You stand 20 ft from a bottle rocket on the ground and watch it as it takes off vertically into the air at a rate of 18 ft/sec. Find the rate at which the angle of elevation from the point on the ground at you feet and the rocket changes when the rocket is 40 ft in the air. At the moment the rocket is 40 ft in the air, the angle of elevation is changing at a rate of rad/se.

Answers

Answer 1

Answer:

9/50 rad/sec

Step-by-step explanation:

let the angle be represented as ∅

distance form bottle rocket on the ground = 20 ft

height of rocket = 40 ft

solution

first we differentiate w.r.t.time

= sec²(∅)*(d(∅)/dt))=(1/20)*dh/dt   --------- ( 1 )

=  d(∅)/dt = (1/20)cos²(∅)* (dh/dt)   ------- ( 2 )

note :  1/sec(∅) =cos(∅)

therefore ; dh/dt = 18 ft/sec

applying Pythagoras theorem

Tan ∅ =  40 / 20

 h^2( hypotenuse )  = a^2( height )  + b^2 ( distance from bottle rocket )

                     h = √ 40^2 + 20^2 =  √ 2000

also cos ( ∅ ) = b / h  =  20 / √ 2000

hence cos²∅ = 1/5

Back to equation 2

d(∅)/dt=(1/20)×(1/5)×(18)

= 18/100  = 9/50 ( changing rate of angle of elevation )

   


Related Questions

Whats the answer to part b and above?

Answers

Answer:

4/5 would be at the 8th line, and 3/10 would be on the 3rd

Step-by-step explanation:

I will GIVE BRAILYEST
Mario has 20 yards to mow this week. By Wednesday, he had mowed 50%or the yards. How many yards had he mowed by Wednesday?
2
5
10
15​

Answers

Answer: 10 yards

Step-by-step explanation: 50% = 1/2

1/2 x 20 = 10

15 yeards mowed by Wednesday

Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for f(h(x))

Answers

Answer:

2x - 4

Step-by-step explanation:

f(x) = x - 7

= 2x + 3 - 7

= 2x - 4

how to solve this? im not sure if i get the correct answer

Answers

Answer:

k = 3.5

Step-by-step explanation:

Area of a rectangle = length × width

Area of the bigger triangle - Area of the smaller triangle = 35 cm²

Thus:

(2k + 6)(k) - (3)(k) = 35 cm²

2k² + 6k - 3k = 35

2k² + 3k - 35 = 0

Factorise

2k² + 10k - 7k - 35 = 0

2k(k + 5) -7(k + 5) = 0

(2k - 7)(k + 5) = 0

2k - 7 = 0

2k = 7

k = 3.5

Or

k + 5 = 0

k = -5

The value of k would be the positive number which is 3.5.

Evaluate the following expression using the values given:

Find 5x − 3y − z if x = −2, y = 2, and z = −3

Answers

Answer: -13

Step-by-step explanation:

just substitute the letters for the numbers.

5(-2) - 3(2) -(-3)

then, remove the parenthesis.

-10 - 6 + 3

finally, just calculate it.

-13

A table of values of a linear function is shown below.

Answers

Answer:

Slope is -2

y intercept is -3

Equation :y=-2x-3

Step-by-step explanation:

I need this fast please

Answers

Answer: It is B/Spinner 2

its B! hope this helped! <3

Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below: A(-1,2) B(-1,5) C(-3,5) D(-3,2) A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2)
What transformation did Kim perform to create rectangle A'B'C'D? (5 points)
A)Reflection across the y-axis
B)Rotation of 270 degrees counterclockwise about the origin
C)Reflection across the x-axis
D)Rotation of 90 degrees counterclockwise about the origin

Answers

Answer:

C) Reflection across the x-axis.

Step-by-step explanation:

From Linear Algebra we define the reflection across the x-axis is for [tex]P(x,y) =(x,y)[/tex]:

[tex]P'(x,y) = (x, -y)[/tex] (1)

If we know that [tex]A(x,y) = (-1, 2)[/tex], [tex]B(x,y) =(-1,5)[/tex], [tex]C(x,y) = (-3, 5)[/tex] and [tex]D(x,y) =(-3, 2)[/tex], then the reflected points are, respectively:

[tex]A'(x,y) = (-1, -2)[/tex]

[tex]B'(x,y) = (-1,-5)[/tex]

[tex]C'(x,y) = (-3,-5)[/tex]

[tex]D'(x,y) = (-3,-2)[/tex]

In consequence, Kim performed a reflection across the x-axis to create triangle A'B'C'D'. The correct answer is C.

This question is based on the reflection of x- axis. Hence the correct answer is C, reflection across the x-axis.

Given:

Transform  rectangle ABCD to rectangle A'B'C'D',

The vertices of rectangle ABCD is A(-1,2) B(-1,5) C(-3,5) D(-3,2).

The vertices of rectangle A'B'C'D is A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2).

We need to determined the transformation that Kim perform to create rectangle A'B'C'D.

From Linear Algebra we define the reflection across the x-axis is for,

P(x,y) = (x,y)

P(x,y) = (x,-y)                                .....(1)

It is given that  A(-1,2), B(-1,5), C(-3,5) and D(-3,2).

Therefore from equation (1)  above point becomes,

A'(x,y) = (-1,-2)

B'(x,y) =(-1,-5)

C'(x,y) =(-3,-5)

D'(x,y) =(-3,-2)

Therefore, It is observe that Kim performed a reflection across the x-axis to create triangle A'B'C'D'. Hence the correct answer is C, reflection across the x-axis.

For further details, please refer this link:

https://brainly.com/question/25095797

Definition of dilation in geometry

Answers

Answer:

Geometry

Step-by-step explanation:

the enlargement or shrinking of an image, in where the change depends on a scale factor

WILL MARK BRAINLIEST
what type of transformation is described by (x,y) —> (x+2, y+16)?

Answers

This transformation takes a vector (x,y) and maps it to the vector (x+2, y+16). In other words, it moves the X coordinate of the vector 2 units to the right, and the Y coordinate of the vector is moved 16 units upwards.

If you would take a set of points and apply this transformation, you would see the entire set moving upwards and to the right, with no stretching ou rotating. This type of transformation is called a translation transformation.

i need some help here

Answers

Answer:

the answer above is correct

Answer:

boxes

7

8

58.1

119.7

Step-by-step explanation:

look when u solve this it equals

8.3(7)+7.7(8)=119.7 but it tells u to add 61.6 so u go backwards subtract

119.7-61.6

58.1

just plug in

8.3(7)+7.7(8)=____+61.6

plug in

58.1+61.6

119.7

graph the line whose x-intercept is -6 and whose y-intercept is -7

Answers

9514 1404 393

Answer:

  see below

Step-by-step explanation:

When the intercepts are given, plot those and draw a line through them.

_____

Additional comment

The equation shown with the graph is the equation of a line in "intercept form." It is especially useful in a case like this where the intercepts are given.

5.00 minus2.40minus1.33= plz show me how you got that answer step by step

Answers

Answer:

5.00 -2.40= 2.60

2.60-1.33= 1.27

The answer is 1.27

Step-by-step explanation:

a bowling alley charges $4.00 per game and will rent a pair of shoes for $2.00 for any number of games. The bowling alley has an earnings goal of $400 for the day. write the linear equation.

Answers

Answer:

We need 130 games to reach the goal

Step-by-step explanation:

Answer this please i need help

Answers

Answer:

Slope m = -3

y-intercept (0, 0)

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

y = -3x

Step 2: Break Function

Identify Parts.

Slope m = -3

y-intercept b = 0

Question #5
Consider the equation.
72 +48 = 8
1+6)
Enter the unknown number that makes the equation true.
Your answer
Σ

Answers

X=9 how to solve: 72+48=8x+48
72=8x 8*9=72

Choose the diagram that correctly represents the ordered pairs below.
(1,4), (4, -1), (2,3), (-3, 1), (0,-5)

Answers

Answer:

Step-by-step explanation:

Is there a picture

PLZ HELP if u know the answer for sure​

Answers

the answer is b (-2 5/6)

Which equation is represented by the graph below

Answers

Maybe show the graph.....

pamela ran 7/10 miles on tuesday and 3/8 mile on thursday. How much farther did she sun on tuesday ?

Answers

Answer:

she ran 0.325 more on tuesday then tursday

Step-by-step explanation:

because i know

3) Luan is borrowing $5000 to buy Sacramento Kings season tickets
for her family. She is planning to pay it back over three years.
She can borrow the money from a finance company at a 6.5% add-on
interest rate for three years or she can borrow it instead from
her credit union, making 36 monthly payments of $164.50. Find the
total amount Luan will have to pay back with each option and the
APR (to the nearest half percent) of each loan.

Answers

Answer:

16000

Step-by-step explanation:

it works bebeaoc usfztbee jdxeevehe ue

Manuel ate lunch in 5 minutes. How many seconds is this?

Answers

Answer:

300 seconds

Step-by-step explanation:

1 minute= 60 seconds

5 x 60 = 300

Answer:

1 minute is 60 seconds, so 60 x 5 is 300. So your answer is 300 seconds

A cell phone manufacturer samples cell phones from the assembly to test. She noticed that the number of faulty cell phones in a production run is usually small and that the quality of one day’s run seems to have no bearing on the next day.

a) What model might you use to model the number of faulty cell phones produced in one day?

(write a name of this probability model)


An analysts estimates the mean number of defective cell phones to be 2 per day.

b) What is the probability of having a day with no faulty cell phone in a production run?
(write to 3 decimal places)

c) What is the probability of having a day with more then 3 faulty cell phones in a production run?

probability:

Answers

Answer:

b

Step-by-step explanation:

probability can't be defined

A baker had additional flour at the end of the day. He uses 1/8 of a bucket of flour to bake two cakes. How much flour did he use to make one cake?

Answers

Answer:

0.0625

Step-by-step explanation:

You can convert this into a fraction by entering this into a calc

Please give me the correct answer ​

Answers

Answer: Many people assume that because DNA is so small, we can't see it without powerful microscopes. But in fact, DNA can be easily seen with the naked eye when collected from thousands of cells.

When a bunch of dna and I mean thousands of dna squish together we are actually able to see dna

There are 2400 students in a school 45% of them are boys how many boys are in the school

Show your work in the answer

Answers

Answer:

1080 boys

Step-by-step explanation:

2400 x 0.45 = 1080

g(x) = x3 - 4
h(x) = x2 + 2
Find h(-2) - g(-1)

Answers

Answer:

11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

g(x) = x³ - 4

h(x) = x² + 2

h(-2) is x = -2

g(-1) is x = -1

Step 2: Find h(-2) - g(-1)

Substitute:                    ((-2)² + 2) - ((-1)³ - 4)Exponents:                   (4 + 2) - (-1 - 4)Add/Subtract:               6 - (-5)Subtract:                       11

what fraction is equal to 5%​

Answers

Answer:

5/100

1/20

Step-by-step explanation:

Answer: 5/100

Step-by-step explanation:

Constructing a frequency distribution for grouped data
Ten cyclists were each asked the distance in miles they biked last week.
Their responses are given below.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of distances in that class.
(Note that we are using a class width of 5.)
Distance in miles
Distance in miles
Frequency

3
20
6
3
7
8
13
10
18
12
6 to 10
11 to 15
16 to 20 and 1 to 5

Answers

The grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

Given that, ten cyclists were each asked the distance in miles they biked last week. The distance travelled by 10 cyclists is 3, 20, 6, 3, 7, 8, 13, 10, 18 and 12.

We need to complete the grouped frequency distribution for the data.

What is the grouped frequency distribution?

In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.

Now, the frequency distribution for the given intervals is as follows:

That is, for intervals 1 to 5 the frequency is 2.

For intervals 5 to 10 the frequency is 4.

For intervals 11 to 15 the frequency is 2.

For intervals 16 to 20 the frequency is 2.

Therefore, the grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

To learn more about the grouped frequency distribution visit:

brainly.com/question/4679134.

#SPJ2

What the equivalent (2×)(5y)(5y)

Answers

Answer:

50xy

Step-by-step explanation:

(2x)(5y)(5y)

~Simplify

(2x)(25y)

~Multiply

50xy

Best of Luck!

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