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3 years ago

Which of the following shows this trapezoid rotated 90°

Mathematics

2 answers:

Alenkasestr [34]3 years ago

8 0

Answer:

its the second option...

Step-by-step explanation:

vlada-n [284]3 years ago

3 0

Answer:

Graph (2) is the answer.

Step-by-step explanation:

Rule to rotate a point (x,y) 90° clockwise about the origin

(x,y) ⇒ (y,-x)

Then translated 3 units up

(y,-x) ⇒ (y,-x + 3)

So rule is (x,y) ⇒ (y, -x+3)

Now we take all the points of the trapezoid

(0, -1) ⇒ (-1, 3)

(1.5, -2.5) ⇒ (-2.5, 1.5)

(1.5, -3.5) ⇒ (-3.5, 1.5)

(0, -3.5) ⇒ (-3.5, 3)

These coordinates match with the points in figure (2)

Therefore, Graph (2) is the answer.

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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>

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qwelly [4]

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