Solve by graphing. x + 3y = -9 5x + 3y = 3

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

Determine whether the following statement regarding the hypothesistest for two population proportions is true or false.

murzikaleks [220]

Answer:

False

Step-by-step explanation:

Let p1 be the population proportion for the first population

and p2 be the population proportion for the second population

Then

$H_{0}$ p1 = p2

$H_{a}$ p1 ≠ p2

Test statistic can be found usin the equation:

$z=\frac{p1-p2}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}}$ where

p1 is the sample population proportion for the first population

p2 is the sample population proportion for the second population

p is the pool proportion of p1 and p2

n1 is the sample size of the first population

n2 is the sample size of the second population.

As |p1-p2| gets smaller, the value of the test statistic gets smaller. Thus the probability of its being extreme gets smaller. This means its p-value gets higher.

As the p-value gets higher, the null hypothesis is less likely be rejected.

7 0

3 years ago

Please help I cant fuigure this outtttttttttttttttttttttttttttttttttt

krek1111 [17]

Answer:

18 ft. By 13 ft.

Step-by-step explanation:

8 0

3 years ago

A postulate is not __________.

Molodets [167]

A postulate isn't required to be proven

6 0

3 years ago

A triangular bandana has an area of 74 square inches. The height of the triangle is 9 1 4 inches. Enter and solve an equation to

Lilit [14]

Hi there!

The formula for the area of a triangle is A = 1/2(b x h). Using the information provided, all we have to do is plug in what we know and solve!

WORK:
74 = 1/2(b x 9.14)
148 = b x 9.14
b = 16.2 inches (approximately)

Hope this helps!! :)

6 0

3 years ago

Solve by graphing. x + 3y = -9 5x + 3y = 3 ​

Solve by graphing. x + 3y = -9 5x + 3y = 3