100POINTS In 1603, German astronomer Christoph Scheiner began to copy and scale diagrams using an instrument that came to be known as the pantograph. By moving a pencil attached to a linkage, Scheiner was able to produce a second image that was enlarged. Do some brief research on Scheiner’s invention. Describe how the pantograph works and how it is able to produce an enlarged image.

How does the operation of the pantograph relate to dilations and similarity? How can you use similar triangles to describe why the pantograph works as it does? Write an abbreviated paragraph proof using similar triangles to explain the design. In many instances, the pantograph has been replaced by other means for enlarging images. What has the pantograph been replaced by? Explain.

you have 6 cupcakes

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2

correct

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12