Find three mixed numbers so that the sum is 18 and the difference between the greatest number and least number is 5 1/5

1 answer:

7 0

Suppose y=0. That means
x+z = 18 
x-z = 26/5 

x = 58/5 
z = 32/5 

So, the largest x can be is 58/5 
Now, suppose we toss in y. If we subtract y/2 from both x and z, then the difference between x and z is still 26/5, and the sum is 

(x-y/2) + y + (z-y/2) = x+z = 18 

For example, if y = 4, 

x = 48/5 
y = 20/5 
z = 22/5 

x-z is still 26/5, and the sum is still 18.

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How can the average rate of change be identified for a function?

Digiron [165]

Answer:

$Rateofchange=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where x₁ and x₂ are values in the interval [x,y] respectively

Step-by-step explanation:

Well, first to determine the average rate of change of a function, you should have the interval of the values of x for the function.

So lets assume you have a function;

$f(x)=x^3-4x$

And the interval as [1,3]

Then the average rate of change for the function f(x) will be;

$=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where x₁ and x₂ are the interval coordinates x,y respectively. In this case x₁=1 and x₂=3

To find the average rate of change in this example will be;

$=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\\\=f(x_2)=f(3)=3^3-4(3)=27-12=15\\\\=f(x_1)=f(1)=1^3-4(1)=1-4=-3\\\\\\=x_2-x_1=3-1=2\\\\\\=\frac{15--3}{2} \\\\=\frac{18}{2} =9$