The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes.
What does the slope of the linear equation that models the data indicate?
1 answer:
The volume of helium inside the balloon decreased at a rate of 0.1 cubic feet per minute. The linear equation that represents the given data is y = -0.1x + 6 and its slope m = -0.1.
<h3>What is the equation of a line passing through two points?</h3>The equation of the line passing through the points (x1, y1) and (x2, y2) is
(y - y1) = m(x - x1).
Where m is the slope of the line and is calculated by
m = (y2 - y1)/(x2 - x1)
<h3>Calculation:</h3>The given data in the table represents the volume of helium (cu ft), inside a balloon relative to the elapsed time in minutes.
x: 5, 10, 15, 20, 25, 30, 35, 40
y: 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2
From this table, consider two points (5, 5.5) and (10, 5)
So, the equation of the line is
y- y1 = m(x - x1)
Where slope m = (y2 - y1)/(x2 - x1)
⇒ m = (5 - 5.5)/(10 - 5)
⇒ m = -0.5/5
∴ m = -0.1
Thus, the equation is
y - 5.5 = -0.1(x - 5)
⇒ y - 5.5 = -0.1x + 0.5
⇒ y = -0.1x + 0.5 + 5.5
⇒ y = -0.1x + 6.0
∴ y = -0.1x + 6
Since the slope of the line is negative, the volume of the helium inside the balloon decreased at a rate of 0.1 cubic ft per minute.
So, option 2 is correct.
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Answer:
Here the degree of the polynomial is 11.
Step-by-step explanation:
To find the degree of the multivariate polynomials, we need to add up the powers of all the variables. So the total degree is given by the sum of all the powers of the highest powers terms.
Now in the given polynomial
the term with the highest total powers is and thus the total power is 6+5=11.
And hence the degree of this polynomial is 11.