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
11. Anna's goal is to walk 12 miles a week. This week, she walked 1 and 2/3
elena-s [515]

Answer:

2 Miles

Step-by-step explanation:

1  2/3 x 6 = 10

( She needs to walk 2 more miles )

Tomorrow Anna should run 2 miles to reach her goal.

Please vote for me, i really want to level up, thank you!

7 0
2 years ago
in peter's garden, 3/4 of the flowers are tulips. of the tulips, 2/3 are yellow. what fraction of the flowers in peter's garden
bekas [8.4K]
Half of the flowers are yellow tulips.

3 of the 4 columns are marked T for tulips.

Of those 3, 2 of them are yellow.

This shows us that 6 of the 12 boxes, 1/2, are yellow tulips.

8 0
3 years ago
A movie theater is located on a map of a city represented by a coordinate plane. The location of the movie theater is at (−4, 2)
Romashka [77]

See the graph

<h2>Explanation:</h2>

Remember to write complete questions in order to get good and exact answers. Here you haven't provided any option, but it's easy to plot this point on a coordinate system in order to know the location of the movie theater. We know that this theater is at the point:

(-4,2)

So let's plot this point in the cartesian plane:

  • The x-coordinate is -4
  • The y-coordinate is 2.

So the graph is shown below. Remember that the horizontal axis is called the x-axis while the vertical axis is called the y-axis.

  • x > 0 for the x-values to the right of the origin.
  • x < 0 for the x-values to the left of the origin.
  • y > 0 for the y-values above the origin
  • y < 0 for the y-values below the origin.

<h2>Learn more:</h2>

Cartesian coordinate system: brainly.com/question/2141683

#LearnWithBrainly

7 0
2 years ago
Determine both the x and y intercepts. Please help! Will mark brainliest!
Mademuasel [1]

Answer:

y-intercept: (0, 2.5)

x-intercept: (1.67, 0)

Step-by-step explanation:

Right now, you have 3x + 2y = 5. You want to change it into slope-intercept form to make the problem easier to solve.

2y = -3x + 5

y = -3/2x + 5/2

From here, you can see that the y-intercept is (0, 5/2). You can also say that the y-intercept is (0, 2.5).

To get the x-intercept, substitute 0 for y.

0 = -3/2x + 5/2

3/2x = 5/2

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0). You can also say that the x-intercept is (1.67, 0).

Hope this helps!

3 0
3 years ago
Read 2 more answers
What is the height ? Please help, I need it! Urgent !
Vika [28.1K]

Answer:

207.24 inch^2

Step-by-step explanation:

A=2*3.14*9+2.3.14*3*8

=56.52+150.72

=207.24 square inches

4 0
2 years ago
Other questions:
  • Mason is growing tomatoes in his garden this year. Ever 1.5 ft of stalk yields about 3.4 pounds of tomatoes. He has four plants
    10·1 answer
  • Financial planning does or does not require preparation
    9·1 answer
  • How do you change 0.35 to a whole. number
    5·1 answer
  • Alyssa bought a dress for $52 and 3 pairs of jeans. She paid a total of $125. Write an equation to represent this word problem
    12·2 answers
  • What does "area" mean in a circle?​
    5·1 answer
  • Kaitlyn is remodeling her kitchen the table shows the cost of items she wants to buy with her credit card it Kaitlyn has a $2,00
    11·1 answer
  • How would the domain of the function y = 4(12)^x be affected if it were to be changed to y = 4(24)^x?
    6·1 answer
  • Q2) A meat pie contains chicken and turkey in the ratio 4 : 1.    ( 3 marks)
    7·1 answer
  • 25 pts, please help ASAP
    7·1 answer
  • Bobby is buying ribs for his 4th of July cookout. The ribs are on sale for $3.50 per pound. If Bobby buys 5.5 pounds of ribs, ho
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!