Mikala initially launches a toy rocket from a height of 3 feet above the ground. After 2 seconds, the rocket reaches its highest point of 11 ft and then returns to
the ground
.
• Create a model that can be used to determine the height of the toy rocket at a given time. Define your variables and show your work or explain how your
equation models the situation.
• Use the model to determine at what time the toy rocket will land on the ground. Show your work or explain your answer.
Enter your answers and explanations in the box.

Answers

Answer 1
Given the vertex, the model is given by:

[tex]y = -2x^2 + 8x + 3[/tex]

Using the model above, it is found that it lands on the ground after 4.35 seconds.

The equation of a quadratic function of vertex (h,k) is given by:

[tex]y = a(x - h)^2 + k[/tex]

The vertex is the maximum point, which is (2,11), hence [tex]h = 2, k = 11[/tex]. Then:

[tex]y = a(x - 2)^2 + 11[/tex]

The initial height is of 3 feet, then when [tex]x = 0, y = 3[/tex], and this is used to find a.

[tex]y = a(x - 2)^2 + 11[/tex]

[tex]3 = 4a + 11[/tex]

[tex]4a = -8[/tex]

[tex]a = -\frac{8}{4}[/tex]

[tex]a = -2[/tex]

Then:

[tex]y = -2(x - 2)^2 + 11[/tex]

In standard format, the model is:

[tex]y = -2x^2 + 8x - 8 + 11[/tex]

[tex]y = -2x^2 + 8x + 3[/tex]

It hits the ground when [tex]y = 0[/tex], so:

[tex]-2x^2 + 8x + 3 = 0[/tex]

[tex]2x^2 - 8x - 3 = 0[/tex]

Which has coefficients [tex]a = 2, b = -8, c = -3[/tex]. So

[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(-3) = 88[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + sqrt{88}}{4} = 4.35[/tex]

[tex]x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - sqrt{88}}{4} = -0.35[/tex]

Time is positive, so it lands on the ground after 4.35 seconds.

A similar problem is given at https://brainly.com/question/17987697


Related Questions

plsss help me with this:(((​

Answers

Answer:

[tex] \frac{2 {a}^{2} }{3 {b}^{3} } \div \frac{6 {a}^{3} }{5 {b}^{2} } = \frac{2 {a}^{2} }{3 {b}^{3} } \times \frac{5 {b}^{2} }{6 {a}^{3} } = \frac{5}{9ab} \\ \\ \frac{ {x}^{2} - 5x + 6}{ {x}^{2} - 6x + 9} + \frac{4x - 12}{{x}^{2} - 6x + 9} \\ = \frac{{x}^{2} - 5x + 6 + 4x - 12}{{x}^{2} - 6x + 9} \\ = \frac{{x}^{2} - x - 6}{{x}^{2} - 6x + 9} \\ = \frac{(x - 3)(x + 2)}{(x - 3)(x - 3)} \\ = \frac{(x + 2)}{(x - 3)} \\ \\ \frac{3a}{a - b} - \frac{a + 2b}{a - b} \\ = \frac{3a - a + 2b}{a - b} \\ = \frac{2a - 2b}{a - b} \\ = 2\frac{a - b}{a - b} \\ = 2[/tex]

Tổng các góc của tứ giác bằng bao nhiêu

Answers

Answer:

tổng các góc của tứ giác bằng 360 độ

Step-by-step explanation:

ha? what language is that?

50 POINT QUESTION!!!!
f(x)=12x^(2)+4x-5

find the zeroes of the function...

Answers

Answer is in picture below

:)

FRANK has a paper clip.it has a mass of 9g and a volume of 3cm3.what is its density?

Answers

Answer:

3 g/cm³

Step-by-step explanation:

The density of a substance can be found by using the formula

[tex]density = \frac{mass}{volume} \\[/tex]

From the question we have

[tex]density = \frac{9}{3} = 3 \\ [/tex]

We have the final answer as

3 g/cm³

Hope this helps you

Please help me solve this ASAP please !

Answers

This is a Reflection :) Have a great day !

Reflection because it is the same just flipped over the line, and all the points are the same.

A dog kennel charges a daily boarding rate as shown on the graph. use the information to mark 5-8 as true or false. if false, rewrite the statement correctly. 1. The dog kennel charges $60 per day. 2. The equation y = 30x can represent the graph. 3.Third is It costs $200 to board a dog for 7 days 4. The graph will contain the coordinate (9,270) Please give me all answers to all questions or i will go into trouble

Answers

The relationship between the cost charged for the daily boarding of dogs

by the kennel is a directly proportional relationship.

The correct responses are;

1. The dog kennel charges $60 per day is; False

Correct statement; The dog kennel charges $30 per day

2. The equation y = 30·x can represent the graph; True

3. It costs $200 to board a dog for 7 days is; False

Correct statement; It costs $210 to board a dog for 7 days

4.The graph will contain the coordinate point (9, 270); True

Reasons:

Points on the graph of the given graph of the Cost to Number of days are;

(2, 60), (4, 120)

The slope of the graph is [tex]m = \dfrac{120 - 60}{4 - 2} = 30[/tex]

Equation of the graph is therefore; y - 60 = 30·(x - 2)

Which gives;

y  = 30·x - 2×30 + 60 = 30·x

The equation of the graph is; y = 30·x

Therefore, the statement;

2. The equation y = 30·x can represent the graph is; True

The cost of the dog kennel a day is given by the value of 'y', when x = 1, as

follows;

Cost per day, y = 30 × 1 = 30

The cost per day = $30 per day

Therefore;

1. The dog kennel charges $60 per day is; False

The correct statement is; The dog kennel charges $30 per day

3. The statement; It costs $200 to board a dog for 7 days is; False

The amount it costs to board a dog for 7 days is y = $30×7 = $210

Therefore, the correct statement is; It costs $210 to board a dog for 7 days

4. When x = 9, we have; y = 30 × 9 = 270

Therefore, the statement; the graph will contain the coordinate point (9, 270) is; True

Learn more here:

https://brainly.com/question/5281177

Can y'all help me this question ASAP this all I need

Answers

5/8x + 1/5x can be written with a common denominator:
25/40x+ 8/40x = 99

This can be simplified to:
33/40x = 99

Next times both sides by 40
33x = 3960

Then, divide both sides by 33
x = 3960/33
x = 120

WILL GIVE BRAINLIEST TO ANSWER

Answers

Answer:

A , D , E

Step-by-step explanation:

Substitute x = 2 into f(x) and check if the result is 4

(a)

f(2) = 2² = 4 ← then f(2) = 4

(b)

f(2) = 2 + 6 = 8 ≠ 4

(c)

f(2) = 4(2) + 2 = 8 + 2 = 10 ≠ 4

(d)

f(2) = 2² = 4 ← then f(2) = 4

(e)

f(2) = 8(2) - 12 = 16 - 12 = 4 ← then f(2) = 4

Find the slope of the line
(18, 7) (8, 10)

Answers

Answer -.3

So what I did was subtract 10-7 which is 3 then subtract 8-18 which is -10 then divide 3 divide by -10 and you get -.3

Mathematics Ratio
Help plz​

Answers

Answer:

480

Step-by-step explanation:

Check out the solution

how would I solve this??

Answers

Answer:

y = 140

Step-by-step explanation:

you'd do:

y=25(7)-35

y=175-35

y=140

to double-check your math:

140 = 25(7)-35

both sides will equal 140 (or the same value) if done properly

Taylor has $150 to spend on small canvases and paints for her art classes. The art supply store sells a four-pack
of small canvases for $4.00 and paints for $6.25, including tax.
Which inequality represents this situation where is the number of four-packs of canvases and p is the number of
paints Taylor purchases?
O4c+ 6.25p < 150
O 40+ 6.25 > 150
O 6.25c+ 4p > 150
O 6.25c +4p < 150

Answers

Answer:A

Step-by-step explanation:

C. Directions: Copy and answer. Write in the circle the final sum of
the given number.
1.
98
2.
40
3.
123
-13
47
150
70
1180
-59
321
1-300
다.
1
5.
1326
6.
109
66
11-51
39
139
7
7433
88
77​

Answers

Answer:

98

Step-by-step explanation:

kuisssss


hi how are you?

[tex] \sf {3}^{2} \div 9 = [/tex]

pakai cara​

Answers

Answer:

1

Step-by-step explanation:

[tex] {3}^{2} \div 9 = \\ =(3 \times 3) \div 9 \\ = 9 \div 9 \\ = 1 [/tex]

Moga Membantu ^-^

Answer:

The solution is 1

Step-by-step explanation:

3²÷9

= 9÷9

= 1

Victor has 2 times as many trophies as dean . Together, victor and Dean have 27 trophies . How many trophies does victor have?

Answers

Answer:

18

Step-by-step explanation:

9 + 18 = 27

9 x 2 = 18

express -121 in simplest form

Answers

Answer:

An expression is in simplest form when no terms can be combined. To express 3 + (2 × 5) in simplest form: First: perform the operation within parantheses. Next: perform the addition. thank me later

8 divided by 1 4/5 Arithmetic operation

Answers

Answer:

4.4

Step-by-step explanation:

Can someone please show me y=2x-2 and x=4 on a graph please. ( IF U CAN PLEASE SHOW ME WHERE THE LINES GO THROUGH EACH OTHER ON A GRAPH)

Answers

Here is the graph. Work is shown in the picture. I hope this helps.

=
?
(5
4
⋅b
−10
)
−6

Answers

[tex](5^{4} *\frac{1}{b^{10} }) ^{-6}[/tex]

[tex](\frac{5^{4} }{b^{10} } )^{-6}[/tex]

[tex]\frac{b^{60} }{5^{24} }[/tex]

I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best :D

Answers

Answer:

1. 4x=36

2. x+3 = 15

Step-by-step explanation:

so for 1 if one cupcake is $4.00 that means multiplying it by x gets you $36.00

and the 4 next to the x means multiplyand x is sam and 15 is marco sam is 3 years younger so x+3=15 and x being 12 <3 hope this helps

Find the slope of the line that passes through (10,10) and (1,2)

Answers

Answer:

8/9

Step-by-step explanation:

[tex]m = \frac{10 - 2}{10 - 1} = \frac{8}{9} [/tex]

Let f(x) = x − 3 and g(x) = x + 11. Find f(x) ⋅ g(x).

x2 − 8x − 33
x2 − 8x + 14
x2 + 8x + 14
x2 + 8x − 33

Answers

Multiply them
(x-3)(x+11)
x^2 + 11x - 3x - 33
x^2 + 8x - 33
Solution: D

Answer:

D) x^2 + 8x - 33

Step-by-step explanation:

I took the quiz and got a 100%

4/s-3 + s/2 = -2
Need help please​

Answers

Step-by-step explanation:

Given equation is 4/(s-3) + (s/2) = -2

=> [(4×2)+s(s-3)]/2(s-3) = -2

=> (8+s²-3s)/(2s-6) = -2

=> 8+s²-3s = -2(2s-6)

=> 8+s²-3s = -4s+12

=> s²-3s+8+4s-12 = 0

=> s²+s-4 = 0

The standard form is s²+s-4 = 0

Kim has no more than $500 to spend on home repairs. HandyMan Co is charging her $125 for supplies needed and $25 per hour. Write and solve an inequality to show how many hours of repair she can afford.

Answers

5 hours.

Divide the numbers.
$125 divded by $25 = 5

Answer: Kim can afford 5 hours lf repair time. (Brainlest?)

Have a good rest of your day/night!!

i’m just stuck on #6, is it d or c???

Answers

It’s D because the angles are found in the same relative position on different intersections


What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.

Step-by-step explanation:

y coordinate

m = slope

x = x coordinate

b = y intercept

Justify each step
-12p+45-7p

Answers

Answer:

Given, Associative, Commutative, Associative, Addition

Step-by-step explanation:

-12p + 45 -7p           Given

-12p + (45 - 7p)        Associative

-12p + (-7p + 45)      Commutative

(-12p + -7p) + 45     Associative

-19p + 45                Addition

A functionf(x) is graphed on the coordinate plane.


What is the function rule in slope-intercept form?



Enter your answer in the box.

f(x)=

Answers

Answer:

y = -1/2x + b  meaning f(x) = -1/2x + b

Step-by-step explanation:

Use two points on the graph that you can find the value of  or use Slope = raise/run

let use points (2,0) and (0, 1)

slope = (change in the y-value)/(change in the x-value.

slope = (1 - 0)/(0 - 2)

slope = 1/-2 or -1/2

Or starting at point (2, 0) the run(x movement) = -2 and the raise is 1.

slope = raise/run

slope =  1/-2 or -1/2

Using one point (2,0) and the slope of -1/2, substitute into the slope intersect form, y = mx + b, and solve for "b" .

y= mx + b

0 = -1/2(2) + b

0 = -1 + b

1 = b

Now write your equation: y = mx +b where m = -1/2 and b = 1

y = -1/2x +b

Kayla bought 16 bagels. Each bagel cost $1.50. She paid a total of $20. Write an equation to determine how many bagels she bought.

Answers

Answer: 16 x 1.50 = 20

I think it’s that, hope this helps

In Pedro’s rose garden, 9 of the rose bushes are blooming and the other 6 rose bushes are not blooming. what is the ratio of the number of bushes that are not blooming?

Answers

Answer:9:6

Step-by-step explanation:

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