Direct Variation With Musa
See kahnacademy.org for more direct variation videos.
Mathography
I studied various math related ideas. Some would include; standard addition, subtraction, long division, and algebra. Being in a class like Math 25, it has helped me to grow as a student and a problem solving guru.
I studied various math related ideas. Some would include; standard addition, subtraction, long division, and algebra. Being in a class like Math 25, it has helped me to grow as a student and a problem solving guru.
Assuming you have watched the video, lets get into the problems...
Problem 1 The problems about the Exeter spring and the
Canadian plains contain relationships that are called
direct variations. In your own words, describe what it means for one quantity to vary directly with another. Which of the following describe direct variations?
Canadian plains contain relationships that are called
direct variations. In your own words, describe what it means for one quantity to vary directly with another. Which of the following describe direct variations?
- (a) The gallons of water in a tub and the number of minutes since the tap was opened.
(b) The height of a ball and the number of seconds since it was thrown.
(c) The length of a side of a square and the perimeter of the square.
(d) The length of a side of a square and the area of the square.
Direct Variation is a equation wrote in y=kx form. These lines go through zero because they do not have y-intercepts. Letters A&C represent direct variation because they x varies directly with y.
Problem 2 Each beat of your heart pumps approximately 0.006 liter of blood.
(a) If your heart beats 50 times, how much blood is pumped? 50·0.006=0.3 liters
(b) How many beats does it take for your heart to pump 0.45 liters? 0.45L=0.006x x=75 times
Problem 3 Direct-variation equations can be written in the form y = kx, and it is customary to say that y depends on x. Find an equation that shows how the volume V pumped depends on the number of beats n. Graph this equation, using an appropriate scale, and calculate its slope. What does the slope represent in this context? y=0.006x. As shown in the equation, there is no y intercept so the line goes through zero.
(a) If your heart beats 50 times, how much blood is pumped? 50·0.006=0.3 liters
(b) How many beats does it take for your heart to pump 0.45 liters? 0.45L=0.006x x=75 times
Problem 3 Direct-variation equations can be written in the form y = kx, and it is customary to say that y depends on x. Find an equation that shows how the volume V pumped depends on the number of beats n. Graph this equation, using an appropriate scale, and calculate its slope. What does the slope represent in this context? y=0.006x. As shown in the equation, there is no y intercept so the line goes through zero.
Problem 4 Each of the data sets at right represents points on a line. In which table is one variable directly related to the other? Why does the other table not represent a direct variation? Fill in the missing entry in each table.
. The second graph is the direct variation because the table starts at zero meaning the line goes through zero, zero. When wrote in equation form, the second table is, also, y=kx. The other table is not direct variation because
Problem 5 The data in each table fits a direct variation. Complete each table, write an equation to model its data, and sketch a graph.
In table one the equation is y=1.5x. I found this equation by dividing y by x(3÷2;6÷4). Also, when graphed, this can be found by calculating rise over run. In the second table, the equation is y=-4x. The process of find this equation is the same as the previous question. As shown in both graphs, the lines run through zero, zero(No slope meaning there is a y-intercept of zero) making these direct variation equations.
Reflection