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
Leviafan [203]
3 years ago
7

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high

er than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast (in m/s) is the boat approaching the dock when it is 5 m from the dock
Mathematics
1 answer:
Agata [3.3K]3 years ago
5 0

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

You might be interested in
The scale used on a map is 1:250,000 the distance measures 8.5 centimetres what is the actual distance ?
LUCKY_DIMON [66]
8.5 × 250, 000 =

2,125,000

the actual distance is 21,250 m or 2125 km
8 0
3 years ago
What is 245 the the power of 8?​
vlabodo [156]

Answer:

1.2981614e+19

Step-by-step explanation:

you can always use a calculator for powers.

7 0
2 years ago
Write the system of equations corresponding to the augmented matrix shown below ⎡⎣⎢⎢−8−2150−9−6−11−21−1⎤⎦⎥⎥ Note: Write an equat
olganol [36]

Answer:

idk sry search it up

on photo math  just take a pic and it will give you the answer

6 0
3 years ago
What is the answer PLEASEE
umka2103 [35]

Answer:

3^{-4}

Step-by-step explanation:

3^5\cdot \:3^{-9}=3^{5-9}=3^{-4}

8 0
3 years ago
I need help please im only in the 7th grade &’ i don’t know what to do !
dedylja [7]

Answer: In the chart, put 6 in place of the question mark.

The equation should be something like w = 2/3 p

W is the number of quarts of water. P is the number of quarts of Pineapple juice.

This week they will need 3 times the previous week so 18 quarts of pineapple juice and 12 quarts of sparkling water.

Step-by-step explanation:

If the basic recipe is 2 water to 3 juice, and they used 4 quarts if water, you can see that is <u>double the amount of</u> water so you need <u>double the amount  </u> of juice. 2 times 3 is 6.

<em>Unit rate</em> means for ONE quart of juice, how much sparkling water is used. that should be  1 Pineapple Juice for 2/3 Sparkling water

OR

for EACH quart of sparkling water, how much juice do you need.

that would be 1 unit of Sparkling Water for 1 1/2 units of Pineapple Juice

4 0
2 years ago
Other questions:
  • •
    10·1 answer
  • Which one of these four sets of side lengths will form a right triangle?
    5·2 answers
  • If 10 people fill a 3 ft by 5 ft room, how many will fill a 9 ft by 5 ft room?
    7·1 answer
  • Richard goes to the electronics store. He buys 2 memory cards that cost $8.99 each and 3 packages of batteries that are on sale
    14·2 answers
  • I will give 15 points
    5·2 answers
  • Estimate the value of 98.5 x 13<br><br> And<br><br> 102.3 divided by 4.7
    9·2 answers
  • The new 12 mile hiking trail is 150% of the length of the original trial. How long was the original trial?
    14·1 answer
  • A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at a rate of 40 miles per hour, what
    14·1 answer
  • A researcher carefully calculates the correlation coefficient and gets a value of r=1.23. What does this value mean?
    7·1 answer
  • BRAINLIEST TO CORRECT QUICK
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!