As.

Mathematics

1 answer:

Natalka [10]3 years ago

6 0

9514 1404 393

Answer:

4/13 h ≈ 0.308 h
22 9/13 km ≈ 22.7 km

Step-by-step explanation:

Mary and Amaruk are starting 35 -15 = 20 km apart. Their closing speed is 40 +25 = 65 km/h. The time it will take to close the gap between them is ...

t = (20 km)/(65 km/h) = 20/65 h = 4/13 h ≈ 0.308 h

They will pass each other after 4/13 hours, about 18 minutes 28 seconds.

In that time, Mary will have increased her distance from Hall Beach by ...

d = (4/13 h)(25 km/h) = 100/13 km = 7 9/13 km

Her distance from Hall Beach when she passes Amaruk will be ...

15 km + 7 9/13 km = 22 9/13 km ≈ 22.7 km . . . . . distance from Hall Beach

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Note:
The area of a circle with radius r is πr².
An entire circle has a central angle of 360°.

For the sector with radius = (3+4) = 7cm and a central angle of 120°, the area is
$A_{1}= \frac{120}{360}*(49 \pi ) = \frac{49}{3} \pi \, cm^{2}$

For the sector with radius = 3 cm and a central angle of 120°. the area is
$A_{2}= \frac{120}{360} *(9 \pi ) = 3 \pi \, cm^{2}$

The area of the shaded sector (see the figure) is
$A=A_{1}-A_{2} = ( \frac{49}{3} -3) \pi = \frac{40}{3} \pi \, cm^{2}$

Answer: $\frac{40}{3} \pi \, cm^{2}$