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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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Let's use 8 days as the maximum time we are going to be renting the car.

Putting that into the equation means, 500$ for Harry's Rentals and Smilin' Sam's at $600.

Therefore, Happy Harry's Rentals are better for the 7th and 8th days while Smiling Sam's are the better from day's 1 to 6.

Work:

500$ is a fixed value so it doesn't change (constant)

200 + 50x

x = days

8 days = 8x

200 + 50(8)

200 + 400 = 600

8 0
2 years ago
Choose the correct simplification of (3x3 + 2x2 − 5x) − (8x3 − 2x2)
zmey [24]
(3x³ + 2x² - 5x) - (8x³ - 2x²<span>) =
</span>3x³ + 2x² - 5x - 8x³ + 2x² =
-5x³ + 4x² - 5x
5 0
2 years ago
Read 2 more answers
What is the following quotient 3 sqrt 8/ 4 sqrt 6
adell [148]
We have that
(3√8)/(4√6)

we know that
√8---------> √(2³)-----> 2√2
so
(3√8)/(4√6)=(3*[2√2])/(4√6)---> 6√2/(4√6)
√6=√(2*3)---> √2*√3
6√2/(4√6)=6√2/(4√2*√3)----> 6/(4√3)----> 6/(4√3)*(√3/√3)-----> 6√3/(4*3)----> √3/2

the answer is
√3/2

7 0
2 years ago
Read 2 more answers
the graph of g(x) is a translation of the function f(x) = x2. the vertex of g(x) is located 5 units above and 7 units to the rig
bulgar [2K]
Translation of 7 units to the right ⇒ subtract 7 units to the argument ⇒ f(x-7)

Translation of 5 units up ⇒ add 5 units to the function ⇒ f(x) + 5

g(x) = f (x-7) + 5 = (x-7)^2 + 5

The subtraction of 7 units to the argument of the function (this is x) translates the function 7 units to the right.

Adding 5 units to the function f, translates the graph 5 units up.
6 0
2 years ago
Read 2 more answers
Soup ordinarily priced at 2 cans for .33 cents may be purchased in lots of one dozen for 1.74, what is the savings per a can whe
Sidana [21]

Answer:

Savings per can would be 0.02 cents when purchased in lots.

Step-by-step explanation:

Given:

Ordinary price of soup 2 cans = 0.33 cents.

When purchases in lots 12 cans = 1.74

We need to find the saving per can when purchased in Lots.

Solution:

Ordinary price of soup 2 cans = 0.33 cents.

1 can  = Cost of 1 can when purchased ordinary.

By Using Unitary method we get;

Cost of 1 can when purchased ordinary = \frac{0.33}{2} = 0.165\ cents/can

Now we will find the Cost of 1 can when purchased in lot.

12 cans = 1.74

1 can = Cost of 1 can when purchase in lot.

Again by using Unitary method we get;

Cost of 1 can when purchase in lot = \frac{1.74}{12} = 0.145\ cents/can

Savings = Cost of 1 can when purchase in lot - Cost of 1 can when purchased ordinary

Savings = 0.165-0.145=0.02\ cents/can

Hence Savings per can would be 0.02 cents when purchased in lots.

5 0
2 years ago
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