# Computation of a Mathematical Equation (Math Problem Sample)

1:sOLVE x^2-2x-15=0 USING THREE METHODS OF SOLVING QUADRATIC EQUATION.

2:a>b then 1/a>1/b which implies that 5>2 then 1/5>1/2

3: Calculate total bowling costs

4:Given that n have the property that the sum of the digits of n and the sum of digits of n + 1 are odd numbers. FIND HOW MANY NUMBERS ARE IN N

MATHEMATIC ASSIGNMENT 0005

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Question 1 Answer

Factoring method

x2-2x-15=0

Find the product and the sum of the equation

Product=1×-15=-15 and sum=-2

Expand the equation

x2-5x+3x-15=0

Factorise

x+3x-5=0

Set each equation equal to zero

x+3=0 or x-5=0

x=-3 or 5

Quadratic method

ax2+bx+c=0

x=-b±b2-4ac2a

x2-2x-15=0

Apply the quadratic formula

x=2±(-2)2-(4)(1)(-15)2(1)

x=2±4+602

x=2±642

Simplify the equation

x=2±82

x=2+82 or2-82=0

x=102 or-62=0

x=5 or-3

Completing Square method

Put the equation in the form of ax2+bx=-c

x2-2x=15

Make sure a=1

Using the value of b from new equation, addb22 to both sides of the equation to form a perfect square on the left side of the equation

c=-222=1

x2-2x+1=15+1

x2-2x+1=16

Find the square root on both sides

x-1=±4

Solve the result of the equation

x=4+1 or-4+1

x=5 or-3

Question 2 Answer

To prove this let assume that a=5 and b=2

Following the theorem

a>b then1a>1b which implies that 5>2 then15>12

Which negate the property. Thus a>b then1a>1b is false

Question 3 Answer

(a) Number of teenagers = 26 Computation of Cinema Costs Cinema charges = 4×26= £104 Transport charges to cinema = £90

Hence, total cinema cost = 104+ 90 = £194

Computation of bowling costs

Bowling alley charges = 5.5×26= £143 Transport charges to bowling = £45

Hence, total bowling costs = 143 + 45 = £188

Question 4 Answer

Given: n have the property that the sum of the digits of n and the sum of digits of n + 1 are odd numbers

To Find: How many numbers

Solution:

Case 1: Sum of digit of n + sum of digits of n + 1 is odd

if sum of digit of n is even then sum of digit of n + 1 is even + 1

Hence, we get 2(even) + 1 = odd

if sum of digit of n is odd then sum of digit of n+1 is odd + 1

Hence, we get 2(odd) + 1 = odd

But there is case where n + 1 digit does not have sum 1 extra

whenever it changes like 9 to 10, 19 to 20 and so on

so, numbers which does not satisfy

9, 19, 29, 39 ,49, 59, 69, 79, 89 ( 99 is exceptional)

109, 119 , 129 , 139 , 149 , 159 , 169 , 179 , 189 , 199

up-to 1999

Numbers f

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