Enlargement

Phil and Fran are photographers who develop their own pictures and also restore old photographs. They have an enlargement and reducing machine that can change the size of photographs. A customer asks Fran to enlarge a 3 inch by 5 inch photograph to 8 inch by 10 inch. Can this be done without cutting or distorting the picture? Explain.

Finding the Equation of a tangent to a circle.

You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.

Calculating angles given the sides.

Given a,b,and c, find three angles A, B and C?

The Radius of the Circumscribed circle for a triangle

The circumscribed circle is the circle passing through the three vertices of a triangle ABC. Assume the following results from geometry. The perpendicular bisectors of the sides of a triangle meet in a point O that is the center of the circumscribed circle. a) According to a theorem from geometry, the measure of the angle AOC is twice that of angle B. What theorem is this? (State the theorem in complete sentences) b) Draw a perpendicular from the center O to AC, meeting AC at T. Denoting the length of the side opposite to the angle B by b, explaing why AT=TC-b/2. c) Explain why triangle ATO is congruent to triangle CTO. d) Use the results in parts (a) and (c) to show that... click for more

Manipulation of a summation with application to finance math and interest rates.

Please see the attached file for the fully formatted problem. In financial mathematics, when valuing cash flows, an important function is the so-called immediate annuity-certain, a_n, which is defined by the relation a_n = v + v^2 + v^3 + ....... + v^n where v:=(1+i)^(-1) and i represents the effective rate of interest per annum. Prove that a_n = (1-v^n)/i If the effective rate of interest is 3% pa, find a_4 to 3 decimal places.