Write an equation to the model scenario.
1 answer:
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Answer:
Step-by-step explanation:
<u>Graphs</u>
The graph shows the amount of water in gallons as a function of time in seconds.
We are required to find the amount of water in the bucked after 1 second. Since the graph does not show an exact location for t=1, we must find the equation of the line.
Two points are clear on the graph: (0,0) (12,5). This gives us the necessary information to find the equation of the line, which has the form:
Where w is the amount of water in the bucket, t is the time, and m and b are two constants to be determined.
Using the point (0,0):
It follows that b=0
The equation now takes the form:
Using the point (12,5):
We find m:
The final equation is:
Substituting t=1:
The bucket has 5/12 gallons of water at t=1 second. Expressing the answer as an ordered pair:
<h3>Answer:</h3>
An exponent represents repeated multiplication. For example, ...
... x^3 = x·x·x
... x^2 = x·x
If we divide these, the x's in the denominator cancel an equal number in the numerator:
... (x·x·x)/(x·x) = x
If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:
... (x^3)/(x^2) = x^(3-2) = x^1 = x
Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.