Suppose a and b vary inversely, and b = 8 when a = 6. Write a function that models the variation and find b when a = 30. Explain
1 answer:
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Since the ratio of of second variable to the ratio of first variable remains constant i.e y/x =8 so, the linear relationship is direct variation.
Step-by-step explanation:
A relationship is said to have direct variation if ratio of second variable to the ratio of first variable remains constant.
A relationship is direct variation if where k is the constant.
Now checking if the given data is having direct variation or not.
x y
3 24
4 32
5 40
6 48
Now finding y/x
if y=24 and x = 3 then y/x = 24/3 = 8
if y=32 and x = 4 then y/x =32/4=8
if y=40 and x = 5 then y/x =40/5 =8
if y=48 and x = 6 then y/x =48/6= 8
Since the ratio of of second variable to the ratio of first variable remains constant i.e y/x =8 so, the linear relationship is direct variation.
Keywords: Direct Variation
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Answer:
x ≥ 7
Step-by-step explanation:
|x - 7| = x - 7
A. For each absolute, find the intervals
x - 7 ≥ 0 x - 7 < 0
x ≥ 7 x < 7
If x ≥ 7, |x - 7| = x - 7 > 0.
If x < 7, |x - 7| = x - 7 < 0. No solution.
B. Solve for x < 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
-x + 14 = x
14 = 2x
x = 7
7 ≮7. No solution
C. Solve for x ≥ 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
True for all x.
D. Merge overlapping intervals
No solution or x ≥ 7
⇒ x ≥ 7
The diagram below shows that the graphs of y = |x - 7| (blue) and of y = x - 7 (dashed red) coincide only when x ≥ 7.
