Question
Hey, we recently started a topic in class that I don't understand well, I just want to post 6 of the problems and ask if they're right or not (some of them I have no idea how to do).
1. If a varies directly as b and b = 18 when a = 27, find a when b = 10.
For this I did 27/18 = a/10 and my answer was a = 15.
2. If y varies inversely as x and y = -3 when x = 9, find y when x = 81.
For this I did -3/81= = y/9 and my answer was y = -1/3.
3. If y varies jointly as x and z, and y = 18 when x = 6 and z = 15, find y when x = 12 and z = 4.
For this I did 18/12*4 = y/6*15 and my answer was y = 33.75.
Direction variation can be expressed in the form of y = kx and inverse variation can be expressed in the form of y = k/x, right?
Last off is the part I didn't understand.
Is the relationship between the variables in set of data a direct variation, inverse variation, or neither? Indicate the constant of variation, if applicable.
a. {(0.5, 1.5), (2, 6), (6, 18)} I said this is direct variation though no idea how to get the constant of variation.
b. {(0.2, 12), (0.6, 4), (1.2, 2)} I said this was inverse variation but yet again no idea how to get the constant of variation.
c. {(1, 2), (2, 1), (3, 0.5)} I said this was neither, and I expect there is no constant of variation?
I do understand this is quite long, for whoever and if someone even does help me with this, thank you!
1. If a varies directly as b and b = 18 when a = 27, find a when b = 10.
For this I did 27/18 = a/10 and my answer was a = 15.
2. If y varies inversely as x and y = -3 when x = 9, find y when x = 81.
For this I did -3/81= = y/9 and my answer was y = -1/3.
3. If y varies jointly as x and z, and y = 18 when x = 6 and z = 15, find y when x = 12 and z = 4.
For this I did 18/12*4 = y/6*15 and my answer was y = 33.75.
Direction variation can be expressed in the form of y = kx and inverse variation can be expressed in the form of y = k/x, right?
Last off is the part I didn't understand.
Is the relationship between the variables in set of data a direct variation, inverse variation, or neither? Indicate the constant of variation, if applicable.
a. {(0.5, 1.5), (2, 6), (6, 18)} I said this is direct variation though no idea how to get the constant of variation.
b. {(0.2, 12), (0.6, 4), (1.2, 2)} I said this was inverse variation but yet again no idea how to get the constant of variation.
c. {(1, 2), (2, 1), (3, 0.5)} I said this was neither, and I expect there is no constant of variation?
I do understand this is quite long, for whoever and if someone even does help me with this, thank you!
Answers
Reiny
you did your first 3 questions by using ratios.
This is fine as long as you know where to put the numbers.
since you appear to understand that
direct variation ---> y = kx
inverse variation ---> y = k/x
perhaps that is the approach you might take at the beginning.
1. It says direct variation, so a = kb
we are told, a=27, and b = 18, so
27 = 18k
k = 27/18 = 3/2
so we know a = (3/2)b
now if b = 10
a = (3/2)(10) = 15
2. is correct
3. Using the k method:
y = k(xz)
given: x=6, y=18, z=15
18 = k(90) ---> k = 1/5
so y = (1/5)xz
when x=12, z=4 , then
y = (1/5)(12)(4) = 48/5
Your last part:
recall that for direct variation: y = kx, so k = y/x
now look at the ordered pairs, is
18/6 = 6/2 = 1.5/.5 ??? yes, all 3 are equal to 3, so it is a direct variation
for in inverse we have y = k/x ---> k = xy
look at your given points
In all cases, xy = 2.4 , so your answer of inverse is correct
for c) points are (1,2), (2,1), (3, .5)
1x2 = 2x1 ≠ 3x.5, so it is not inverse variation
2/1 ≠ 1/2 , no point going further, not direct
so neither is the correct answer
This is fine as long as you know where to put the numbers.
since you appear to understand that
direct variation ---> y = kx
inverse variation ---> y = k/x
perhaps that is the approach you might take at the beginning.
1. It says direct variation, so a = kb
we are told, a=27, and b = 18, so
27 = 18k
k = 27/18 = 3/2
so we know a = (3/2)b
now if b = 10
a = (3/2)(10) = 15
2. is correct
3. Using the k method:
y = k(xz)
given: x=6, y=18, z=15
18 = k(90) ---> k = 1/5
so y = (1/5)xz
when x=12, z=4 , then
y = (1/5)(12)(4) = 48/5
Your last part:
recall that for direct variation: y = kx, so k = y/x
now look at the ordered pairs, is
18/6 = 6/2 = 1.5/.5 ??? yes, all 3 are equal to 3, so it is a direct variation
for in inverse we have y = k/x ---> k = xy
look at your given points
In all cases, xy = 2.4 , so your answer of inverse is correct
for c) points are (1,2), (2,1), (3, .5)
1x2 = 2x1 ≠ 3x.5, so it is not inverse variation
2/1 ≠ 1/2 , no point going further, not direct
so neither is the correct answer