A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h2 where h and d are measured in feet. What is the rocket's height when the distance between you and the rocket is 100 feet?

Answers

Answer 1

Answer:

iam thinking the answer is ""-262,5ft""

Answer 2

The height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.

What is the height?

The height is a vertical distance between two points. It is given that A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h² where h and d are measured in feet.

The height will be calculated by forming the two equations from the given data in the question.

25  =  625  +  h²

100  =  4  (  625   +  h² )

100  =  ( 2500   +  4h²  )

By solving both the equations:

100  -  25  =  2500  -  625  +  4h²   -   h²

3h²   =  1800

h   =   √600

h   =   24.49 feet

Therefore the height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.

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Related Questions

if the length of diagonal of a square is 4-√2 cm, find it's length, perimeter and area.​

Answers

Step-by-step explanation:

1) the length of the side is:

[tex]\frac{4-\sqrt{2} }{\sqrt{2}}=2\sqrt{2}-1.[/tex]

2) the required perimeter is:

[tex]P=4(2\sqrt{2} -1)=8\sqrt{2} -4.[/tex]

3) the required area is:

[tex]A=(2\sqrt{2} -1)^2=9-4\sqrt{2}.[/tex]

Answer:

Side length = (2√2 - 1) units

Perimeter = (8√2 - 4) units

Area = (9 - 4√2) units²

Step-by-step explanation:

Properties of a square:

It is a quadrilateralThe opposite sides are parallelAll four sides are equal in lengthAll interior angles measure 90°

The diagonal of a square creates two right triangles, with the diagonal being the hypotenuse, and the sides of the square being the 2 legs.

Let x = side length of the square

Using Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ x² + x² = (4 - √2)²

⇒ 2x² = 18 - 8√2

⇒ x² = 9 - 4√2

⇒ x = ±(2√2 - 1)

⇒ x = 2√2 - 1  only (as distance is positive)

Perimeter of a square = 4x

                                    = 4(2√2 - 1)

                                    = 8√2 - 4

Area of a square = x²

                            = (2√2 - 1)²

                            = 9 - 4√2

If sodium 24 has a half life of 15 hours if there are 800g of na-24 initially how long will it take for 750g of na-25 to decay so that only 50g remains

Answers

It would take about 60 hours to decay so that only 50g of the sodium remains

How to calculate half life?

The half life is 15 hours and there are 800 g initially. Let N(t) represent the amount of sodium after t hours. Hence:

[tex]N(t)=800(\frac{1}{2} )^\frac{t}{15} \\\\For\ 50g\ to \ remain:\\\\50 = 800(\frac{1}{2} )^\frac{t}{15}\\\\t=60\ hours[/tex]

It would take about 60 hours to decay so that only 50g of the sodium remains

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five years ago, Nina was twice as old as Sam. In five years she will be 1.5 times as old as Sam. How old are Nina and Sam now?

Answers

The age of Nina and sam are 15years and 10 years respectively now

System of equations

They consists of equations and unknown variables

Let their current age be x and y

If five years ago, Nina was twice as old as Sam then;

x - 5 = 2(y-5)

If in five years she will be 1.5 times as old as Sam, then;

x = 1.5y

Substitute

1.5y - 5 = 2y -10

-0.5y  = -5

y =5/0.5

y = 10

Since x = 1.5y

x = 15years

Hence the age of Nina and sam are 15years and 10 years respectively now

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Jackson is organizing textbooks on his bookshelf. He has an English textbook, a math textbook, and a history textbook. How many different ways can he line the textbooks up on his bookshelf?

Answers

Answer:

6

Step-by-step explanation:

Since this problem is easier, you can just do counting or you can use 3!

Which is 6

Find the area of this triangle

Answers

Answer:

22

Step-by-step explanation:

22 is the area of the given traingle

The triangles on the grid below represent a translation.
4
3
0
2
1
b
8
54-32-14
1 2
3
b
8
To form the image, the pre-image moved
five units right and three units up.
two units right and three units up.
Mark this and return
Save and Exit
Next

Answers

Answer:

Five units right and three units up.

If you notice there's a ' on the green triangle (a',b',c')

That means that the blue triangle was translated to get to the green triangle

Suppose the Federal Reserve set the reserve requirement at 20%. Assume that banks lend all reserves that are not required to be held. Round the answers to two decimal places.

Answers

Answer:

whaaaat iisss these. answeeeeeeer??

Tim bought all of the 2 3/4 lb packages for a party. How many pound of meat did tim buy?

Answers

1 and 1/2 of pounds of meat

The number is a/an...

Answers

The number is an irrational number

What is the root of 12x=9+5x2

Answers

Answer:

Step-by-step explanation:

Answer:

(6 ± 3i)/5

Step-by-step explanation:

12x = 9 + 5x²

5x² - 12x + 9 = 0

Method 1

Factors that add to = b (-12) and multiply to = ac (45):  3 and -15

5x² + 3x - 15x + 9 = 0

5x(x - 3) + 3(x + 3) = 0

(x-3) and (x+3) do not match !!!!

Method 2 - Quadratic Formula

-b ± √(b² - 4ac)/2a

12 ± √((-12)² - 4(5)(9))/2(5)

12 ± √((-12)² - 4(5)(9))/2(5)

12 ± √(144 - 180)/10

12 ± √-36/10

(12 ± 6i)/10

(6 ± 3i)/5

I hope this helps!

help!
Can you please give me the area of this. I would really like it.

Answers

Answer:

The answer is 340 ft²

To find the total area we make two squares and a big rectangle.

1st square

3x5=15

2nd square

5x5=25

Rectangle

20x15=300

Total Area

15+25+300 = 340ft²

Unit 6 lesson 10 surface area and volume unit test

Answers

Answer:

You have to ask a question

Step-by-step explanation:

Just answer

1 + 23 =
i give you 100 pts
I quit

Answers

hmm a tough one ima go with 24

I think 24. Not rlly sure tho

please help me Find M

Answers

The answer for your question is : 80

Decide if each set might produce one or more gaps when represented by a histogram. 1.The ages of students in a sixth-grade class. 2. The ages of people in a elementary school. 3. The ages of people eating in a family restaurant.
4. the ages of people who watch football. 5. The ages of runners in a marathon.

Answers

The set of data that might produce one of more gaps on thr histogram are:

the ages of people who watch football; andthe ages of people eating in a family restaurant.

What is a Histogram?

A histogram is a graphical representation of data such that the data is organized by data points into user-specified ranges.

The categories of people highlighted above will cause gaps because there is an increased likelihood that their ages will vary greatly or be distanced from the mean.

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The lengths of the sides of a triangle are 9​, 12​, and 15. Classify the triangle as​ acute, right, or obtuse.

Answers

Answer:

right angle triangle

Step-by-step explanation:

by applying Pythagoras theorem

[tex] RHS ={9}^{2} + 12 ^{2} = 81 + 144 = 225=√225 =15=LHS[/tex]

hence proved

Simplify the following expression.
6.64 ÷ 8

A.
1.245
B.
0.664
C.
0.83
D.
0.93

Answers

Answer:

[tex]0.83[/tex]

Step-by-step explanation:

[tex]6.64 \div 8[/tex]

[tex]0.83[/tex]

Answer:

The answer should be C.)0.83, hope this helps.

What would the answer be?

Answers

Answer:

3 2/4

Step-by-step explanation:

1 3/4 + 1 3/4 = 6 2/4

because 3/4 +3/4 = 6/4 = 1 2/4

and 1+1+1 =3

Answer:  [tex]3 \frac{1}{2}[/tex]

This is the same as writing 3 & 1/2 to mean "3 and a half".

Check out the diagram below. I've shaded the pizza slices to represent the mixed numbers being added. Notice in the bottom row I've moved one red slice over to make a full pie. Overall we have 3 full pies plus an extra half, when all is said and done.


Is the graphed function linear?
Yes, because each input value corresponds to
exactly one output value.
Yes, because the outputs increase as the inputs
increase
O No, because the graph is not continuous.
No, because the curve indicates that the rate of
change is not constant

Answers

Answer:

No Because the curve indicates that the rate of change is not constant!

Step-by-step explanation:

Linear functions are straight lines diagonally!

This function shows a rate of growth through time which isn't describing constant growth.

Constant = Linear


Which expression is equivalent

Answers

Answer:

the answer is 1/27. C :))

f an angle of a regular 18-gon measures 3x-6. Find the value of x.

Answers

The value of x in a 18-gon that has an interior angle measurement of 2x - 6 is 55.33

What are polygons?

Polygons are 2-dimensional shapes that are made of straight lines.

Therefore,

sum of interior angle of polygon = 180(n - 2)

where

n = number of sides

Therefore,

sum of interior angle of polygon = 180(18 - 2)

sum of interior angle of polygon = 180(16)

sum of interior angle of polygon = 2880

Since, it is a 18-gon, the value of x can be found as follows;

2880  / 18 = 160 degrees

Therefore,

3x - 6 = 160

3x = 160 + 6

3x = 166

x = 166  /3

x = 55.3333333333

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Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before delivering the bill to each customer, the waitress selected one of the index cards without reading it and wrote on the bill the same message that was printed on the card. Twenty of the cards had the message "The weather is supposed to be really good tomorrow. I hope you enjoy the day!" Another 20 cards contained the message "The weather is supposed to be not so good tomorrow. I hope you enjoy the day anyway!" After the customers left, the waitress recorded the amount of the tip (percentage of bill) before taxes. The tips for those receiving the good‑weather message are as follows.

20.8 18.7 19.9 20.6 21.9 23.4 22.8 24.9 22.2 20.3
24.9 22.3 27.0 20.5 22.2 24.0 21.2 22.1 22.0 22.7
The tips for the 20 customers who received the bad weather message are as follows.

18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 14.0
17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 18.2 19.4
Click to download the data in your preferred format.

CSV Excel JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt!

Back‑to‑back stemplots of the tips are shown.

Good Weather Tips Bad Weather Tips
13 6
14 0
15
16 1 8
17 0 5
7 18 0 0 2 4 5 8 8
9 19 0 1 2 4
8 6 5 3 20 0 2
9 2 21
8 7 3 2 2 1 0 22
4 23 2
9 9 0 24
25
26
0 27
Because the distributions are reasonably symmetric with no extreme outliers, the procedures will work well.

Is there good evidence that the two different messages produce different percentage tips?

Bruce Rind and David B. Strohmetz, "Effect of beliefs about future weather conditions on restaurant tipping," Journal of Applied Social Psychology, 31 (2001), pp. 2160–2164.
Carry out a two‑sample test. What is the test statistic? Give your answer to three decimal places.

=

What is the -value? Give your answer to three decimal places.

-value:

Answers

The test statistic and p-value of the given data are 6.274 and 0.0001 respectively.

Test Statistic

The test statistic can be calculated using the formula below

[tex]t = \frac{x-\mu}{\sigma / \sqrt{n} }[/tex]

Solving for the mean and standard deviation, we can substitute the values into the above equation which will be

[tex]t = \frac{x-\mu}{\sigma / \sqrt{n} } = 6.274[/tex]

P-Value

Using the data from the test statistic, we can calculate the p-value of the data

[tex]p-value = p(z < 6.274)= 0.0001 = 0.00[/tex]

From the calculation above, the test statistic and p-value of the given data are

6.2740.0001

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22. Four years ago, age of X was 3 times Y. Six years from now X will be twice Y. Ages of X and Y
now are:
A.
034 and 14
B.
034 and 13
C.
033 and 14
D.
035 and 14

Answers

Answer:

a 34 and 14

Step-by-step explanation:

let present age be x and y

equation 1

x-4=3(y-4)

x=3y-8

equation 2

x+6=2(y+6)

x=2y+6

then

2y+6=3y-6

y=14

x=34

Are constant functions periodic? The reason I ask this is because a function is periodic if it has a period but in a constant function the period could be infinitely small.

Answers

Answer:

A function f:R→R is periodic if there exists some number t>0 such that

f(x)=f(x+t)

A constant function is periodic since you can take t=1,t=2, etc. (Hint: Hover over the tag "periodic-functions". What do you see?)

The fundamental period of f is the smallest of such t's. Since t cannot be 0, you are looking for the minimum of (0,∞), which does not exist.

Step-by-step explanation:

Choose the equation for the graph.

Answers

Answer:

B. y = -|x - 2| + 5

Step-by-step explanation:

Here the parent function is |x|. It is flipped and translated upward by 5 units and shifted to the right by 2 units.

y = - |x - 2| + 5

hope this helps!! p.s. i really need brainliest :)

Select the correct answer.
Tatum plans to buy some personalized sticky notes for her home office. The graph shows a proportional relationship between the number of packs of sticky notes she can buy and the total price. If Tatum has $30.50 to spend on sticky notes, how many packs can she buy? Assume that she can buy only whole packs.



A. 1
B.2
C.3
D.4

ANSWER FAST I NEED THIS NOWW

Answers

It is C I have done this assignment before C is the correct answer

Find the area

(Please would mark Brainily

Answers

Answer:

195.5 m²

Step-by-step explanation:

A = bh/2

A = (23)(17)/2

A = 391/2

A ≈ 195.5 m²

Mrs Silverstein has 14 boys and Il girls in her
class. She must select two students at random to
serve as the class presidents What is the
probability that she will choose a boy followed by a
giri?

Answers

Answer:

Step-by-step explanation:

Here, I will instead go through the process for finding the probability of choosing two girls. Then once you understand how it was done, hopefully you will be able to answer the actual question for yourself.

Finding the probability of choosing two girls. Let's make it simpler by starting with the probability of choosing the first girl only.

Probability of choosing the first girl. (Note: the letter chosen to represent the event is not important. Pick something that makes sense to you and be consistent)

P(G1) = # of girls / # of total outcomes

So the number of girls we know to be 11. What is the number of total outcomes? Well a boy or a girl can be chosen, and there are 14 boys and 11 girls, for a total of 25 students.

       P(G1) = 11/ 25

Let's find the probability of choosing the second girl from here.

P(G2) = # of girls / # of total outcomes

However, this time things have changed. We've already chosen one girl, so the number of girls remaining to choose from is reduced 11 to 10. And the total number of students to choose from is reduced from 25 to 24.

P(G2) = 10 / 24

Now we have the probability of choosing the first girl and the probability of choosing the second girl. From here, we just need to combine them to find the probability of both things happening together. To calculate the probability of two different events occurring, you multiply the two probabilities together.

 Probability of choosing two girls. Let's use T for Two girls.

     P(T) = P(G1) × P(G2) = (11 /25) × (10/24)

From here you can use a calculator to find the answer. This answer can either be written as a fraction, a decimal, or a percentage.

             

                   = 0.19     = 19 / 100      = 19%

How can we use the distributive property to find an expression equivalent to
10(5 – 2x)? Place the steps in order.

Answers

Answer: multiply 10 to both terms and subrtact products

Step-by-step explanation:

10(5 - 2x)

multipy 10 to both terms

50  20x

subtract products

50 - 20x

Answer:

1. subtract 2×from get 3.×= 682+ 4672

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1. Suppose three companies A, B and C dominate the market for a certain product and are
competing against each other for a large share of the market. Currently company A has 2/9 of the
market, company B has 4/0 of the market and company C has 1/3 of the market. The market
survey indicates that every 6 months Company A retains of its customer and loss 1/6 to
company B and 1/12 to company C. Company B retains 12 of its customers and loss 1/3 to
company A and 1/6 to company C. Company C retains 3/8 of its customers and loss A to
company A and 3/8 to company B. Find the market share of each company in the long run is
about

Answers

The market share of the companies is an illustration of fractions.

The market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

How to determine the market shares in the long run

The current market shares are:

Company A = 2/9Company B = 4/9Company C = 1/3

After 6 months, we have:

Company A:

Retains 3/4Losses 1/6 to BLosses 1/12 to C

Company B:

Retains 1/2Losses 1/3 to ALosses 1/6 to C

Company C:

Retains 3/8Losses 1/4 to ALosses 3/8 to B

The amount of customers lost by each company is

Lost = Market share * [Share retained - Share lost to the other two companies].

So, we have:

A = 2/9 * [3/4 - 1/6 - 1/12] = 1/9

B = 4/9 * [1/2 - 1/3 - 1/6] = 0

C = 1/3 * [3/8 - 1/4 - 3/8] = -1/12

The amount of customers gained by each company is

Gain = Market share of company gained from * Share gained

So, we have:

A = 1/3 * 4/9 + 1/4 * 1/3 = 25/108

B = 1/6 * 2/9 + 3/8 * 1/3 = 35/216

C = 1/12 * 2/9 + 1/6 * 4/9 = 5/54

The total gain in 6 months is:

Total Gain = Gain + Loss.

This gives

A = 25/108 + 1/9 = 37/108

B = 35/216 + 0 = 35/216

C = 5/54 - 1/12 = 1/108

Hence, the market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

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