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Mademuasel [1]
3 years ago
15

Where do I start with this? it is a calc question. I thought perhaps relating the height to the length to get everything in term

s of one variable by setting both legs to equal the hypotenuse with the Pythagorean theorem but I'm having trouble. dunno if that's even a good way of going about it.

Mathematics
1 answer:
Oksanka [162]3 years ago
5 0

Answer:

See below.

Step-by-step explanation:

You are correct in your approach. You can calculate the hypotenuse via Pythagoras, so you will know |AB|.

Then, I would do the following:

Denote the upper left corner of the rectangle that intersects with AB, a point D. Then call "a" the distance |AD|. Call the rectangle height x, and width y.

Use triangle similarity to set up a system of equations: A choice of "a" induces a rectangle x-by-y where

\frac{x}{a}=\frac{|BC|}{|AB|}\implies x = \frac{|BC|}{|AB|}\cdot a\\\frac{y}{|AB|-a}=\frac{|AC|}{|AB|}\implies y = \frac{|AC|}{|AB|}\cdot (|AB|-a)=|AC|-\frac{|AC|}{|AB|}\cdot a

Now, we can get 2*(x+y)  (aka, the perimeter) from those two equations:

2(x+y)=2(\frac{|BC|}{|AB|}\cdot a+|AC|-\frac{|AC|}{|AB|}\cdot a)=2a\frac{|BC|-|AC|}{|AB|}+2|AC|

which is a function of one variable "a" and you can  minimize that using a derivative.

But here's where I am finding this problem not a very good one: as you surely noticed the perimeter is <em>linear</em> in "a." As such, it's derivative will be constant and uninteresting. Even without the derivative you can see that to minimize the perimeter expression above, you should minimize "a."  In other words "a" should become infinitesimal and the rectangle will be basically (epsilon) by (|AC|-epsilon), where epsilon is as small as possible.

I imagine this problem would become only then "interesting" (in that a derivative would give you something), if the question was to minimize the <em>area </em>of the rectangle.

Please feel free to let me know if you have questions.


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neonofarm [45]

The sum of the expression (–x² + x) and (x² – 3x – 1) will be –2x – 1. Then the correct option is D.

<h3>What is Algebra?</h3>

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression can be written as

(–x² + x) and (x² – 3x – 1)

Then the sum of the expression (–x² + x) and (x² – 3x – 1) will be

(–x² + x) + (x² – 3x – 1) = –2x – 1

Then the correct option is D.

More about the Algebra link is given below.

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2 years ago
I NEED HELP PLEASE! :)<br> thanks!
BigorU [14]

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7 + 9 + 3 + 6 = 25 chips

Since there are 6 blue chips (6/25), that's the probability of just getting once.

When you pick a blue chip and it doesn't get replaced, then that means there is one fewer blue chip and one fewer from the total amount.

5/24

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3 years ago
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Vikki [24]

The scenario can be described using a piecewise function like:

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<h3>When the value exists but the limit does not?</h3>

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Then, we can just define a piecewise function of the form:

f(x) = 1/x                  if  x < c.

f(x) = x                    if   x = c

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Clearly, this is not a continuous function.

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f(c) = c.\\\\ \lim_{x \to c^{-}} f(x) = 1/c\\\\ \lim_{x \to c^{+}} f(x) = 1/(c + 73)

So the limits from left and right are different, then:

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If you want to learn more about limits:

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6 0
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