Answer:
x is in (0, 17)
Step-by-step explanation:
The compound inequality is ...
0 < x < 17
The "equal to" case is not included on either end, so round brackets are used:
(0, 17)
Answer: 2
Step-by-step explanation:
Average rate of change:
So, let's start with the fact that we have two numbers. Let's call one of them "x" and the other one "y." Let's also assume that "y" is the larger number and "x" is the smaller number.
We know that both of them added together (the sum) gives us 74. Mathematically, that means:
x+y=74.
We also know that the larger number ("y") is 4 more than the smaller number ("x"). Another way to say this is, if you have the smaller number and add 4 more to it, you'll end up with the larger number. Mathematically, this means:
y=x+4
Since we know that y=x+4, we can put "x+4" into the first equation for "y", giving us:
x+(x+4)=74
Simplifying gives us:
2x+4=74
-4 -4
---------
2x=70
--- ---
2 2
x=35
Since we now know that x=35, and we know that y=x+4, we now know that:
y=(35)+4
y=39
Now that we have both of the numbers, we should check our work to ensure it's correct:
Does 39+35=74? Yes it does.
Is 39 (the larger of the two numbers) four more than the smallest number (35)? Yes it is.
Let the dimensions of the rectangle be x and y .
And area is given by length times width.
So we will get
Let perimeter is represented byp. And perimeter is the sum of all sides, that is
Substituting the value of x , we will get
Differentiating ,
Differentiating again,
Since p''>0, so we will get maximum perimeter.
Now we need to set P' to 0 and solve for y, that is
So ,
