Which ratio cannot form a proportion with 8/18 1. 60/135 2. 12/27 3. 46/108 4. 4/9

If x = (10 − 3i) and y = (3 − 10i), then xy = -109i and x/y =

Yuliya22 [10]

Xy = -109i
We could find the value of i by substitute the algebraic form of x and y to the equation above

xy = -109i
(10 - 3i)(3 - 10i) = -109i
(10)(3) -3i(3) + 10(-10i) - 3i(-10i) = -109i
30 - 9i - 100i -30i² = -109i

multiply both side by -1
-30 + 9i + 100i + 30i² = 109i
30i² + 9i + 100i - 109i - 30 = 0
30i² - 30 = 0
30i² = 30
i² = 1
i = -1 or i = 1

Then find the value of x and y if i = -1
If i = -1, therefore
x = 10 - 3(-1)
x = 10 + 3
x = 13

y = (3 - 10i)
y = 3 - 10(-1)
y = 3 + 10
y = 13

x/y = 13/13 = 1

Then find the value of x and y if i = 1
x = 10 - 3(1)
x = 10 - 3
x = 7

y = (3 - 10i)
y = 3 - 10(1)
y = 3 - 10
y = -7

x/y = 7/-7 = -1

The value of x/y is either 1 or -1

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2 years ago

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If a is an arbitrary nonzero constant, what happens to a/b as b approaches 0

Stolb23 [73]

It depends on how b approaches 0

If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.

On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.

The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.