I need help , I don't understand

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

Agata [3.3K]

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

5 0

3 years ago

0.123 × 0.007 = _______. A. 0.000861 B. 0.00871 C. 0.861 D. 0.000900

melamori03 [73]

The answer is A 0.000861

3 0

3 years ago

Read 2 more answers

Sabe-se que no inventário periódico, o registro contábil do estoque de mercadorias ocorrerá apenas no final de um determinado pe

DedPeter [7]

Answer:

It is known that in the periodic inventory, the accounting record of the stock of goods will occur only at the end of a certain period with the physical count of the existing quantities. Consider the following CVM information = 500.00; Initial Inventory = 700.00 and Purchases = 800.00. Applying the concept of periodic inventory and applying the formula for calculating the CMV, determine the value of the final stock.

ALTERNATIVES

Final stock of 2,000.00.

Final stock of 1,500.00.

Final stock of 1,300.00.

Final stock of 1,200.00.

Final stock of 1,000.00.

Final Stock (EF) = 1,000.00

Step-by-step explanation:

Alternative E - Final stock of 1,000.00.

Given That,

CMV = 500,00

Initial Stock (EI) = 700.00

Purchases (C) = 800.00

Final Stock (EF) = ?

Formula

CMV = Initial Stock (EI) + Purchases (C) - Final Stock (EF)

CMV = EI + C - EF

500 = 700 + 800 - EF

500.00 = 700.00 + 800.00 -X

500 = 1500- EF

500.00 = 1,500.00-X

EF = 1500-500

X = 1,000.00

EF = 1,000.00

Therefore, the final stock is 1,000

3 0

3 years ago

Calculate the mean, median, mode, range, and 5 Number Summary of the following data set: 5,6,8,4,7,5,4,2,5,6,5,2,1,4

Artist 52 [7]

Answer:

mean = 4.57, median = 5 , mode = 5, range =7 ,

five number summary: Minimum value= 1 , First Quartile = 4, Median = 5

Third Quartile = 6, Maximum value = 8

Step-by-step explanation:

First arrange the data in ascending order.

1,2,2,4,4,4,5,5,5,5,6,6,7,8

Mean = sum of all numbers / total numbers

= 1+2+2+4+4+4+5+5+5+5+6+6+7+8 / 14

= 64 / 14

= 4.57

Median:

Since the given data is even number so, we can find median by taking mean of 2 middle numbers.

so the middle numbers are 7th and 8th data i.e, 5 and 5

Median =(5+5)/2

= 5

Mode:

The most repetitive number in the data set is mode

So Mode = 5

Range:

Range can be found by subtracting smallest number from largest number in the data set.

Smallest number = 1, Largest number = 8

Range= Largest number - Smallest number

= 8-1 = 7

Five no Summary

Minimum value= 1

First Quartile ( 25 % mark )= 4

Median = 5

Third Quartile (75 % mark) = 6

Maximum value = 8

First quartile can be found by : consider the data on left of the median and find median among them

Third quartile can be found by: consider the data on right of the median and find median among them

7 0

3 years ago

Select the correct answer.

Burka [1]

The equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

<h3>What is the equation of the direct variation between two variables?</h3>

In this problem we have a case of direct variation between two variables, which is mathematically described by a direct proportionality model, whose form and characteristics are shown below:

b ∝ √c

b = k · √c (1)

Where k is the proportionality constant.

First, we determine the value of the constant of proportionality by substituting on b and c and clearing the variable: (b = 100, c = 4)

k = b / √c

k = 100 / √4

k = 100 / 2

k = 50

Then, the equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

To learn more on direct variation: brainly.com/question/14254277

#SPJ1

7 0

2 years ago