Two students, Ann and Max, factored the trinomial 4x2 − 6x − 4. Ann factored it as 2(x − 2)(2x + 1) and Max factored it as (x −
1 answer:
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Answer:
Dimensions:
Perimiter:
Minimum perimeter: [16,16]
Step-by-step explanation:
This is a problem of optimization with constraints.
We can define the rectangle with two sides of size "a" and two sides of size "b".
The area of the rectangle can be defined then as:
This is the constraint.
To simplify and as we have only one constraint and two variables, we can express a in function of b as:
The function we want to optimize is the diameter.
We can express the diameter as:
To optimize we can derive the function and equal to zero.
The minimum perimiter happens when both sides are of size 16 (a square).
Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase
<em><u>Solution:</u></em>
Given that Two years ago, Sally had 5,000 dogs in her dog shelter
Now she has 24,575 dogs
To find: rate of change
A rate of change is a rate that describes how one quantity changes in relation to another quantity
<h3><u>Steps to follow:</u></h3>- First: work out the difference (increase) between the two numbers you are comparing.
- Increase = New Number - Original Number.
- Then: divide the increase by the original number and multiply the answer by 100.
- % change = Increase ÷ Original Number x 100
Thus the rate of change is 391.5 % increase