Answer:
k = 5,
y = 5x
Step-by-step explanation:
If y is proportional to x,
y ∝ x
Then the equation will be
y = kx
Her k = proportionality constant.
Now we choose a point from the given table.
Let the point is (2, 10).
By putting the values of x and y in the equation,
10 = 2×k
k =
k = 5
This will be true for any point we choose from the table.
And the equation will be y = 5x
Answer:
4. The slope is 1.5 pages per minute
The interpretation is 1.5 pages takes 1 minute to complete
5. The slope is 135 Calorie per mile
The interpretation is 135 calories of energy is required or used in traveling a distance of 1 mile
Step-by-step explanation:
4. The given data are;
Minutes, x; 0, 1, 3, 5
Pages, y; 0, 1.5, 4.5, 7.5
The graph of the data created with MS Excel is included
From the graph, we have;
The slope is given by the rate of change of the y-values to the change in the x-values of the data
∴ Slope = Δy/Δx
The slope = 1.5 pages per minute
The interpretation of the slope is that the number of pages completed per minute is 1.5 pages
5. The given data are;
Miles, x; 0, 1, 2, 3
Calories, y; 0, 135, 270, 405
Please find attached the graph of the data created with MS Excel
From the graph, the slope = Δy/Δx = (270 - 135)/(2 - 1) = 135
The slope = 135 Calorie per mile
The interpretation of the slope is it takes 135 calories to complete 1 mile or vice versa.
Answer:
Step-by-step explanation:
I used calculus for this, as I'm not sure there's any other way to do it and to do it as easily. This is the volume of a solid found by using the disk method of rotation:
where R(x) is the outer shell of the solid and r(x) is the space inbetween the solid and the axis of rotation. There is no space between the solid and the axis of rotation, so r(x) = 0. R(x) is the height of the solid which is 3. Therefore, f(x) = 3 and that's the function we put into the formula with the lower bound of 3 and the upper bound of 5:
and
and integrating:
and using the First Fundamental Theorem of Calculus:
V = π(9(5) - 9(3)) and
V = π(45 - 27) so
V = 18π units cubed or in decimal format,
V = 56.549 units cubed
