The city of Houston received 8 more inches of rain than the town of Groesbeck. Which algebraic expression represents the amount
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:
DE = about 41.843 (rounded to nearest thousandth)
EF= 34.276 (rounded)
Step-by-step explanation:
For DE, we know that the shorter side (the opposite side) is 24, while the angle across form it is 35°. We can use trigonometry to figure this out. SinФ equals the opposite side (in this case, 24) divided by the hypotenuse. Set sinФ equal to a ratio of the sides like this:
sin(35) =
x represents the hypotenuse length, which we don't know; 35 is the angle measure. Next, isolate x so that the equation looks like this:
= x
You will need a calculator for the next part. (and make sure you're in degree mode!). evaluate sin(35) and divide 24 by that value. That is DE's length. DE = about 41.843 (rounded to nearest thousandth)
For EF, we can just use Pythagorean theorem now that we know the other sides' values.
EF^2 + 24^2 = DE^2
*a calculator might also be useful for this part.
EF= 34.276 (rounded)