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
marta [7]
3 years ago
9

A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the poli

ce car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road
Mathematics
1 answer:
pishuonlain [190]3 years ago
6 0

Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.  

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt  be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

You might be interested in
A jar contains jellybeans that are all the same size and shape.
Sergeeva-Olga [200]
G because the first jelly bean was put back so it doesn't matter.
6 0
3 years ago
In Mona’s new video game she earns 30 points for each fish caught and 80 points for each octopus captured, but she loses 15 poin
Aleksandr-060686 [28]
If x is fish, y is octopi, and z is crabs, then you would have to know the numbers.
Then your answer would be c. 30x+80y-15z.
Because x=+30, y=+80, and z=-15.
I hope that helps. If you need any further help on this problem just ask.
5 0
3 years ago
Read 2 more answers
When adding the numbers 4+9+7+6+3 you can make one group of 10.True or False
Keith_Richards [23]

Answer:

false

Step-by-step explanation:

6 0
3 years ago
11to the power of 3 multiply by 21 to the power of three
julia-pushkina [17]

Answer:

12326391

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Which of the following is not an integer? Group of answer choices -1 -2.5 4 25Which of the following is not an integer?
Paha777 [63]
The correct answer is -2.5
6 0
3 years ago
Read 2 more answers
Other questions:
  • 283% of 305 estimate
    13·2 answers
  • Determine whether the point (1, 5) is a solution to the system of equations. Explain your reasoning in complete sentences.
    15·2 answers
  • Which equation has no solution?
    12·2 answers
  • Find the value of x in the icolese triangle below
    12·1 answer
  • Find the value of x. Write your answer in simplest radical form.
    6·1 answer
  • Brita has a monthly budget of x dollars. She spends $1,425 on her mortgage every month. One-third of her remaining budget is spe
    13·1 answer
  • Can someone plz plz plz help me?????
    11·1 answer
  • In the figure below, m∠1 = x and m∠2 = x - 8. Which statement could be used to prove that x = 49?
    13·1 answer
  • Which of the lines that appear in the graph would be parallel to a line with a slope of 3 and a y intercept at 0,3
    7·1 answer
  • 8 x 10*-3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!