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? ...continues

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 ...continues

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 ...continues

Vectors

You are given the vectors X = (1,1,1), y = (2,1,1) and z = (6,2,2). (i) Find the Cartesian equation of the plane Π normal to the vector x containing the point (2,1,1). (ii) Find the parametric equation of the line l through the points (2,1,1) and (6,2,2). (iii) If l' is given parametrically by l' = x + ty (with x ...continues

Geometry: Angles

Suppose

Measurement of a parallelepiped brick's diagonal

You have a brick of parallelepiped shape. You need to measure its diagonal (a distance between two opposite vertexes remote to the maximum). You have in your disposition a ruler and a rectangular edge of the plane surface (of the table, for example). What should you do to measure the diagonal if 1. You have also a pencil to ma ...continues

Algebra : Puzzle Problems

Please see the attached file for the fully formatted problems. 1) Have you ever seen the written form of the Sanskrit language? If so, you probably are amazed at how different this ancient language from India looks from ours. Some English words, however, are based on Sanskrit. For example, cup comes from the Sanskrit work kup ...continues

Tangent Circles

Please see the attached file for the fully formatted problems. Two congruent semicircles lie on the diameter of a third semicircle, each tangent to the other two. A small circle is tangent to all three semicircles. If the area of the shaded region is 45pi, what is the length of the radius of the small circle.