10. A closed rectangular box, having a squarebase, has a total surface area of 16 m2. Ifa main diagonal of the box has a lengthof 3 m, what are the dimensions of thebox?11. An open rectangular box, with a squarebase, has a square area of 128 m2.Ifthe cost per square metre of material forthe sides was£1 and for the bottom was£1.20, and the total cost of the materialwas£131.2, what are the dimensions ofthe box? 4
Math 17 Lecture No 2.7: Word Problems and Variation 12. A cyclist travelled a certain distance ather usual speed.If her speed had been2 km/hr faster, she would have travelledthe distance in 1 hr less time. If her speedhad been 2 km/ hr slower she would havetaken 2 hr longer. Find the distance trav-elled and her usual speed.3Variation1. The circumference of a circle is directlyproportional to its radius.2. What happens to the circumference ofthe circle if the radius is doubled?3. What happens to the circumference ofthe circle if the radius is halved?4. True or False: ifxis directly proportionalto the square ofz, then ifzis doubled,then so isx.5. If the variablezvaries directly as thesquare ofxand inversely as the cube ofy, andz= 2 whenx= 2 andy= 3, thenthe proportionality constant is.6. Ifyvaries directly asxand inversely asthe square ofz, and ify= 2 whenx= 4andz= 2, find the constant of propor-tionality.7. The stiffness of a beam varies jointly asits breadth and depth and inversely asthe square of the length. Find the changein stiffness if the breadth and depth areboth increased by 25% and the length isreduced by 50%.8. If the side of a square is increased by 40%,the area of the square will increase by.9.Pvaries directly as the square root ofmand inversely as the cube ofO. Ifmwerequadrupled andOwere doubled, whatwill be the effect onP?10. If the circumference of the circle is in-creased by 12 cm, by how much does theradius of the circle increase? 5
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- Spring '11
- Math, AURORA, Odette, Solor