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
bearhunter [10]
2 years ago
12

A balloon is rising at a constant speed of 5 ftys. A boy is cycling along a straight road at a speed of 15 ftys. When he passes

under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 s later?
Mathematics
1 answer:
Ket [755]2 years ago
7 0

Answer:

  13 ft/s

Step-by-step explanation:

t seconds after the boy passes under the balloon the distance between them is ...

  d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)

The rate of change of d with respect to t is ...

  dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)

At t=3, this derivative evaluates to ...

  dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13

The distance between the boy and the balloon is increasing at the rate of 13 ft per second.

_____

The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.

The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.

The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...

  d = √((15t)² + (45+5t)²)

You might be interested in
Explain how finding 7x20 is similar to similar to finding 7x2000.then find each product
notka56 [123]
They are both similar because you just have to multiply 7 x 2 and then add the zeros. 7 x 20 is 140 and 7 x2000 is 14000
7 0
3 years ago
Read 2 more answers
Find the area of each trapezoid.
VMariaS [17]
I can not see the trapezoid
5 0
3 years ago
Given: Sine (A) = four-fifths, StartFraction pi Over 2 EndFraction < A < Pi and Sine (B) = StartFraction negative 2 StartR
ELEN [110]

Answer:

D

Step-by-step explanation:

Did test(edge 2020)

8 0
3 years ago
Read 2 more answers
Put the numbers in order from smallest to largest.
AnnZ [28]
In order of problems/numbers - 4, 3, 5, 6, 1, 2
3 0
2 years ago
Someone help me with this please
dmitriy555 [2]

Answer:

the answer is c=34

Step-by-step explanation:

use the pythogoras therom since there is a right angle triangle c2=a2+b2

hope this helped:)

8 0
2 years ago
Read 2 more answers
Other questions:
  • The figure is composed of two rectangular prism. What is the volume of the figure?
    14·1 answer
  • Sandra makes $55,000 and is getting annual raises of $2,500. Ellie makes $62,000 with annual raises of $2,000. How many years wi
    7·1 answer
  • How do you do systems of two equations? Problem: y=-3x+4, y=3x-2
    15·1 answer
  • Makes a manifesto where it expresses a commitment for the respect and tolerance for the other and the other
    6·1 answer
  • What is the value of X and are these angles Complementary or supplementary
    12·1 answer
  • Lynn bought a bag of grapefruit, 1 5/8 pounds of apples, and 2 3/16 pounds of bananas. The total weight of her purchase was 7 1/
    15·1 answer
  • Together Abel and Bob have 49 video games. Abel has 11 more video games than Bob. How many games does each person have.
    15·1 answer
  • HELPPP ASAP PLEASE THE QUESTION IS “ Which equation represents the sentence “the quotient of z and 7 is 9” PLEASE HELP I NEED IT
    13·2 answers
  • a moving sidewalk at an airport moves at a rate of 1.2 ft / SEC. Walking on the moving sidewalk, a person travels 106 ft Ford an
    6·1 answer
  • I need help with this. 2 to the 6 power, +2 to the 3 power, raised to the 3 power. Please tell me the steps you took to get the
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!