Is this linear relationship a direct variation?
1 answer:
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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You must travel at 42 mph for 4 hours
<em><u>Solution:</u></em>
Time varies inversely as rate of motion
Let "t" be the time required
Let "r" be the rate of motion
Then, we get
Where, "k" is the constant of proportionality
<em><u>You travel 3 hours at a rate of 56 mph</u></em>
Substitute t = 3 and r = 56 in eqn 1
<em><u>Find the rate you must travel for 4 hours</u></em>
r = ? and t = 4
Substitute t = 4 and k = 168 in eqn 1
Thus you must travel at 42 mph for 4 hours
Answer:
x=499.83
y=500.16
Step-by-step explanation:
We can solve this problem with a system of equations:
The total quantity of Nerds in the box:
(1)
The amount of Nerds left in the box:
The number of portions Mrs. Konings has taken:
The amount of Nerds left in the box decreases by a third each time she dumps out a portion:
(2)
Substituting (2) in (1):
(3) This is the equation
Let's find :
(4)
Now let's find by substituting (4) in (2):
(5)