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alex41 [277]
3 years ago
12

Someone please help me with my homework! Thanks!

Mathematics
1 answer:
Pie3 years ago
4 0
1.) slope=2
2.) slope= -5/4
3.) slope= 7/5
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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
<img src="https://tex.z-dn.net/?f=%28-5x%5E3%29%5E3%2F%2810x%5E5%29%5E2" id="TexFormula1" title="(-5x^3)^3/(10x^5)^2" alt="(-5x^
marta [7]

Answer:

-\frac{5}{4x}

Step-by-step explanation:

<h2>\left(-5x^3\right)^3\div \left(10x^5\right)^2</h2><h2>\frac{-5^3x^9}{\left(10x^5\right)^2}</h2><h2>\frac{-5^3x^9}{10^2x^{10}}</h2><h2>\frac{-5^3x^9}{5^2\cdot \:2^2x^{10}}</h2><h2>\frac{-5x^9}{2^2x^{10}}</h2><h2>\frac{-5}{2^2x}</h2>

-\frac{5}{4x}

- hope it helps! -

<h2 />

3 0
1 year ago
Landscaping company planted 176 tress in 8 equal rows in the new park. Jow many tress did the company plant in each row
Lynna [10]
22 plants in each row
5 0
3 years ago
9. Mark is filling up crates with watermelons for the food drive. He has large watermelons that weigh 10 pounds each and smaller
abruzzese [7]
9. 10x + 5y is the equation for larger watermelons + smaller watermelons (you did not provide information about the medium watermelons, so we must assume given the options you miswrote one of them). We can hold NO MORE than 500 pounds, so 10x + 5y must be smaller than 500. The best answer is C assuming that "5y" represents your "Medium Watermelons"- because smaller watermelons are stated to be 5 and medium ones should therefore be between 5 and 10, the option provided by A wouldn't make since because 3 pounded watermelons are not "medium" in comparison to the "small ones" that are heavier/bigger. Your best option is C, 10x + 5y < 500, the exact answer technically would be 10x + 5y <= 500.
4 0
3 years ago
Find the vertex of this parabola:<br> y = -x2 + 6x - 8
skelet666 [1.2K]

Answer:

4x-8

Step-by-step explanation:

y=-x2+6x-8

y=4x-8

4 0
3 years ago
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