Please help.. I will give points
2 answers:
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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).
Answer:
13
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem
where<em> a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse.
We know that the legs are 5 and 12. We also know the hypotenuse is x, or unknown.
Substitute 5 in for <em>a</em>, 12 for <em>b, </em>and x for <em>c.</em>
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Evaluate the exponents.
5^2 is the same as 5*5, which is 25.
12^2 is the same as 12*12, which is 144.
Add 25 and 144
We are trying to find out what <em>x</em> is. In order to do this, we have to get <em>x</em> alone. Since x is being squared, take the square root of both sides. The exponent and square root will cancel, leaving x by itself.
The hypotenuse is 13.