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Alenkinab [10]
2 years ago
6

Two row boats start at the same location, and start traveling apart along straight lines which meet at an angle of π3. Boat A is

traveling at a rate of 5 miles per hour directly east, and boat B is traveling at a rate of 10 miles per hour going both north and east. How fast is the distance between the rowboats increasing 3 hours into the journey?
Mathematics
1 answer:
alina1380 [7]2 years ago
5 0

Answer:

  5√3 miles per hour

Step-by-step explanation:

Throughout their journey, the component of velocity of rowboat B to the east is the same as that of rowboat A:

  (10 mph)(cos(π/3)) = 5 mph

Meanwhile, the component of velocity of rowboat B to the north is ...

  (10 mph)(sin(π/3)) = 5√3 mph

Since rowboat A is always traveling in a direction that is at right angles to the direction between the boats, it contributes nothing to their relative speed. Since rowboat B is always directly north of rowboat A, its speed to the north is their relative speed.

The distance between the rowboats is increasing at 5√3 mph ≈ 8.66 mph.

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The segments shown below could form a triangle.
olga2289 [7]

By the Triangle Inequality Theorem, the sum of two sides should be greater than the length of the third side, while the difference of these two sides should be less than the length of this third side. Normally you would take the absolute value of the difference of these two side as you wouldn't know which is greater than the other!

The simplest way to prove whether these line segments can form a triangle, is by going against this theory. Let us prove that the line segment don't form a triangle. As you can see, adding 7 and 1 is greater than 1, respectively 7 and 7 is greater than 1. Thus -

<u><em>Solution = A. True</em></u>

3 0
2 years ago
A dataset has 1000 records and 50 variables with 5% of the values missing, spread randomly throughout the records and variables.
dusya [7]
Answer: 50 

Explanation: 

Since 5% of the values are missing, the expected number of records to be removed is interpreted as the expected value of the records to be removed whose probability of having missing values is 0.05. 

Hence, the number of records that are expected to be removed is given by

Expected Value = (number of records)(probability of having a missing value)
                          = (1000)(0.05)
Expected Value = 50  
8 0
2 years ago
A toaster oven costing $130 offers an extended warranty for 25% of the purchase price. If the local repair shop will fix a toast
pav-90 [236]

Answer:option c is the correct answer.

Step-by-step explanation:

A toaster oven costing $130 offers an extended warranty for 25% of the purchase price. This means that the money value of the warranty is

25/100 × 130 = 0.25 × 130 = $32.5

If the local repair shop will fix a toaster oven for $8, then the number of times that the toaster oven will break in order for the warranty to pay for itself is

32.5/8 = 4.0625

Therefore, it is 4 times

8 0
2 years ago
Marcella ate one cup of air popped popcorn. which equation can Marcelo use to find how many carbohydrates she consumed?
Dahasolnce [82]
She ate 6.2 carbohydrates

8 0
2 years ago
Read 2 more answers
Tickets to a movie cost $5 for adults and $3 for students. A group of friends purchased 18 tickets for $82.00. How many adults t
TEA [102]

Answer:

They purchased 14 adult tickets and 4 kids tickets.

Step-by-step explanation:

14 x 5 = 70

3x4=12

and then add 70 plus 12 to get 82 dollars.

7 0
2 years ago
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