Mathematics, 02.07.2019 08:30 ansley81

1.) what is the equation of the path of firework #1? write your equation in general form. 2.) what is the equation of the path of firework #2? write your equation in vertex form. 3.) what is the domain and range of firework #1?

Answers: 1

Show answers

Answers

Answer from: annikafischer

The path of the fireworks is the path of a projectile and are therefore

parabolic.

The correct responses are;

1.) The equation in general form is; f(x) = 10·x - 0.5·x²

2.) Equation of the path of firework #2 is; f(x) = -0.5·(x - 10)² + 72

3.) The domain of firework #1 is; 0 ≤ x ≤ 20

The range of firework #1 is; 0 ≤ f(x) ≤ 50

Reasons:

1.) The given parameters for the firework #1 are;

Coordinates of the vertex = (10, 50)

Shape of the path = Parabolic

Required:

Equation for the path of firework #1.

Solution:

The vertex form of a quadratic equation is presented as follows;

f(x) = a·(x - h)² + k

Where;

The vertex = (h, k)

Therefore, when f(20) = 0, we get;

f(20) = 0 = a·(20 - 10)² + 50 = 100·a + 50

$a = -\dfrac{50}{100} = -\dfrac{1}{2}$

Which gives;

$f(x) = -\dfrac{1}{2} \cdot (x - 10)^2 + 50 = -\dfrac{1}{2} \cdot x^2 +10 \cdot x = 10\cdot x - 0.5 \cdot x^2$

Height = f(x) = 10·x - 0.5·x²

2.) The equation of the second firework is given as follows;

The vertex of the firework = (10, 72)

f(x) = a·(x - h)² + k

Therefore;

f(x) = a·(x - 10)² + 72

when f(22) = 0, we get;

f(22) = 0 = a·(22 - 10)² + 72 = 144·a + 72

$a = -\dfrac{72}{144} = -\dfrac{1}{2}$

The equation of the path of the firework in vertex form is therefore;

$f(x) = -\dfrac{1}{2} \cdot (x - 10)^2 + 72$

f(x) = -0.5·(x - 10)² + 72.

3.) The domain and range of firework one #1 is given as follows;

The domain = 0 ≤ x ≤ 20

The range of firework #1 is therefore;

0 ≤ f(x) ≤ 50

Learn more here:

Answer from: Catgirl7060

1. I'm assumig that the paths are perfect parabolas

this means that their general forms can be written in y=ax^2+bx+c

it's easier to find vertex form first then expand to get general form

vertex form is y=a(x-h)^2+k where the vertex is (h,k) and a is a constant

firework #1

vertex is (10,50), so (h,k)=(10,50) and h=10, k=50

h_1=a(t-10)^2+50

to find the value of , subsitute another point

(0,0)

0=a(0-10)^2+50)

0=100a+50

$a=\frac{-1}{2}$

so the equation in vertex form is $h_1=\frac{-1}{2}(t-10)^2+50$

expand to get general form

$h_1=\frac{-1}{2}(t^2-20t+100)+50$

$h_1=\frac{-1}{2}t^2+10t-50+50$

$h_1=\frac{-1}{2}t^2+10t$

same as last time

vertex is (10,72) so (h,k)=(10,72) so h=10 and k=72

equation is h_2=a(t-10)^2+72

find

use another point

(0,22)

22=a(0-10)^2+72

22=100a+72

-50=100a

$a=\frac{-1}{2}$

so the equation in vertex form is $h_2=\frac{-1}{2}(t-10)^2+72$

range is the numbers that h is allowed to be

think about what h represents. it represents the height of the rocket

from the graph, we can see that the lowest possible height is 0yd and the highest height is 50yd

so range is 0 to 50 or 0≤h≤50

domain is the numbers that t is allowed to be

think about what t represents. it represents how long the rocket has been flying

it will stop flying when it hits the ground or at t=20

it starts flying at t=0

so domain is from 0 to 20 or 0≤t≤20

Answer from: Quest

segment bisector

step-by-step explanation:

line segment bisector. definition: a line, ray or segment which cuts another line segment into two equal parts. try this drag one of the orange dots at a or b and note the the line ab always divides the line pq into two equal parts.

mark brainliest!

Answer from: Quest

step-by-step explanation:

idk

i know the way

and

idk

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 23:30, cranfordjacori

Ateam of runners is needed to run a 1 2 -mile relay race. if each runner must run 1 4 mile, how many runners will be needed?

Answers: 3

continue

Mathematics, 22.06.2019 02:30, fr996060

(2, 4) (2, 1) (6, 12) (4, -5) (-2, 4) |(2, -4) (6, -12) (-4,5) quadrilateral abcd is reflected over the x-axis. quadrilateral abcd is translated 2 units right and 1 unit down. quadrilateral abcd is dilated by a scale factor of 3. quadrilateral abcd is rotated 180° clockwise about the origin. reset next

Answers: 3

continue

Mathematics, 22.06.2019 04:30, lilgetald

329 people went to an amusement park. $906 was made that day. $1.5 per kid. $4 per adult. how many kids and adults went?

Answers: 1

continue

Mathematics, 22.06.2019 04:50, carlosatniel47

Q.1 dr. frank needs to choose 3 students from her advanced biology course to attend a conference in hawaii. the course has 40 students. which of the following methods could dr. frank use to choose a simple, random sample of 3 students? select all that apply. 1 dr. frank could have the students line up from shortest to tallest, then use her birthdate, 2/5/39, to select 3 students from the line (the 2nd student, the 5th student, and the 39th student). 2. dr. frank could upload her class roster into a spreadsheet and use a ranom-number generating function to produce 3 random numbers. the students whose names are located in the rows with these 3 numbers on the spreadsheet would be chosen. 3. dr. frank could choose the students with the 3 highest grades in the class. 4. dr. frank could count to three, then the first students to come to the front of the classroom and grab a golden ticket from her hand would be selected. 5. dr. frank could ask all students to write their name on a card, place all of the cards in a hat, shake the hat, and then pull 3 cards out from the hat. the students whose names appear on those 3 cards will be selected. 6. dr. frank could ask for volunteers to go to the conference, then choose the first 3 students who raise their hands. q2. now, choose one of the methods that you did not select and explain why this method would not result in a simple, random sample:

Answers: 2

continue

You know the right answer?

1.) what is the equation of the path of firework #1? write your equation in general form. 2.) what...