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# An Introduction To Mathematics with Applications to Science by Isaiah Leslie Miller

By Isaiah Leslie Miller

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Extra resources for An Introduction To Mathematics with Applications to Science and Agriculture

Sample text

30] Problems 1. The 2. height of a cylinder volume as a function press the radius. The is 5 feet greater than the radius. Ex- of the height; as a function of the altitude of a right triangle is k feet Express the hypotenuse in terms of the base less than the base b. b. 3. How many cubic yards must be excavated in digging a ditch 300 rods long, 18 inches wide at the bottom, 6 feet wide at the top and 5 feet deep? 2 feet per second? 4. How much concrete is there in a circular silo whose walls are 9 inches thick, 14 feet outside diameter and 32 feet high?

35] Eliminate z between (1) and (2). This may be done by multiplying (1) by 2 and adding the result to (2), Solution. we have, 6x 5x + 4y - 3y + llx+ Now 2z = 8, (4) 2z = 5, (5) = 13. (6) y eliminating z between (1) and 9x + 6y - 6x - 4y + (3), solve (6) Multiply (6) and = 12, (7) 30 = 7, (8) = 19. (9) = x and y as illustrated in Art. 34. 2 and add the result to (9) and by Substituting x (9) for 1 in (6), 7x = 7, x = 1. we = 1, y = 2 in and solving y = 2, 2 = and 3. Exercises Solve for x, 1. 2s 5x x - 4y 3y y, and z: + 5* = 18, = = 19.

X FIG. 10. 14. Surface S of a sphere of radius 2 , or r, 5 = or diameter D. V 29 FUNCTIONS ART. 30] Problems 1. The 2. height of a cylinder volume as a function press the radius. The is 5 feet greater than the radius. Ex- of the height; as a function of the altitude of a right triangle is k feet Express the hypotenuse in terms of the base less than the base b. b. 3. How many cubic yards must be excavated in digging a ditch 300 rods long, 18 inches wide at the bottom, 6 feet wide at the top and 5 feet deep?