Expert: Sherman D. - 4/20/2006

Question
Hello Mr. or Dr. Sherman,

I have seven short math problems for which I have the answer
but not a solid understanding. Perhaps you can shed some light
on the thinking proccess involved, ie: the steps:

1) If y=(x+4)/(x-1), which of the following represents x?
ANS: (4y-2)/(y-1)

2) The value of sec t is equal to?
ANS: 1/(cos t)

3) Which line is parellel to the y-axis?
ANS: x= (2/y)b

4) Kate has six different books. Assuming the order of selection
doesn't matter, how many ways can Kate select, from these six
books, two different books?
ANS: 15

5) The distance a train travels varies directly according to its rate
times the time it takes to complete the trip. If the rate and one
time are both quadrupled, the distance?
ANS: becomes 16 times greater

6) The value of sin(pie/3)= the value of?
ANS: sin (2pie/3)

7) Which of the following is the equation of the line that contains
point (3,-1) and is perpendicular to the line y=3x+3?
ANS: y=(-1/3)x

Thank you for any help you can offer! My math skills are very
rusty!
Daniela

Answer
1.)
If y = (x + 4)/(x - 1), which of the following represents x?

Sorry, i don't quite understand it, if i had other possible answers to go by, i could understand it better.

ANS: (4y-2)/(y-1)

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2) The value of sec t is equal to?
ANS: 1/(cos t)

www.math.com/tables/trig/identities.htm

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3) Which line is parellel to the y-axis?
ANS: x = (2/y)b

y = (2/x)b
x = (2b)/y
x = (2/y)b

Basically any value that has no slope, and is in the form of x = b, is parallel to the y-axis, in this case, the only thing being multipled is the x-instercept. Although there is a y in the formula, "b" is the intercept and not the slope.

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4) Kate has six different books. Assuming the order of selection doesn't matter, how many ways can Kate select, from these six books, two different books?
ANS: 15

a,b,c,d,e,f

There are 2 ways to answer this, one way is to use the nCr on a calculator, click 6, nCr, 2, and this will give you 15, or

a,b:a,c:a,d:a,e:a,f:b,c:b,d:b,e:b,f:c,d:c,e:c,f:d,e:d,f:e,f

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5) The distance a train travels varies directly according to its rate times the time it takes to complete the trip. If the rate and one time are both quadrupled, the distance?
ANS: becomes 16 times greater

D = RT
D = (4R)(4T)
D = 16RT

Distance becomes 16 times greater than when it was just Rate * Time

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6) The value of sin(pie/3)= the value of?
ANS: sin (2pie/3)

sin(pi/3) = sin(180/3) = sin(60) = .866025
sin(2pi/3) = sin(360/3) = sin(120) = .866025

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7.) Which of the following is the equation of the line that contains
point (3,-1) and is perpendicular to the line y=3x+3?
ANS: y=(-1/3)x

Lines are perpendicular, if when you multiply the exponents, you get -1.

(3,-1), m = (-1/3)
-1 = (-1/3)(3) + b
-1 = -1 + b
b = 0
ANS : y = (-1/3)x