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Zanzabum
3 years ago
7

Solve for x x^2+3x<28

Mathematics
1 answer:
Klio2033 [76]3 years ago
6 0
X² + 3x < 28
x² + 3x - 28 < 0
(x+7)(x-4) < 0

the zeros will be at x = -7  and x =4

∴ the solution of inequality
x ∈ (-7,4)

See the attached figure



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Match each scenario involving projectile motion with the equation that describes the height of the object at time t. Tiles h = -
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Answer:

  1. h = -16t^2 + 73t + 5
  2. h = -16t^2 + 5
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Step-by-step explanation:

The general equation we use for ballistic motion is ...

  h(t)=\frac{1}{2}gt^2+v_0t+h_0

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)

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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).

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Which best describes the orthocenter of a triangle?
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