25. If l, w, and h are given in inches, the number of gallons in a rectangular tank is To what depth must a tank 30" by 18" be filled to contain 30 gal.? to contain 12 gal.? 26. If you have a rectangular tank in your school, find to what depth it must be filled to contain 5 gal.; 11 gal. 27. Find the value of F if C is 15° in the equation 28. Engine-builders use the following formula in making safety-valves, 22.5G A = P + 8.62 If A is 8 and G is 40, what is the value of P? 29. Write the formula for the average of a basket-ball team from the number of games won and lost. If the average of a team last year was 0.583, how many games would the team expect to lose for every 5 won? What does a fraction mean that is less than 0.5? that is more than 0.5? 30. How many would the team expect to win for every 6 games lost? for every 9 games lost? 31. If you have a basket-ball team, compute its average. How many games do you expect to win out of 8 played? of 11 played? -b" h=.5" -B=9′′ 33. The bases of a trapezoid are 23 dm. and 18 dm. respectively. Find the altitude if the area is 110 dm.2; if the area is 150 dm.2; if the area is 320 dm.2. 114. Literal Roots. An equation containing two or more literal numbers may be solved for any one of the literal numbers. Its root will contain all of the other literal numbers. Thus, 1. 5k +3 = at Solve for k in Exs. 1-20. Check all roots: 8. (a+b)k = (a + b)2 It is often necessary to change a formula to another form by solving the equation for some certain letter. 26. State by a formula that the distance travelled equals the velocity times the time. Solve this for v; for t. One form of a mechanic's formula is 28. Stand-pipes, as here shown, are often used to secure 29. What will be the pressure per square inch and per square foot for a stand-pipe 50' high? 60' high? 30. If a city has a stand-pipe 65' high, what pressure per square inch must its water-pipes be able to stand? 31. If there is a stand-pipe in your city, find its height and from that the pressure per square inch upon the waterpipes. 32. Solve the equation in Ex. 27, page 112, for F. 33. Solve the equation in Ex. 28, page 112, for P. Solve the equation in Ex. 28, page 112, for G. 35. The amount of money loaned at interest is 34. Solve this for P; solve for R; solve for T. 36. What principal amounts to $2500 in 2 yr. at 5%? 37. In what time will $1000 amount to $1200 at 5% ? V COMMON FRACTIONS-DECIMALS-PER CENTS 115. Common Fractions and Decimals. Decimals are really common fractions whose denominators are powers of 10. Hence, to change a decimal to a common fraction, merely place the required denominator under the decimal part and reduce to lowest terms. Thus, A common fraction is reduced to a decimal by carrying out the division of the numerator by the denominator. Thus, = 14 ÷ 25 = 0.56. 17. Show that 34 is a close approximate value for π, which as a decimal is nearly 3.1416. V 18. Show that the following formulas are equivalent, = D3 and V = .5238D3. Hold a number contest on the reduction of decimals to common fractions and common fractions to decimals. |