Tutor profile: Jeenal C.

If Sin(theta) = 1 , find cos(theta) and tan (theta).

Step 1 : Read the problem and gather the given information sin (theta) = 1 Step 2 : Determine the unknowns cos (theta) and tan (theta) Step 3: Develop equations ******************************************************************************************************************** We know the relation between sine and cosine, [sin (theta) ]^2 + [cos (theta) ] ^2 =1 Rearranging the equation to shift unknown terms on the left-hand side. [cos (theta) ] ^2 = 1 - [sin (theta) ]^2 [cos (theta) ]^2 = 1 - [1]^2 ..................................................... { Given information } cos(theta) = 0 ........................................................................ { Result 1 } ******************************************************************************************************************** Relation between sine, cosine, and tan tan (theta) = sin(theta) / cos (theta) tan (theta) = 1 / 0 ......................................................................{ From given information and Result 1 } Any number divided by zero is undefined. tan (theta) = undefined .......................................................{ Result 2}

The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2 ?

Step 1 - Read the problem and fetch the given information The arithmetic mean of 5 consecutive integers starting with 's' is 'a' Step 2 : Assigning variables M1 = Mean of 5 consecuitve integers starting with 's' = a M2 = Mean of 9 consecutive integers starting with 's+2' (To be determined) For the problem at hand, Mean = (Sum of consecutive integers) / (Number of consecuitve integers) Therefore- **************************************************************************************************************** M1 =[ (s) + (s+1) + (s+2) + (s+3) + (s+4) ] / 5 a = [ 5s + 10 ] / 5 We will now try to find the value of 's' in terms of known value 'a'. So rearranging the equation. a = s + 2 s = a -2 .......................................................................{ Result 1 } ***************************************************************************************************************** Now, determining the unknown. M2 =[ (s+2) + (s+3) + (s+4) + (s+5) + (s+6) + (s+7) + (s+8) +(s+9) + (s+10) ] / 9 M2 = [ 9s + 54 ] / 9 M2 = s + 6 M2 = ( a - 2) + 6 ....................................................... { Using value from Result 1 } M2 = a + 4 = Mean of 9 consecutive integers starting with 's+2' ...... { Result 2 }

The braking distance for a car traveling at 70 miles per hour is 5 feet less than twice the braking distance at 50 miles per hour. If the braking distance is 381 feet at 70 miles per hour, what is the braking distance at 50 miles per hour?

This is a very good example of a word problem. Solving these type of questions involve steps such as reading the problem, determining the knowns and unknowns of the question, and generating equations that relate them. Step 1 - Assigning variables d1= braking distance at 70 miles/hours = 381 feet d2=braking distance at 50 miles/hour ( To be determined) Step 2 - Creating equations Braking distance @ 70 miles/hr = twice the braking distance at 50 miles/hr - 5 feet less d1 = 2 * d2 - 5 Step 3 - Solving the equations Rearranging the equation to shift the unknown variable on the left-hand side of the equation. d1 = 2 * d2 - 5 2*d2 = d1 + 5 d2 = (d1+5)/2 d2 = (381+5)/2 ...................................... { Using value from step 1 } d2 = 193 feet = stopping distance at 50 miles/hr.