The wheel of a car has an outer radius of 25 cm. Calculate: a) how far the car has travelled after one complete turn of the wheel, b) how many times the wheel turns for a journey of 1 km.

A child's toy wagon has an axle with a nominal diameter of $5 / 8 \mathrm{in}$. For the wheel bore and axle, specify the class of fit, the limits of size, and the limits of clearance. Use the basic shaft system.

Rolling is a combination of __________ motion and _____________motion.

When you're riding a slow Ferris wheel, you may feel slightly lighter at the top of the wheel, and a little heavier at the bottom. If the wheel keeps accelerating, however, at a certain speed of rotation you'll feel weightless at the top, and double your normal weight at the bottom. What's special about this particular rotation speed?

Evaluate the following: a) $6 \times 4-3 \times 8$ b) $15 \div 3+2 \times 7$

The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate:

a) the perimeter of the garden.

b) the total area of the garden.

a) A number is trebled and then 7 is added to it. If the total is 28, find the number. b) Multiply a number by 4 and then add 5 to it. If the total is 29, find the number. c) If 31 is the result of adding 1 to 5 times a number, find the number. d) Double a number and then subtract 9. If the answer is 11, what is the number? e) If 9 is the result of subtracting 12 from 7 times a number, find the number.

A garden in the shape of a trapezium is split into three parts: flower beds in the shape of a triangle and a parallelogram; and a section of grass in the shape of a trapezium, as shown below. The area of the grass is two and a half times the total area of flower beds. Calculate:
a) the area of each flower bed, b) the area of grass, c) the value of x.

All of the following are strategies involved in revision except:

a. checking for redundant language b. getting rid of euphemisms and clichés c. removing overly complicated language d. coming up with new ideas and topics

Consider a 20-cm-diameter hemispherical enclosure. The dome is maintained at 600 K and heat is supplied from the dome at a rate of 50 W while the base surface with an emissivity of 0.55 is maintained at 400 K. Determine the emissivity of the dome.

Sketch a line and a point not on the line. Describe the shortest distance between the point and the line.

A cylindrical container with an extended rectangular back and semicircular ends is all fabricated from the same sheet-metal stock. Calculate the angle $\alpha$ made by the back with the vertical when the container rests in an equilibrium position on a horizontal surface.

The gazebo in the photo is built in the shape of a regular octagon. Each side is 6 ft long, and the enclosed area is 172.8 ft². What is the length of the apothem?

Write an essay on air-, water-, and soil-based heat pumps. Discuss the advantages and the disadvantages of each system. For each system identify the conditions under which that system is preferable over the other two. In what situations would you not recommend a heat pump heating system?