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4 years ago

What features of the graph of the equation y-y1=m (x-x1) can you identify?

Mathematics

1 answer:

Ahat [919]4 years ago

7 0

That is point slope form

y-y1=m(x-x1)

passes through the point (x1,y1) and has a slope that is m

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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

Allisa [31]

Answer:

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

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

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

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

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

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

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

Multiply both sides by -1

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

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

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

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

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

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

Work out the value of 7^2-3^3

kow [346]

Answer:

Step-by-step explanation:

7^2=49

3^3=27

49-27=22

8 0

3 years ago

Tuto

soldier1979 [14.2K]

Answer:

1/2 jar

Step-by-step explanation:

2 jars * 1/4 = 2/4 = 1/2

6 0

3 years ago

Guys please help on this

Jet001 [13]

The volume of the window is 12,597 feet cubed.
Hope this helps!

6 0

3 years ago

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If two angles are both vertical and supplementary, then the angles are

docker41 [41]

Ur answer would be RIGHT angle!!!

Hope its right!

6 0

4 years ago

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