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13 Maths Exercise Solutions

Show that if x^{2} – 5x + 6 = 0, then x = 3 or x = 2

Prove that the function f : R → R defined by f (x) = 2x + 5 is one-one.

Show that if

Show that in any triangle ABC a = b cos C + c cos B

Show that the set of all prime numbers is infinite.

Show that if a matrix A is invertible, then A is non-singular.

Find the height of a given tower using mathematical modelling.

Let a business firm produces three types of products P_{1}, P_{2} and P_{3} that uses three types of raw materials R_{1}, R_{2} and R_{3}. Let the firm has purchase orders from two clients F_{1} and F_{2}. Considering the situation that the firm has a limited quantity of R_{1}, R_{2} and R_{3}, respectively, prepare a model to determine the quantities of the raw material R_{1}, R_{2} and R_{3} required to meet the purchase orders.

Let a business firm produces three types of products P_{1}, P_{2} and P_{3} that uses three types of raw materials R_{1}, R_{2} and R_{3}. Let the firm has purchase orders from two clients F_{1} and F_{2}. Considering the situation that the firm has a limited quantity of R_{1}, R_{2} and R_{3}, respectively, prepare a model to determine the quantities of the raw material R_{1}, R_{2} and R_{3} required to meet the purchase orders. In case

A = , B =

and the available raw materials are 330 units of R_{1}, 455 units of R_{2} and 140 units of R_{3}.

A = , B =

and the available raw materials are 330 units of R

Suppose P_{1}, P_{2}, P_{3} and R_{1}, R_{2}, R_{3}. Let a business firm produces three types of products P_{1}, P_{2} and P_{3} that uses three types of raw materials R_{1}, R_{2} and R_{3}. Let the firm has purchase orders from two clients F_{1} and F_{2}. Let the firm has 330 units of R_{1}, 455 units of R_{2} and 140 units of R_{3} available with it and let the number of raw materials R_{1}, R_{2} and R_{3} required to manufacture each unit of the three products is given by

B =

How many units of each product is to be made so as to utilise the full available raw material?

B =

How many units of each product is to be made so as to utilise the full available raw material?

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