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3 years ago

Find y using Pythagorean theorem or proportion

Mathematics

1 answer:

Tcecarenko [31]3 years ago

4 0

We have three similar triangles, let's see if we can get this right, right vertex first, then other vertex from small side:

EDF ~ GDE ~ GEF

As ratios that means

ED:DF:EF = GD:DE:GE = GE:EF:GF

x:20:y = 5:x:GE = GE:y:15

Since we're after y we choose

20/y = y/15

20(15) = y²

y² = 300

y = 10√3

y ≈ 17.32

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How many times does 3 go into 5?

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Evaluate 8w - 2p if w = 6 and p = -5

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Under the normal curve, approximately what percent of scores fall between and -1 to +1 standard deviations around the mean?

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4 years ago

Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

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Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

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$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

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Multiply both sides by -1

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Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

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Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

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$S(1) = 1 + 1$

$S(1) = 2$

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3 years ago

If A=p+prt, than t equalls?

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Answer:

$\boxed{t=\frac{A-p}{pr}}$

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