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klio [65]
2 years ago
10

Help Pleasee Reflect shape A in the line x = -2

Mathematics
1 answer:
Cerrena [4.2K]2 years ago
4 0

Answer: Check out the diagram below

The reflected image is shown in red.

=================================================

Explanation:

Draw a vertical line through -2 on the x axis. This is the mirror line.

Now focus on the upper right corner of the figure, which is at (-3, -1). Notice how the horizontal distance from this corner point to the mirror line is exactly 1 unit. If we move another 1 unit to the right, then we'll arrive at (-1,-1) which is where the reflected point lands or ends up.

In short, the upper right corner point (-3,-1) reflects over x = -2 to land on (-1,-1)

----------------------

As another example, the upper left corner point (-5, -1) will move exactly 4 spaces to the right to get to the mirror line. Then we move another 4 spaces to the right to get to (2,-1).

So the upper left corner (-5,-1) will ultimately move to (2,-1) after the reflection over x = -2.

Apply these steps to the other corner points and you'll end up with what is shown below.

Take note that a point like A(-5,-1) moves to A'(1,-1), and similar to the other points as well. Also, notice that when going from A to B to C, etc we are moving clockwise. We move counterclockwise when going from A' to B' to C' etc. Reflections always swap the orientation.

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Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

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The area of the rectangle is given by xy,

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P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}

For the amount of fencing to be minimum, then

\frac{dP}{dx} =0 \\  \\ \Rightarrow1- \frac{576}{x^2} =0 \\  \\ \Rightarrow \frac{576}{x^2} =1 \\  \\ \Rightarrow x^2=576 \\  \\ \Rightarrow x=\sqrt{576}=24

Now, recall that

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Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

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<h3>Volume of the remaining solid = 628 cm^2</h3>

<h3>Whole surface area = 659.4 cm^2</h3>

Step-by-step explanation:

Now, Given that:-

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So, Radius (r) = 10/2 = 5cm

Height of the cylinder = 12cm.

volume \: of \: the \: cylinder \:  =  \pi {r}^{2} h

=  > \pi \times  {5}^{2} \times  12 {cm}^{3}   = 300\pi {cm}^{3}

Radius of the cone = 5 cm.

Height of the cone = 12 cm.

slant \: height \: of \: the \: cone \:  =  \sqrt{ {h}^{2}  + \:  {r}^{2} }

=  >  \sqrt{ {5}^{2}+{12}^{2} } cm \:  = 13cm

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therefore, The whole surface area of the remaining solid

= curved surface area of cylinder + curved surface area of cone + area of (upper) circular base of cylinder

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<h3>Hope it helps you!!</h3>

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