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AnnyKZ [126]
2 years ago
14

Help with the following problem please

Mathematics
1 answer:
Effectus [21]2 years ago
3 0
Given:
The largest circle has a radius of R=7 units.
Let x be the radius of the large shaded circle.
The small shaded circles have a radius of 1/5 of the large shaded circle.
=> the small shaded circles have a radius of r=x/5

By adding up radii, we have the equation
2(r+x+r)=2(x/5+x+x/5)=2R=2*7=14
Simplify:
7x/5=14/2
x=5
=> r=1

Area of outer circle                  = \pi R^2=\pi7^2=49\pi
Area of large shaded circle      = \pi x^2=\pi5^2=25\pi
Area of 4 small shaded circles = 4\pi r^2=4\pi1^2=4\pi
Total area of shaded circles     =25\pi+4\pi=29\pi

Shaded area as a fraction of that of the outer circle 
=\frac{29\pi}{49\pi}=29/49

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A bus travels from Station A to Station B, and a truck travels from Station B to Station A on the same road. The speed of the bu
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Answer:

The distance between the two train stations is 1728 km

Step-by-step explanation:

The speed of the bus = 54 km/h

The speed of the truck = 48 km/h

When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck

Let the distance between the two train stations = x

Let the location where they first meet be y from station A we have;

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Location where they

The time for the truck and the bus to meet again = t

Therefore, 54 × t - 48 × t = 216 km

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t = 36 hours

Therefore, the time for the bus to travel x + 216 km = 36 hours

54 × 36 = 1944 = x + 216

x = 1944 - 216 = 1728 km

The distance between the two train stations = 1728 km.

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