Glenesse's Math Question

My question is # 28 in chapter 2.4.

Question:

The period, t, in seconds, of a pendulum is the time for a complete swing back and forth. The period can be calculated from the length, l, in metres, of the pendulum using the formula t = √4l. Determine the period of a pendulum with each of the following lengths. Express each answer to the nearest hundredth of a second.

a) 1.6 m

b) 2.5 m
c) 50 cm

Answers:

a) The period of a pendulum with the length of 1.6 m is 2.53 (s) seconds.

I first multiplied the length, which was 1.6, by 4 and got 6.4. I then square rooted that and got 2.53 s.

b) The period of a pendulum with the length of 2.5 m is 3.16 (s) seconds.

I first multiplied the length, which is 2.5, by 4 and got 10. I then square rooted that and got 3.16 s.

c) The period of a pendulum with the length of 50 cm is 1.41 (s) seconds.

I first multiplied the length, which is 50, by 4 and got 200. I then square rooted that and got 14.14, but I had to divide that by ten because we need to get from cm to m. I then got 1.41 s.

Julibella's Math Question

Chapter 2.4

Question 18)
A frame measures 30 cm by 20 cm. Can you mount a square picture with an area of 500cm^2 in the frame? Explain.


So you're frame is 20cm x 30cm which gives you an area of 600cm^2. You're trying to put a picture with an area of 500cm^2 which dimensions are 22.36cm x 22.36cm. The picture will not fit because it is too big.

Question 19)
A square picture with an area of 100 cm^2 is mounted on a square piece of matting. The matting has 2.5 times the area of the picture. Is the picture is centered on the matting, what width of the matting is visible around the outside of the picture? Give your answer to the nearest tenth of a centimeter.

First find the area of the matting:
100cm^2 x 2.5 = 250cm^2

Fing the side length of the picture:
sqrt 100cm^2 = 10cm

Find the side length of the matting:
sqrt 250cm^2 = 15.81cm

Subtract side lengths to find visible matting:
15.81cm - 10cm = 5.81cm

Make equal on both sides of the picture to find width of visible matting:
5.81 ÷ 2 = 2.9cm

The width of the matting visible around the outside of the picture is 2.9cm.