How does an equation show thw relationship between variables and other quantities in a situation
2 answers:
Answer:
An equation is basically a way to show a relationship of variables (x,y,a,b, etc) and numbers. The relationship between these numbers and variables is a lot like a laundry bag. If you are given a laundry bag that only has your pants in it, you could call this laundry bag "x". Then you have your other laundry bag which only has your shirts in it, this could be called laundry bag "y". The amount of shirts and pants in each of those laundry bags could be counted separately, or if you combine them, counted together.
Step-by-step explanation:
This could be shown like:
total amount of clothes.
If you have 5 shirts which equals y, and 2 pants which equals x, you could quickly count how many clothes in total you have.
Total amount of clothes
Place x=2 and y=5 into that equation.
Which gives you your total clothes.
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Given:
The linear function for average test score in your math class is
where x is the number of the test taken.
The linear function g(x) in the given table represents the average test score in your science class, where x is the number of the test taken.
To find:
Part A: The test average for your math class after completing test 2.
Part B: The test average for your science class after completing test 2.
Part C: Which class had a higher average after completing test 4?
Solution:
Part A:
We have,
Put x=2 in the above function, to find the test average for your math class after completing test 2.
Therefore, the test average for your math class after completing test 2 is 80.8.
Part B:
From the given table it is clear that g(x) =79 at x=2.
Therefore, the test average for your science class after completing test 2 is 79.
Part C:
Put x=4 in f(x), to find the test average for your math class after completing test 4.
From the table it is clear that the value of g(x) is increased by 1 as x is increased by 1. So, the value of function g(x) at x=4 must be 1 more than 80.
It is clear that,
Therefore, math class had a higher average after completing test 4.
Answer:
Step-by-step explanation:
In single-variable calculus, the difference quotient is the expression
,
which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).
This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.
.
Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as <em>h</em> approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.
Therefore,
