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shutvik [7]
3 years ago
8

An umbrella sprinkler is positioned on a ceiling at a point whose x- coordinate is 0. Negative values of a indicate distances, i

n meters, to the left of the position of the sprinkler, and positive values indicate distances to the right. The path of water from the sprinkler can be modeled by the quadratic function
w(x) = -1/4(x^2 -12 ) where w(x) is the height of the water, in meters, at position x.

Required:
Which equivalent expressions displays the height of the ceiling as a constant or coefficient?
Mathematics
1 answer:
vodka [1.7K]3 years ago
8 0

Answer:

-1/4x² + 3

Step-by-step explanation:

Given that:

Path of sprinkler is modeled by the quadratic function :

w(x) = -1/4(x^2 -12 )

w(x) = height of the water, in meters, at position x

The height of ceiling as a constant or Coefficient = w(x)

Expanding w(x)

-1/4(x^2 -12 )

-1/4 * x² + 1/4 * 12

-1/4x² + 3

The height of ceiling is -1/4x² + 3

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80 Hundreds = ____ Thousandths
allsm [11]
The answer would be 0.8, because 800 hundreds go into 8 thousandths, but there is only 80 hundreds, so the answer is 0.8 thousandths.
Answer: 0.8 thousandths

PLZ MARK MINE THE BRAINLIEST ANSWER!!!
3 0
3 years ago
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) afte
Vlad1618 [11]

A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

<h3>What is a quadratic equation?</h3>

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The complete question is:

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is  16 feet. Round your answer(s) to the nearest hundredth.

The time at which the height of the ball is 16 feet can be found by,

h = 2 + 31t - 16t²

16 = 2 + 31t - 16t²

16 - 2 - 31t + 16t² = 0

16t² - 31t + 14 = 0

t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\

t = 0.717 , 1.221

Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

Learn more about Quadratic Equations:

brainly.com/question/2263981

#SPJ1

4 0
2 years ago
A linear function and its inverse are given.
jarptica [38.1K]

Answer:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13        for the function.

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4         for the inverse.

Step-by-step explanation:

we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:

g(y) = x.

now we have

y=4x-3

y=(1/4)x+3/4

The only table that works for our first function is:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13

You can see this by replacing the values of x and see if the value of y also coincides.

Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.

The second table is that one:

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4

7 0
2 years ago
Read 2 more answers
1.
DaniilM [7]
Um answer f I don’t know math I’m really bad at it
7 0
2 years ago
Match each scenario involving projectile motion with the equation that describes the height of the object at time t. Tiles h = -
olga55 [171]

Answer:

  1. h = -16t^2 + 73t + 5
  2. h = -16t^2 + 5
  3. h = -4.9t^2 + 73t + 1.5
  4. h = -4.9t^2 + 1.5

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.

_____

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)

_____

<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).

4 0
3 years ago
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