HEY!!! YES, YOU!!! WANNA HELP OUT A FELLOW SUFFERING VICTIM OF MATH? NOWS YOUR CHANCE!!! PLEASE HELP! 10 PTS!!!
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Answer:
- h = -16t^2 + 73t + 5
- h = -16t^2 + 5
- h = -4.9t^2 + 73t + 1.5
- h = -4.9t^2 + 1.5
Step-by-step explanation:
The general equation we use for ballistic motion is ...
where g is the acceleration due to gravity, v₀ is the initial upward velocity, and h₀ is the initial height.
The values of g commonly used are -32 ft/s², or -4.9 m/s². Units are consistent when the former is used with velocity in ft/s and height in feet. The latter is used when velocity is in m/s, and height is in meters.
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Dwayne throws a ball with an initial velocity of 73 feet/second. Dwayne holds the ball 5 feet off the ground before throwing it. (h = -16t^2 + 73t + 5)
A watermelon falls from a height of 5 feet to splatter on the ground below. (h = -16t^2 + 5)
Marcella shoots a foam dart at a target. She holds the dart gun 1.5 meters off the ground before firing. The dart leaves the gun traveling 73 meters/second. (h = -4.9t^2 + 73t + 1.5)
Greg drops a life raft off the side of a boat 1.5 meters above the water. (h = -4.9t^2 + 1.5)
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<em>Additional comment on these scenarios</em>
The dart and ball are described as being launched at 73 units per second. Generally, we expect launches of these kinds of objects to have a significant horizontal component. However, these equations are only for <em>vertical</em> motion, so we must assume the launches are <em>straight up</em> (or that the up-directed component of motion is 73 units/second).
Answer:
Step-by-step explanation:
The opposite angles in a quadrilateral theorem states that when a quadrilateral is inscribed in a circle, the angles that are opposite each other are supplementary, their degree measures add up to 180 degrees. One can apply this here by using the sum of (<C) and (<A) to find the measure of the parameter (z). Then one can substitute in the value of (z) to find the measure of (<B). Finally, one can use the opposite angles in a quadrilateral theorem to find the measure of angle (<D) by using the sum of (<B) and (D).
Use the opposite angles in an inscribed quadrialteral theorem,
<A + <C = 180
Substitute,
14x - 7 + 8z = 180
Simplify,
22z - 7 = 180
Inverse operations,
22z = 187
z =
Simplify,
z =
Now substitute the value of (z) into the expression given for the measure of angle (<B)
<B = 10z
<B = 10()
Simplify,
<B = 85
Use the opposite angles in an inscribed quadrilateral theorem to find the measure of (<D)
<B + <D = 180
Substitute,
85 + <D = 180
Inverse operations,
<D = 95