Geometry! Find the length of the short leg

a model rocket is launched from the ground with an initial velocity of 60 feet per second. the function g(t)= -16t^2 + 60t repre

Lemur [1.5K]

If we use our trusty ti's this will be a breeze
domain is the numbers we can use
obviously we can't have negative time so therefor the domain is all positive integers (0,1,2,2.3, 3/2,3,pi...)

zeroes is when you set absolute max using ti is
remember vertex form which is
max height of something in
ax^2+bx+c form is -b/2a
-16t^2+60t+0
a=-16
b=60
-60/(2 times -16)
-60/-32=30/16=15/8=1 and 7/8 so subsitute for t
g(15/8)=-16(15/8)^2+60(15/8)=225/4=56.25=max height

zeroes is when the equation equals 0
so set it to zero
0=-16t^2+60t
factor
0=(-4t)(4x-15)
set each to zero
-4x=0
x=0
4x-15=0
add 15
4x=15
divid 4
x=15/4
so the zeros are t=0 and t=15/4

domain is all the nuumbers that can be used logically for time
logically, we cannot have negative time, so all real positive
[0,∞)
(that means from 0 to infinity includng 0 so 0<t<∞))

range is the output
output=height
we find the min height and max height
min=0
max=56.25
so range=0 to 56.25 or
[0,56.25]

max height=56.25 ft (15/8 seconds)
zeroes=0 sec and 15/4 sec
domain=all real positive numbers including zero or [0, ∞)
range=[0,56.25]

3 0

3 years ago

Heather is looking at different options for retirement investing. She finds an IRA that will pay 5% interest on the balance ever

mezya [45]

The formula is
A=p (1+r)^t
A the amount ones she retires ?
P amount invested 5000
R interest rate 0.05
T time 20 years
A=5,000×(1+0.05)^(20)
A=13,266.49

8 0

3 years ago

Read 2 more answers

Let A = {x : 2x² + 3x - 2 = 0} and B = {x : x² + 3x - 4 = 0 } find (A U B) × (A Π B)

ivann1987 [24]

Given :

A = {x: 2x² + 3x - 2 = 0 }
B = {x : x² + 3x - 4 = 0 }

To find :

(A U B ) × (A Π B )

Solution :-

The first set is ,

A ={x : 2x² + 3x - 2 = 0}

Solving the Quadratic equation ,

2x² + 3x - 2 = 0
2x² + 4x - x - 2 = 0
2x( x + 2) -1( x + 2 ) = 0
(2x -1) ( x + 2) = 0
x = 0.5 , -2

Hence ,

A ={0.5, -2}

The second set is ,

B ={ x :x² + 3x - 4 = 0 }

Solving the Quadratic equation ,

x² + 3x - 4 = 0
x² + 4x - x - 4 = 0
x( x + 4)-1 ( x +4) = 0
(x + 4) ( x -1) = 0
x = 1 , -4

Hence ,

B ={1,4}

Now ,

A U B = { 0.5 , 1 , 4 , -2}
A Π B = {∅ }

Since AΠ B is a null set , hence ,

A × B = {∅}

8 0

3 years ago

Solve the inequality. q/3 < 11

castortr0y [4]

Answer:

$q < 33$

Step-by-step explanation:

$q < 11 \times 3$

$q < 33$

<h3>Hope it is helpful....</h3>

8 0

3 years ago

Read 2 more answers

AC = 3x -8, BC = -7 + 2x, and AB = 8. Find BC.

Rainbow [258]

Answer:

AB+BC+AC=180°

8 - 7 + 2x +3x -8= 180°

-7+5x=180°

x=180°+7/5

x=37.4°

again

BC=-7+2*37.4

=67.8°

4 0

1 year ago