A tunnel has a semicircular cross-section and a diameter of 10 m. If the roof of a bus
just touches the roof of the tunnel when
the bus is 2 m from one side, how high is
the bus?

this question is from the IGCSE maths student book1, shape and space 2 for Edexcel

Height of bus = 4 m

Step-by-step explanation:

I have attached an image showing the cross section of this tunnel.

Since the diameter is given as 10m.

Thus, radius = 10/2 = 5 m

Since radius is 5 m, it means that the distance from the center of the circle to the tunnel edge = 5 m

If the bus is 2 m from one side, it means that the centre of the road to the right hand side of the bus will be;

5 - 2 = 3 m

Looking at the image and our values here, it is clear that, the distance from the centre of the road to the point where the bus just touches the roof tunnel = 5

Using Pythagoras theorem, we can find the height of the bus, h;

h² + 3² = 5²

h² + 9 = 25

h² = 25 - 9

h² = 16

h = √16

h = 4 m

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: