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Anit [1.1K]
2 years ago
10

Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while t

he other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?
Mathematics
1 answer:
fgiga [73]2 years ago
4 0

The angle between their paths to the nearest degree is 68⁰.

<h3>Displacement of each boats after 45 minutes</h3>

first displacement, a = 15 km/h  x (45/60)

first displacement, a = 11.25 km

second displacement, b = 18 km/h  x (45/60)

                                     b = 13.5 km

<h3> Angle between their paths to the nearest degree</h3>

c² = a² + b² - 2ab(cosθ)

2ab(cosθ) = a² + b² - c²

cosθ =  (a² + b² - c²)/(2ab)

cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)

cosθ = 0.371

θ = arc cos(0.371)

θ = 68.22 ⁰

Thus, the angle between their paths to the nearest degree is 68⁰.

Learn more about angles here: brainly.com/question/25716982

#SPJ1

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A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon
zmey [24]

Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.

<h3>What is the volume of a sphere?</h3>

The volume of a sphere of radius r is given by:

V = \frac{4\pi r^3}{3}

Applying implicit differentiation, the rate of change is given by:

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

In this problem, we have that:

\frac{dV}{dt} = 500, r = 70

Hence the rate of change of the radius is given as follows:

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

19600\pi\frac{dr}{dt} = 500

\frac{dr}{dt} = \frac{500}{19600\pi}

\frac{dr}{dt} = 0.0081

The radius is increasing at a rate of 0.0081 cm per minute.

More can be learned about implicit differentiation at brainly.com/question/25608353

#SPJ1

4 0
2 years ago
For friends went to a restaurant in bought Two large pizzas and if each pay 5.25 how much was each pizza
guajiro [1.7K]

Answer:

$10.5

Step-by-step explanation:

4(5.25) = $21 (total amount of money spent)

we want to divide that by 2 because we want to find the cost of one pizza

21/2 = $10.5

8 0
3 years ago
Andrea has 18 yards of fabric how many 4 inch pieces can she cut from her original piece
Nikolay [14]
Andrea can cut 4 1/2 (or 4.5) inch pieces from her original piece.

18/4 = 4.5


Hope this helps!
5 0
4 years ago
1.Are AC^line and BE^line congruent? Explain.
Ksivusya [100]
Line AC has 7 spaces and line BE has 8

to know this you count from letter A to C which is 7.  and then B to E which is 8

They ARE NOT CONGRUENT 
3 0
3 years ago
Hi, I need help.
slavikrds [6]

Answer:

B, 24 (second answer choice)

Step-by-step explanation:

4r+7s=23

r-2s=17

8r+14s=46

7r-14s=119

15r=165

r=11

11-2s=17..........by putting value of r in ii

-2s=17-11

2s= -6

s= -3

3r+3s=3*11+3(-3) you get this by putting values of r and s

       =33-9

       =24    (B)

7 0
3 years ago
Read 2 more answers
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