Find the missing y-value that makes the table represent a linear function.

I needs help with it

Slav-nsk [51]

Answer:

a) initial height = 0 m

b) 8 s

c) vertex = (4, 32)

maximum height = 32 m

Step-by-step explanation:

<u>Given equation</u>:

$h=-2t^2+16t$

where:

h is the height of the arrow about the ground (in metres)
t is the time (in seconds)

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

$\implies h=-2(0)^2+16(0)$

$\implies h=0$

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

$\implies -2t^2+16t=0$

Factor out -2t:

$\implies -2t(t-8)=0$

Therefore:

$\implies -2t=0 \implies t=0$

And:

$\implies t-8=0 \implies t=8$

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the <u>turning point</u> of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is <u>negative</u>, the parabola <u>opens downwards</u> and so its <u>vertex</u> is its <u>maximum point</u>.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

$\implies h=-2(4)^2+16(4)$

$\implies h=-32+64$

$\implies h=32$

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

6 0

1 year ago

Killian went to the movies with his mother, 2 brothers, and 2 sisters. The theater had choices of 2 different types of soda and

bazaltina [42]

Yeshhh it is possible !

7 0

2 years ago

It takes a barber 12 minutes to shave a face and 30 minutes to give a haircut. The barber works for 6 hours straight and spends

Mrrafil [7]

Answer:

7 customers

Step-by-step explanation:

7 0

2 years ago

The volume of a tree stump can be modeled by considering it as a right cylinder. Justin measures its circumference as 84 in and

lions [1.4K]

Given the values of the circumference and volume, the height of the tree trump to the nearest tenth is 36.0in.

<h3>What is a cylinder?</h3>

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

Circumference of the circular base C = 84in

Volume of the cylinderical tree stump V = 20214in³

First we determine the radius of the circular base.

Since circumference C = 2πr then r = C / 2π.

Hence, the volume of the cylinderical tree stump will be;

V = π × (C / 2π)² × h

V = π × ( C² / 4π² ) × h

V = hC² / 4π

4πV = hC²

h = 4πV / C²

We substitute our given values into the expression

h = ( 4 × 3.14 × 20214in³ ) / (84in)²

h = 253887.84in³ / 7056in²

h = 36.0in

Therefore, given the values of the circumference and volume, the height of the tree trump to the nearest tenth is 36.0in.

Learn more about volume of cylinder here: brainly.com/question/16788902

#SPJ1

7 0

2 years ago

Find x please. Pick any of the choices

garri49 [273]

Answer:

I believe it is 75

Step-by-step explanation:

The total sum of the shape is 360 and since we know that one of them is 60 we can subtract 60 from 360 leaving you with 300. Now with 4 points left you need to divide 300 by 4, which would give you 75. If you want to check, you can do 75x4+60 which should be 360 :)

3 0

2 years ago