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Answers by Rajesh P.

Limit questions (answer)

Let us first simplify the equation. (1-cox5x)/(1-cos7x) .... multiply numerator and denominator by (1+cos5x)(1+cos7x) =[(1-cos5x)(1+cos5x)(1+cos7x)]/[(1-cos7x)(1+cos7x)(1+cos5x)]......remember that (a+b)(a-b)=a2-b2 =[(1-cos25x)(1+cos7x)]/[(1-cos27x)(1+cos5x)] ...

Consider the following special types of polynomials. (answer)

1) use perfect square formula a2+2ab+b2=(a+b)2 16y2 + 24y + 9 = (4y)2 + 2.4y.3 + 32 = (4y+3)2 2) use difference of squares formula a2 - b2 = (a+b)(a-b) 49x2 - 100y2 = (7x)2 - (10y)2 = (7x-10y)(7x+10y) 3) use sum of cubes formula, a3 + b3 =...

Factor the following binomial. (answer)

a) Easiest way to solve this problem is to remember that a2 - b2 = (a+b) (a-b) and recognize the pattern from the problem 100x2-1 = (10x)2 - (1)2 = (10x+1)(10x-1) b) If you do not remember the formula for a2 - b2, then you will need to solve the problem by using usual factoring method...

equation of a locus (answer)

Let the moving point P be (x, y) remember that slope m of line joining points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2) slope of line joining point P(x, y) to A(1, 3) is (y-3)/(x-1) slope of line joining point P(x, y) to B(3, 1) is (y-1)/(x-3) We have been told that, slope of...

Factor completely. (answer)

This polynomial is not prime since it has the factors. 1) Fastest and easiest way to solve this problem is to remember the formula for (a+b)2 and observe the pattern. We know that, a2+2ab+b2 =(a+b)2 16x2 - 24xy + 9y2 = (4x)2 - 2.4x.3y + (3y)2 =(4x-3y)2 2) If...

find profit (answer)

P(x)=P=x2+14x+54 Function y=ax2+bx+c is a parabola with vertex at x= -b/2a. It opens up if a>0 and it opens down if a <0. So function P(x)=P=x2+14x+54 is a parabola with a=1, b=14, c=54. Since a=1 >0, it opens up. Its vertex is at x = -b/2a = -14/2...

for f(x)=-|x+2|, find f(-8) (answer)

f(x) = - |x+2|, substitute x = -8 to get f(-8) = - |-8 +2| f(-8) = - |-6|, absolute value of a negative number is a positive number f(-8) = -6

simplify 4/(2x+1) - 2/(5x-1) as a fraction? (answer)

For converting this to a fraction, we need to combine the two terms in the equation into a single term. This is done by making denominators of both the terms same and then subtracting the numerators. For making the denominator same, we need to find the Least Common Multiple (LCM) of...

extraneous solution (answer)

Absolute value of x is always positive. So |x|+6=2x-3 means x+6=2x-3 only if x is positive              or -(x)+6=2x-3 only if x is negative x+6-x=2x-3-x                                      ...

7/12X-1/4X (answer)

Let driving speed of Fritz = X miles per hour so train speed = X+80 miles per hour Train travels for 15 minutes = 15/60 = 1/4 hours Distance travelled by train = speed x time = (X+80) x 1/4 = (X+80)/4 = (X/4 +20) miles Fritz travels for 35 minutes = 35/60 = 7/12 hours Distance...

A solution of 68% alcohol is to be mixed with a solution of 22% alcohol to form 460 liters of a 61% solution. How many liters of the 68% solution must be used? (answer)

Say A liters of 68% alcohol solution must be used. So it will have a total alcohol contents of Ax68/100=68xA/100 liters Therefore (460-A) liters of 22% alcohol is used with total alcohol contents of (460-A)x22/100 liters Total alcohol contents in 460 liter of 68% alcohol solution is 68xA/100+22x(460-A)/100=(68A+22x460-22A)/100=(46A+10120)/100...