A model rocket is launched from the roof of a building. Its flight path is modeled
by h = -5t^2 +30t +10 where h is the height of the rocket above the ground in
metres and r is the time after the launch in seconds.
What is the rocket's maximum height?

Answers

Answer 1

Answer:

55

Step-by-step explanation:

This is the equation of a parabola. To make things simpler, we can replace [tex]h[/tex] with [tex]y[/tex] and [tex]t[/tex] with [tex]x[/tex]. Therefore, [tex]y=-5x^2+30x+10[/tex]. Because the coefficient of the [tex]x^2[/tex] term is negative, we know the parabola points down, and the maximum height is the vertex. The x coordinate of the vertex of a parabola can be found with the equation [tex]-\frac{b}{2a}[/tex], or [tex]-\frac{30}{-10} = 3[/tex]. Plugging in [tex]3[/tex] into the equation gives us [tex]y = -5(3)^2+30(3)+10 = \boxed{55}[/tex]


Related Questions

Find the value of x.

(9x + 1)
(11x – 23)

Answers

the answer to the question is x=12

Nathan received a package for his birthday the package wait $5,910,000 milligrams select the conversions that are equivalent to 5,910,000. Mark all that apply.
59,100 kilograms
59.1 centigrams
591,000 centigrams
5.91 kilograms

Answers

Answer:

5.91 kilograms

591,000 centigrams

Step-by-step explanation:

These two are WRONG:

59,100 kilograms

59.1 centigrams

Helpp me PlzzzzzZZzz

Answers

Answer: B. Distributive Property

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Distributive Property  

In five years, Angela will be the age that Khalil is now. In three years, Khalil will be twice as old as Angela. How old is each now?

Answers

Answer:

so how you would wNt to go about this is we dont know tge ages so youd use variables

Answer:

Khalil is 7 years old. Angela is 2 years old.

Step-by-step explanation:

I hope this helps

Rotation is a ______?

A. Spin or turn
B.slide
C.mirror or flip
D.move

HURRY PLEASE

Answers

Answer:

A) Spin or turn

Step-by-step explanation:

Acell phone company charges $3.00 to make a phone call plus $0.15 for
each minute for each minute you talk. Which equation would you use to
determine the total cost, c, of a phone call that is m number of minutes
long?
C=0,15 - 300m c-3.00 -0.15m
3.00 = € + 0,19
C = 3,00 + 0.15m

Answers

Answer:

Hi there!

Your answer is:

3+.15m =c

I cannot read your answer choices, but that is your answer. I believe your answer choice that matches is the lowest one; C= 3,00 +.15m

Hope this Helps

Which equation represents the graph shown?

Answers

Step-by-step explanation:

The graph is a linear equation starting at 0.

form y = mx + b.

starts at 0, so b = 0, so the 2nd and 3rd choices are incorrect.

change in y/change in x is the slope,

and you can see it goes up about 35 in the y direction for every 1 in the x, so the slope is 35.

so it's the first answer.

The linear equation of the graph is y = 35x. So, the option first is correct.

What is a linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form y = mx + b.

The graph is a linear equation origin at 0.

Since b = 0, the 2nd and 3rd choices are incorrect.

The slope = change in y/change in x

Here, we can see that it goes up about 35 in the y-direction for every 1 unit of in the x, so the slope is 35.

so the first answer is correct which is y = 35x.

Learn about linear equations here:

brainly.com/question/11897796

four pumpkins weigh 26 pounds altogether. Pumkin one weighs four less than three times the weight of Pumkin threee. Pumkin four weighs twice as much as pumkin One. Pumpkin Two weighs five more pounds than Pumkin three. What does each pumpkin weigh

Answers

Answer:

5, 8, 3, 10 lbs.

Step-by-step explanation:

We can solve this using a system of equations! We will call pumpkins [tex]a, b, c, d[/tex].

Our equations are thus:

[tex]a + b + c + d = 26[/tex]

[tex]a = 3c - 4[/tex]

[tex]d = 2a[/tex]

[tex]b = c + 5[/tex]

So now we just need to solve this system of equations.

We can start by solving for the value of pumpkin [tex]c[/tex] and go from there. So first we substitute some equations around.

First we write out pumpkin [tex]d[/tex] in terms of [tex]a[/tex].

[tex]d = 2a = 2(3c - 4) = 6c - 8[/tex]

And now we put the three equations into the first equation:

[tex]a + b + c + d = 26\\(3c-4)+(c+5)+(c)+(6c-8)=26[/tex]

Then we simplify to get:

[tex]11 c - 7 = 26[/tex]

[tex]11c = 33\\c = 3[/tex]

So we know pumpkin [tex]c[/tex] weighs 3 pounds.

Then we use the equations from before to get the value of the other pumpkins:

[tex]a = 3c-4 = (3*3)-4=9-4=5\\d = 2a = 2*5=10\\b = c + 5 = 3 + 5 = 8[/tex]

And we can check our results by putting into first equation:

[tex]5+8+3+10=26[/tex]

So it works out!

Thus our pumpkins weigh 5, 8, 3, 10 lbs each.

Mary is twice as old as Helen’s age, If 8 is subtracted from Helen’s Age and 4 is added to Mary Age? Mary will be 4 times as old as Helen. What are the ages

Answers

Answer:

set mary is x years old, and helen is y years old.

first sentence:x=2y

second one:4(y-8)=x+4

bring x=2y in 4(y-8)=x+4

=>4y-32=2y+4

=>2y=36

=>y=18

=>x=36

mary:36

helen:18

We want to write and solve a system of equations that models given situation. We will see that Helen is 18 years old, and Mary is 36 years old.

Let's define the variables we will be using.

m = Mary's age.h = Helen's age.

We know that "Mary is twice as old as Helen’s age"

Then:

m = 2*h

"If 8 is subtracted from Helen’s Age and 4 is added to Mary Age, Mary will be 4 times as old as Helen."

(m + 4) = 4*(h - 8)

Then the system of equations is:

m = 2*h

(m + 4) = 4*(h - 8)

To solve it, we can replace m by 2*h in the second equation, so we get:

(2h + 4) = 4*(h - 8)

2*h + 4 = 4*h - 32

4 + 32 = 4*h - 2*h

36/2 = h = 18

And we know that:

m = 2*h = 2*18 = 36

So Helen is 18 years old, and Mary is 36 years old.

If you want to learn more, you can read:

https://brainly.com/question/9351049

A government might try to reduce unemployment in order to:
A. Allow businesses to invest money more freely.
B. set limits on its own economic growth.
C. keep inflation from rising too quickly
D. make sure its people can find jobs
If you get it correct will give brainly

Answers

Answer:

Make sure people can find jobs

Step-by-step explanation:

Answer: D, Make sure it’s people can Find job’s.

Step-by-step explanation: it’s the Answer I just did the quiz.

(1 point)
Calculate the directional derivative of f(x, y) = cot-'(xy) in the direction of v = -4i + 5j at the point P = (0.5, 0.5).
Remember to normalize the direction vector.
DS(0.5, 0.5) =

Answers

Looks like f(x, y) = cot⁻¹(xy), as in the inverse cotangent.

If you're like me and you don't remember the derivative of the inverse trig functions, we can derive it as follows. Let y = cot⁻¹(x), so that for appropriate x we can write cot(y) = x. By the chain rule, differentiating both sides gives

-csc²(y) y' = 1

y' = -sin²(y) = -sin²(cot⁻¹(x)) = - 1 / (x² + 1)

Next, recall that the derivative of a function f(x, y) at a point (a, b) in the direction of a vector v is given by

f(a, b) • v

Compute the gradient ∇ f(x, y) :

f(x, y) = - y / ((xy)² + 1) i - x / ((xy)² + 1) j

At the point P, we have

f(x, y) = - 8/17 i - 8/17 j

So, the derivative of f at P along v = - 4 i + 5 j is

(- 8/17 i - 8/17 j) • (- 4 i + 5 j) = - 8/17

Can someone please help, ty!!

Answers

Answer:

(-1,0)

Step-by-step explanation:

Answer:

(-1, 0)

Step-by-step explanation:

The x-axis is the horizontal line in bold. It's basically asking what points in the form (x,y) are touching said line.

So we use our eyes and determine that the line intercepts the x-axis at -1 because that vertical bold line is the y-axis and it determines that the left side of the graph is negative and the right side is positive.  

Since it is an x-intercpet, when the y-value is 0 the y-term in

(x,y) is 0

and the x-term would be the -1

6. When you barter, you must ________
in order to buy something.

Answers

Answer:

When you barter, you must trade it for something else in order to buy something.

Step-by-step explanation:

When you barter, you must  exchange in order to buy something.

What is barter?

Barter, the direct exchange of goods or services—without an intervening medium of exchange or money—either according to established rates of exchange or by bargaining. It is considered the oldest form of commerce.

Given: A person barters

Therefore he must trade it for something else (exchange) in order to buy something.

Hence, When you barter, you must  exchange in order to buy something.

Learn more about barter here:

https://brainly.com/question/14903216

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A 3-column table with 4 rows. Column 1 has entries Computer repair, sales tax, gratuity, shipping. Column 2 is labeled Store A with entries 1,200 dollars, 6 percent, 15 percent, Free. Column 3 is labeled Store B with entries 1,350 dollars, 7 percent, 15 percent, 2 percent of total price.
How much sales tax will be charged at Store B?

Answers

Answer:

72 on edge

Step-by-step explanation:

Answer:

94.50

Step-by-step explanation:

Please see question below in picture

Answers

Your answer is going to be 6:5 as there are 6 circles and 5 triangles

find the distance between (-6,0) and (-9,-4)

Answers

Answer:

5 units

Step-by-step explanation:

d=

[tex] \sqrt{(x2 - x1}^{2} ) + \sqrt{(y2 - y1) {}^{2} } [/tex]

Twelve decreased by twice a number equals -34. What is that number?

Answers

Answer:

12 - 2x = -34

Step-by-step explanation:

Im not entirely sure if this is correct but yeee

High Hopes^^

Barry-

Number is 23 because 12-2x=-34 is equivalent to the number 24

In training for a swim meet, Logan swam 750 meters in \large \frac {1}{3}
3
1
​ of an hour. His swimming partner, Mila, swam \frac {2}{3}
3
2
​ of Logan's distance in \frac {1}{4}
4
1
​ of an hour. 2. What is Mila's average swimming speed? Show your work.

Answers

Answer:

500

Step-by-step explanation:

How far has the car gone

Answers

Answer:

uhh how am i suposed to know that u ahve o image

Add an image so I can help answer the question

Please help me I can’t figure it out

Answers

Answer:

its C.

Step-by-step explanation:

omg that took forever to solve

what is 4/9 times what equals 12

Answers

Step-by-step explanation:

4/9A = 12

A = 12×9/4

= 27

......

Simplify the following expressions ?
-9x+9x^2+8x^2+4x

Answers

Answer:

-5x+17x^2

Step-by-step explanation:

Hope that helps good luck

9514 1404 393

Answer:

  17x^2 -5x

Step-by-step explanation:

"Simplify" in this context means "combine like terms." It can help to group the terms with the same variables.

  -9x+9x^2+8x^2+4x

  = 9x^2 +8x^2 -9x +4x

  = x^2(9+8) +x(-9+4)

  = 17x^2 -5x

Solve for x. 4(x+1)= -3x-10

Answers

Answer:

4x+4=-3x-10

   4x+3x=-10-4

      x= -14

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

P.E.M.D.A.S

4(x + 1) = 4x+4

now we have 4x + 4 = -3x - 10.

now we can combine like terms which are x

4x and -3x, to combine like terms we can either subtract 4x on both sides or -3x on both sides, but lets do 4x.

now we have this

4x + 4 = -3x - 10.

-4x          -4x

= 4 = -7x - 10

now we can isolate x by its self so we have to add 10 on both sides

4 = -7x - 10

+10       +10

and we get

14 = -7x

now we can divide -7 to get x by its self

14/-7 = -7/x

we get for our final answer

x = -2

cómo se escribe el número 88,317​

Answers

Answer:

Eighty-Eight thousand three hundred seventeen

Step-by-step explanation:

Answer:

ochenta ochenta mil trescientos diecisiete

Step-by-step explanation:

No estoy seguro de lo que quiere saber. Asumo que estás preguntando cómo escribirlo en palabras. Pero todavía no estoy tan seguro. Por favor, avíseme si necesito resolverlo de otra manera.

1 2 TIME REMAIN 50:24 How could Theo check his work? Check all that apply. Theo solved n + 5 = 11 for the unknown. The steps he took are shown. He started with 5 tiles. He could substitute 5 forn in the original equation and add. He could substitute 6 for n in the original equation and add. Then he added tiles as he counted up to 11. He could subtract 5 from 11 and check that the answer is 6. He realized he added 6 more tiles to his original 5 to make 11. So he found the unknown to be 6. He could subtract 11 from 5 and check that the answer is 6. O He could put all the tiles in 1 pile to count them to see if there are 11 in all.​

Answers

Answer:

so first you do the work than check

Step-by-step explanation:

If the variance of the data values in a population is 225, what is the standard
deviation of the data values?
a.15
b.17
c.11
d.13
(apex)

Answers

Answer:15

Step-by-step explanation:

Apex

PLEASE HELP ME I NEED THE ANSWER VERY BADLY JUST PLEASE GIVE ME THE ANSWER CHOICE AND DONT GUESS!!!!!!!!!!!!!!
the equations below are representations of linear equations in two variables.
I. y=-2/3x+4
II. y-2=2/3(x-9)
III. 2x+3y=12.

Which linear equation(s) in two variables represent a line that contains the point(9,-2) and with a slope of -2/3?

A. I,II and III
B. I and II only
C. I and III only
D. II and III only

Answers

Answer:

ITS B

Step-by-step explanation:

HOPEFULLY THIS WORKS!!!

What is this question 23474+ 4749

Answers

Answer:

The answer to this is 23474 + 4749 = 28223

Step-by-step explanation:

Hope this helps :)

Answer:

Sum:: 28223

Step-by-step explanation:

If your referring to write it in question form::

What is the sum of 23,474 plus 4,749 ?

What does this even mean??? I accidentally went on college

Answers

Answer:

I think what the teacher wants is for you to calculate it and then put said calcuated number on number line

Step-by-step explanation:

FOR EXAMPLE: if the DIFFERENCE is 7, put 7 on the number line

I think the greatest number

How many feet are in 120 inches?
Enter your answer in the box.
ft

Answers

10 feet are in 120 inches

The required converted value is 10 feet, which is 120 inches into feet.

As we know that unit conversion is the process of converting a quantity from one unit of measurement to another. It refers to multiplying the given quantity by a conversion factor that blends the two proportional units.

To convert inches to feet, we use the conversion factor:

1 foot (ft) = 12 inches (in)

Therefore, to convert 120 inches to feet, we divide by the conversion factor:

120 inches / 12 in/ft = 10 feet

So, there are 10 feet in 120 inches.

Learn more about the unit conversion here:

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