JUNE 1897. (b) 1. A tree 90 feet high stands on the bank of a stream. At a certain hour it casts a shadow directly across the stream and just reaching the opposite bank. If at the same time a telegraph pole 40 feet high casts a shadow 30 feet in length, what is the width of the stream? 2. Find by logarithms the value of 3/34875 X .087624 V(6.323) × 73.47 3. The area of a regular hexagon is equal to 961/3 sq. inches. Find the perimeter of the hexagon. 4. Find in square yards the area of a circle of which the radius is 39.87 meters. (Use logarithms.) 5. Define a logarithm, and explain why the multiplication of numbers is performed by the addition of their logarithms. pute the value of the expression to three decimal places. 5. Given a + x = √/a2 + x√/b2 + x2, to find x. 6. Solve the equations x + y = 12, x2 + y2 = 74. : 7. If A B C : D, prove by the principles of proportion that A2 B2: B2 C2 — D2 : D2. JUNE 1887. 1. Resolve the following expressions intò three factors: a1b + 8ac3bm, 4c3x2 + 4c2xy + cya. 5. Solve mx' + mn = 2mV/nx + nx. 6. Given (15x): (21 y) = 3: 7, and x'y' = 9, to find x and y. 37, 7. Expand by the binomial theorem 3by/2x — y. JUNE 1888. 1. Remove the parenthesis from the following expression and reduce it to its simplest form. 5x — (3x 4) [7x (29x)]. 2. Resolve each of the following expressions into as many factors as possible: (a) x' — 1; (b) (x2 + — y2 z3)2 - 4x3y'. 5. Solve the equation √x — 3 — √2x + 8 = — 3. 6. Solve the equation x3 -x=256. 7. Multiply x + 3 — 27—1 by x + 3 + 21—1. 8. Expand (x2 + b) to four terms. 9. Given the series, y = x — 1⁄2 x2 + 4x3-%x' + etc., to find the value of x in terms of y. |