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
How does the calculator get 48.8? mean (45, 80, 15, 10, 94)
jok3333 [9.3K]

Answer:

mean= sum of all observations /no.of observation

mean=45+80+15+10+94/5

mean=244/5

mean=48.8

this is how the calculator gets 48.8

5 0
3 years ago
60 cars to 20 cars indenify percent of change
Margaret [11]

Answer: -66.67%, but if the answer is supposed to positive then the answer is 66.67%.

<em>* Hopefully this helps:) </em>

7 0
2 years ago
A new lawn has a perimeter of 278ft. And a width of 64ft. A bag of grass seed will cover 384ft of ground. How many bags of grass
Anit [1.1K]

Answer:

13 bags

Step-by-step explanation:

Area of the lawn: A=lw

w= 64 ft

P= 2(l+w)= 278 ft ⇒

  • l= 278/2- 64= 75 ft
  • A= 64*75= 4800 ft²

bags of seed required:

  • 4800/384= 12.5 so 13  full bags needed
7 0
3 years ago
Please help me fill in the missing number ​
adelina 88 [10]

Answer:

6

Step-by-step explanation:

3/4 / 6 = 3/4 x 1/6, which equals 3/24

and prodigy is a good game :D

8 0
3 years ago
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two
Vikentia [17]

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

Y \sim P( \beta = 2)

the probability mass function can be represented as follows:

\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}

\mathtt{P(y =0) = \dfrac{0.1353  \times 1}{1}}

P(y =0) = 0.1353

4 0
2 years ago
Other questions:
  • 30% of 85 on a percent ruler
    15·1 answer
  • Will mark ya brainliest for the right answer!
    6·2 answers
  • Estimate___________.<br><br><br> 1,374<br> x 6<br> ______
    13·1 answer
  • Find the equation of the line in slope-intercept form containing the points (6,-1) and (-3,2)
    8·1 answer
  • PLEASE HELP!!!! I WILL GIVE BRAINLIEST AND 10 POINTS IF ITS GOOD!!
    8·1 answer
  • 100 POINTS NEEDED RIGHT NOW! On a graph plot the points where the following function crosses the x-axis and y-axis g(x) = -5^x+5
    10·1 answer
  • What’s the value of x???
    8·1 answer
  • Question Progress
    15·1 answer
  • Write the product(2+7i)(2-7i) in the form a+bi
    11·1 answer
  • Althea has $100. She divides it evenly among her 4 children. Her oldest child, Raul, spends $15 of the amount he receives. How m
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!