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USE OF LOGARITHMS.

1. Given the sides of a triangle, a= 450.2 ft., b = 430.3 ft., c = 420.1 ft., to calculate the angles A, B, C, by the formulae

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2. (a) Calculate amount (A) of $1 at compound interest for 25 years, at the rate of four per cent. per annum, by the formula

A = (1.04).

(b) Calculate the present value (P) of $1 due 25 years hence, interest considered as in (a), by the formula

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3. The volume of a sphere being 500.4 cubic inches, find its diameter.

4. Determine the smallest angle whose logarithmic cotangent is 0.0938

September. 1899

1. Prove the following relations:

sin (-x) =- sin x; cos(x) = cos x; cosec (- x)

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sin x; tan (+x) = tan x; cos (T+x)

2. Express each of the other simple trigonometric functions in terms of sin x.

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5. Assuming tan a and tan (m-1) a to be known, derive a formula for expressing the value of tan ma.

6. From the equation a sec2 0 = b + 2 c tan 0, find tan 0. 7. Write the formulae for solving a triangle ABC when two sides, a and b, and the included angle C, are given; and explain briefly their application.

Use of Logarithms.

1. Given two sides of a triangle, a = 576.5, b = 555.2, and the angle A (opposite a) = 58° 10. 2. to solve the triangle. Check your work.

2. Find approximately the time it will require for $1 to double itself at compound interest, at the rate of 4 per cent. per annum-using the formula (1.04)* = 2, x being the required time in years.

3. Compute the value of the following expression:

3 0.3756 X 0.265

0.227

4. Determine the smallest angle whose logarithmic cosine is 9.84105—10.

ALGEBRA.

JUNE, 1899. To QUADRATICS.

I. Find the highest common factor of

2x2+4x2 + 2x and 3x+9x2 + 6x.

2. Find the value in its simplest form of

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5. A has a hours to spare for an outing. How far can he ride with a friend at the rate of b miles an hour and just consume the time in walking back at the rate of c miles an hour?

6. Extract the square root of

x*

x-4x2+8x' - 8x +4.

7. Simplify the following expressions:

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5. A tank has three feed pipes; A, B, and C. A and B can fill it in L minutes, A and C in M minutes, and B and Cin N minutes.

How long will it take each alone to fill it?

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