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aivan3 [116]
3 years ago
14

A boat attempts to sail due east at 15km/h, but is taken off course by a current of 5 km/h flowing in the southwest direction. F

ind the resultant speed of the boat and the bearing on which it travels.
Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
8 0

Answer:

Resultant speed = 12 km/h.

Bearing is 107.14 degrees.

Step-by-step explanation:

This can be represented by a triangle of velocities with lengths 15 and 5 with the included angle = 45 degrees.

To find the velocity of the resultant  we use cosine rule:

v^2 = 15^2 + 5^2 - 2*5*15cos 45

v^2 = 143.934

v = 12.0 km/h to the nearest tenth.

To find the bearing we use the sine rule to find the angle down from due east>

12 / sin 45 = 5/ sin x

sin x =  5 sin 45 / 12 = 0.2946278

x = 17.14 degrees.

Bearing is therefore 90 + 17.14 = 107.14 degrees.

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Glen, Andre, and Ramón share the cost of renting a vacation cottage. The total cost is $960. Glen pays 30% of the total cost. An
SashulF [63]

Answer:

Ramon pays $240.

Step-by-step explanation:

30% of $960 is $288, so Glen pays $288

0.45 = 45%

45% of $960 is $432, so Andre pays $432

30% + 45% = 75% meaning Ramon pays 100% - 75% which is 25%.

25% of $960 is $240. So, Ramon pays $240.

You could also add up the payments of Andre and Glen and subtract that sum from $960 to get the same answer.

8 0
3 years ago
50 PTS BRAINLIEST
Montano1993 [528]

Answer:

it has 5 hopefully this helps you with work

4 0
3 years ago
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Please help with number 9 & 10
aniked [119]

Answer:

9. Triangle ABQ is congruent to Triangle BAP because of SAS congruency

10. x=5, y isn't shown anywhere

Step-by-step explanation:

9. The side AB is shared between the two triangles.

It is given that angle A and angle B are congruent.

It is given that AQ is congruent with BP.

Using these three, you can say that  Triangle ABQ is congruent to Triangle BAP because of SAS congruency.

10. 7x-4=31 (given)

x=5

Do the same thing with y.

7 0
3 years ago
The diagram shows parallel lines cut by two transversal lines creating a triangle. Which statements are true? Check all that app
vitfil [10]

Answer:

m

m

m

Step-by-step explanation:

<u>Verify each statement</u>

case A) m

The statement is True

we know that

The measure of angle A is equal to the angle marked 20\° by corresponding angles

case B) ∠B and the angle marked  60\° are alternate exterior angles

The statement is False

Because, ∠B and the angle marked  60\° are corresponding angles

case C) m because it is a vertical angle to the angle marked 100\°

The statement is True

we know that

m ------> by vertical angles

case D) ∠B and ∠C are supplementary angles

The statement is False

we know that

m ---> the sum is less than 180\°

case E) m

The statement is True

we know that

m

and remember that

m

so

substitute

m

3 0
3 years ago
Read 2 more answers
PLEASE HELP ILL MARK BRAINIEST
Pachacha [2.7K]

Answer:

Answer:

P(t) = 10t - 400

Step-by-step explanation:

Selling price of each ticket = $10

Cost of setting up the dance= $400

Profit = Revenue - cost

Revenue = price × quantity

Revenue that will maximize profit = 10t

where t= quantity of tickets that maximises profits

Cost = $400

Profit(t) = Revenue - cost

P(t)= 10t - 400

Step-by-step explanation:

Hope this helps, have a great day!

6 0
3 years ago
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