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3 years ago

13

A composition of reflections across two parallel lines is a _____

2 answers:

S_A_V [24]3 years ago

8 0

It's transilation (if that's how you spell it)

daser333 [38]3 years ago

7 0

Answer:

A translation

If it were across two intersecting lines, it would have been a rotation.

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Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

Will give brainliest Question on the picture

raketka [301]

Answer:

12

Step-by-step explanation:

since i helped can i have brainlist please :D

3 0

2 years ago

Which side lengths form a right triangle?

Stels [109]

Answer:

B) 1, 8, √65

Step-by-step explanation:

For 3 side lengths to form a triangle the sum of two random sides must be bigger than the third side and their differences must be smaller than the third side.

1+8 > √65 because √65 is approximately 8.1

8-1 < √65

4 0

3 years ago

Read 2 more answers

Which has the least absolute value?<br>A. 5<br>B. 30<br>C. -10<br>D. -50

ziro4ka [17]

Absolute value means the total distance from zero. So you get rid of any negative signs and then look at which number has the lowest value (which is the smallest number without any negative signs).

7 0

2 years ago

Read 2 more answers

140 + (-122) + (-10), I also need it with work.

Aleks04 [339]

Answer:

8

Step-by-step explanation:

140-122=18

18-10=8

6 0

3 years ago

Read 2 more answers