A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is pi/6, and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?

Answers

Answer 1

Answer:

0.533 miles/min

Step-by-step explanation:

Calculate how fast  the balloon is rising at the moment : dy /dt

location from the lift-off point = 4 miles

angle between the observer's line-of-sight and the horizontal ( ∅ )  = [tex]\frac{\pi }{6}[/tex]

d∅ / dt = 0.1 rad/min

tan ∅ = y / 4

derivate

sec^2 ∅ . d∅ / dt  = 1/4 . dy/dt

= sec^2 [tex]\frac{\pi }{6}[/tex] . 0.1 = 1/4 . dy/dt

= ( sec^2 0.5238 * 0.1 ) * 4 = dy/dt

dy/dt = 8 / 15  miles/min


Related Questions

What is the slope m in the equation y = -2x + 5

Answers

Answer:

m = -2

General Formulas and Concepts:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step-by-step explanation:

Step 1: Define function

y = -2x + 5

Step 2: Break function

Slope m = -2

y-intercept (0, 5)

22. Find the slope and Y intercept of the line 3x+4y-9=0​

Answers

hi there! here's my answer for you...

Answer:

slope:

m = -3/4

y-intercept:

y = −3x/4 + 9/4

hope this helped. have a good one!

Lara created a 15-pound platter of three different types of cookies for a banquet. The peanut butter cookies sell for $2 per pound, the sugar cookies sell for $3 and the chocolate chip cookies sell for $3.60 per pound. The entire platter is worth $40. The quantity of peanut butter cookies was 3 more than chocolate chips. How many pounds of each cookie was there. Answered with a chart.

Answers

Answer:

i need a bad bleep

Step-by-step explanation:

addison rae

simplify (3x+2) (y-2) - (7y+3) (y-3)

Answers

Answer:

3 x y − 7 y 2 − 6 x + 20 y + 5

Step-by-step explanation:

Danny bought 8 rolls of paper towels. He has 204.8 meters of paper towels in all. How many meters of paper towels are on each roll? A) 21.52 B) 25.12 C) 25.60 D) 26.52​

Answers

Answer:C) 25.60

Step-by-step explanation:204.8÷8=25.60

Answer:

:C) 25.60

Step-by-step explanation:

it takes Molly 0.25 hours to drive to school. her route is 16 km long. what is Molly's average speed on her drive to school?​

Answers

Answer:

64

Step-by-step explanation:

16 divided by 0.25 gives you 64 .... welcome

Answer:

64 km/h

I answered it correctly on a mid term

-4x+6y=-7
-13x-2y=-4
Elimination or substitution

Answers

Answer:

substitution

Step-by-step explanation:

Which of the following equations demonstrates the Identity Property of One? A. 3 - 2 = 1 B. 4 • 1 = 14 C. 1 • b = b D. 0 + 1 = 1

Answers

Answer: C

The identity property of 1 is that any number multiplied but it remains the same.

Hence

1 x b = b

Which equation has the correct sign on the product?
A 45(-4)=180 B 13•3= -39
C (-8)(-8)= -64 D (-18)4 = -72​

Answers

answer:

the answer is a

Answer is D because (-18)4 equals -72.... it’s right.

a leaky faucet is losing water and it is filling a 5 gallon bucket every 12 hours. At the rate, how many gallons of water will the faucet leak 48 hours

Answers

Answer:

20 gallons

Step-by-step explanation:

First start off by dividing 48 by 12 to see how many times 12 goes into 48.

48 / 12 = 4

now that you know that 12 goes into 48 4 times, multiply 4 by 5 to see how many gallons the leaky faucet will fill in 48 hours.

4 x 5 = 20

therefore the answer is 20 gallons

I hope this helps ^^

The temperature drops from 7°F to -17°F. By how much did the temperature decrease?

Answers

Answer:

24 degrees

Step-by-step explanation:

If you use 0 as kind of a benchmark it is really useful, frist you subtract 7, because it is our positive number., then you subtract 17 from 0, making -17.

7+17=24

7 degree F minus -17 degree F
Is 24 degree F

If 1 inch represents 10 miles on a map then how many inches will represent 120 miles ?

Answers

Answer:

12 inches

Step-by-step explanation:

We can write this as a proportion:

inches/miles = inches/miles

1/10 = x/120

Solving for x, we get 12 inches.

Please find measure of angle s. PLEASE HELP FAST!!

Answers

Answer:

27

Step-by-step explanation:

15x-31 = 9x+11

6x-31 = 11

6x = 42

x = 7

15x -31 + 9x + 11 + s = 180

15(7) -31 + 9(7) + 11  + s = 180

105 - 31 + 63 + 11 + s = 180

153 + s = 180

s = 27

it costs 13$ for admission to amusement park, plus 1.50$ for each ride.if you have a total of 35.50 to spend, what is the greatest number of rides you can go on

Answers

Answer:

Thus, the greatest number of rides I can go on is 15 rides

Step-by-step explanation:

I have $35.50 to spend for admission plus rides in the amusement park.

Admission costs $13. That leaves me with

$35.50 - $13 = $22.50

to spend on rides.

Considering each ride costs $1.50, we can find the maximum number of rides by dividing the remaining money by the cost per ride as follows:

$22.50 / $1.50 = 15

Thus, the greatest number of rides I can go on is 15 rides

72.05-29.69?????????????????

Answers

Answer:

42.36

Step-by-step explanation:

Big boi questions just use the caculator

Which ordered pair is a solution to the equation below? 3x + 2y = 10
Question 1 options:

(4, 0)

(6, -4)

(-1, 4)

Answers

Answer:

(6,-4)

Step-by-step explanation:

I have tried replacing each option with x, y in the equation.

Let's replace (6, -4) with x and y

3x+2y=10

3(6)+2(-4)=10

3(6)= 18 2(-4)= -8

18+(-8)=10

in other words:

18-8=10

The statement is true, so the correct answer is:

(6, -4)

11. Find the product of (4x-5) and (2x+7) in simplest form.

Answers

8x^2 + 18x - 35


(4x - 5)(2x + 7)

8x^2 + 28x - 10x - 35

8x^2 + 18x - 35

There are 24 female performers in a dance recital. The ratio of men to women is 7:8. How many men are in the dance recital?

Answers

I need help to I’m struggling at math

equation of the line with slope 1/2 that passes through the point
(-6, 1).
O 1
y = 2x - 4
v
О
1
y=2x-
-5
W
o
y = 2x + 5
-x
О 1
y = 2*+4

Answers

Step-by-step explanation:

let eqn be y = 1/2x + b

sub (-6, 1):

1 = 1/2(-6) + b

b = 4

therefore, eqn is y = 1/2x + 4

Topic: coordinate geometry

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

.
Determine the value of each of the following expressions

a.
25+310


b.
56−13


c.
45×78


d.
67÷34

Answers

a. 515
b. 43
c. 3510
d. 1.9705

What is a mutual fund’s

Answers

A pool of money where investors buy shares and a fund manager invests them and gives the investor the return; the way that most Americans invest their money because of the ease. hope that helps!

romona has $800 in her bank account

Answers

Um not sure what you're asking for bud you didn't finish.

Answer:

Okay?????? I don't think you finished

Step 1:Choose the lowest common denominator

Find the sum of 1/5 and 7/10

The expression written in equation from with common denominator is______

The sum is___​

Answers

Answer:

-6/8 +5/8 and -1/8

Step-by-step explanation:

just got done doing it.

Determine the expression

Answers

trinomial and i believe its a degree of 4

Martin spent $68 on a new drone that he had been saving for. Now, he has $41 left in his savings jar. Click the equation that could be used to find the total of his savings, s, before he bought the drone.

Answers

Answer:

Step-by-step explanation:

109

The answer is 109 (Brainliest Answer Will be appreciated:D)

Juan got grades of 68 and 73 on his first two math tests. What grade must he get on the third test if all were weighted equally and he wants to raise his grade to a 75 average?

Answers

Answer: 84

Step-by-step explanation: Multiply 75 by 3. That is 225, and is the value the three numbers must add up to. 73+68=141. 225-141 is 84.

15 POINTS

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same shade of green paint?

A. 10 : 45

B. 30 : 54

C. 6 : 10

D. 27 : 15
explanation if you know how to explain

Answers

Answer:

The answer is B

Step-by-step explanation:

The problem is asking for the same ratio as 5:9

Multiply both sides by 6 to get 30:54

Flying fish do not actually​ fly, but glide. Suppose that a fish traveled a distance of 1400 feet at a rate of miles 15 per hour. How many seconds would it take to travel this​ distance? (Hint: First convert miles per hour to feet per second. Recall that 1 mile​ = 5280​ feet.)

Answers

Answer:

63.63 seconds, or round up if you need to?

Step-by-step explanation:

#13 Easton is planning on buying a new pair of cowboy boots. When he
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sale. This week, they aren't on sale anymore and they cost $85. What is the
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O 25%
O 45%
O 55%
75%

Answers

It will be 25%

Step-by-step explanation:

These reverse processes are both part of

Answers

Answer:

you forgot the picture

Step-by-step explanation:

Please put a picture

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