t - 350 = 0 -> t = 3.36 seconds

for t = 3.36s,
y = -16.4(3.36)^2 + 60*(3.36) + 4
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which is less than 30ft, so it means that the ball will NOT clear the fence.


Just for fun, let's check what the speed should have been :)

x = v0cos30t + x0 = v0cos30t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + v0sin30t + 4

x = 0 -> v0t = 350/cos30
y = 30 ->
-16.4t^2 + v0t(sin30) + 4 = 30
-16.4t^2 + 350sin30/cos30 = 26
t^2 = (26 - 350tan30)/-16.4
t = 3.2s

v0t = 350/cos30 -> v0 = 350/tcos30 = 123.34 ft/s

So he needed to hit the ball at at least 123.34 ft/s to clear the fence.

You're welcome, Thanks please :)
</span>
6 0
3 years ago
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