If y varies inversely as x. Using the coordinates (5, 3) and (x, 2.5), find the missing value x.
1 answer:
Answer:
(6, 2.5 )
Step-by-step explanation:
Given y varies inversely as x then the equation relating them is
y = ← k is the constant of variation
To find k substitute the coordinate point (5, 3 ) into the equation, that is
3 = ( multiply both sides by 5 )
15 = k
y = ← equation of variation
Using (x, 2.5 ) with y = 2.5 , then
2.5 = ( multiply both sides by x )
2.5x = 15 ( divide both sides by 2.5 )
x = 6
Thus point is (6, 2.5 )
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Explanation:
First, we need to find the values of the sine and cosine of x knowing the value of tan x and x being in the 3rd quadrant. Since tan x = 5/12, using Pythagorean theorem, we know that
Note that both sine and cosine are negative because x is in the 3rd quadrant.
Recall the addition identities listed below:
Therefore, the expression reduces to