1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aleksandrvk [35]
2 years ago
15

A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the

angle between the observer's line-of-sight and the horizontal is π4 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Mathematics
1 answer:
Zigmanuir [339]2 years ago
5 0

Answer:

Step-by-step explanation:

aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:

tanθ = opp/adj = y/x

y = xtanθ

What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):

dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)

We need to find out values for all of the variables:

The observer is not moving, therefore dx/dt = 0.

The observer is standing 4 miles away from the lift-off point, so x = 4.

The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.

The rate of change for the angle, dθ/dt, is 0.1.

Just plug all the numbers in:

dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)

dy/dt = 0 + 1.6

dy/dt = 1.6 mi/min

You might be interested in
Question 1 . What division problem does this area model represent?
Law Incorporation [45]

Answer:

0

Step-by-step explanation:

6 0
2 years ago
Dana is purchasing a new car that costs $24,650. The bank is charging 4% simple interest for 6 years to finance the car. Using I
tia_tia [17]

Answer:

5,916

24650 \times 0.04 \times 6 = 5916

4 0
3 years ago
Help answer this if ya know!
blagie [28]
C) The +10 is because you already have 10 coins, that will not change. The 6x is because with each passing day, the number of coins increase by 6 (x represents days). The equation then turns into y=6x+10

Hope this helps comment for more questions :)
4 0
3 years ago
Which numbers line correctly shows 4.5 - 2.5.? HELP FAST!!!
ElenaW [278]

Answer:

Step-by-step explanation:

The answer would be the first option because it’s starting at 4.5, and if you subtracted 2.5, you would get the answer of 2, and that’s what the first option shows. Hope this helps!

5 0
2 years ago
Two mixed numbers with different denominators to get 4 1/3
nalin [4]

Answer:

1 2/3 and 2 4/6

7 0
2 years ago
Other questions:
  • How many times greater was the temperature in Miami (45) than the lowest in San Diego (25)
    7·1 answer
  • The equation V=13πr2h relates the volume V, the radius r, and the height h of a cone. Write h in terms of V and r.
    11·2 answers
  • Write the formula for finding the volume of a prism
    9·1 answer
  • PLEASE HELP!
    7·1 answer
  • If you fold a normal curve, each half would fit perfectly on top of the other. This characteristic is known as __________.
    7·2 answers
  • Juan invests $7500 at 6% interest in one year. How much money will he have if the interest were compounded A. yearly B. Daily C.
    6·1 answer
  • Luisa is avid Horseback riding. This year, she purchased a new Safety riding helmet for $125 and continues taking lessons at $20
    14·1 answer
  • Amanda has bought 30 pounds of dog food. She feeds her dog 3/5 pounds for each meal. For how many meals will the food last?
    12·2 answers
  • Check if 7 is a solution of the equation 4 ( Z - 3 ) = 16. step by step plz guys. ​
    10·2 answers
  • Solve simultaneous equations <br> 11s+9t=116<br> 5s+9t=92
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!