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Digiron [165]
2 years ago
9

(2 pts.) 9.) Find two equivalent expressions to tan 20° using the cotangent function in degrees.

Mathematics
1 answer:
aniked [119]2 years ago
7 0

tan (u) = a/b = cot (90° – u)

Let u = 20°

Take it from here.

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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
WILL GIVE BRAINLYIST DUE IN 2 HOURS
Alja [10]

Answer:

Step-by-step explanation:

Isn’t this mathematics not science

4 0
3 years ago
One student can paint a wall in 20 minutes. Another student can paint the same wall in 30 minutes. Working together, how long wi
Katarina [22]

1) in one minute for first  wiil be 1/20

the other 1/30, it means that  A paint in one minute  1/20 and B 1/30 then   A+B in one minute 1/20 + 1/30 = 3+2/60 = 5 / 60,  5/60 = 1/12

if in one min they make 1/12 then  in 12  min they  paint all the wall

5 0
3 years ago
The perimeter of a rectangular playground is 494 yards. The length of the playground is 7 more than twice the width. Find the le
lbvjy [14]

Answer:

https://youtu.be/wOH_gVtidns

I recorded a video of myself explaining it hope it helps ;)

Step-by-step explanation:

6 0
2 years ago
Which symbol correctly compares these fractions? 13 20 ___ 7 10
fomenos
These are fractions? Like 13/20 and 7/10? Is so the symbol would be 13/20 < 7/10 because 7/10 is a higher fraction than 13/20
7 0
4 years ago
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