Find the coordinate point for A that would make ABDC a rhombus.
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Answer:
the graph is in the attachment.
the coordinates of the centroid : (2/3,2/3)
Step-by-step explanation:
- y=0 represents x-axis ( you can easily mark it on the graph)
- now draw x=1 line.( It is a line parallel to y axis and passing through the point (1,0) )
- y=2x is a line which passes through origin and has a slope "2"
by using these sketch the region.
I have uploaded the region bounded in the attachment. You may refer it. The region shaded with grey is the required region.
- to find centroid:
it can be easily identified that the formed region is a triangle
- the coordinates of three vertices of the triangle are
(1,2) , (0,0) , (1,0)
( See the graph. the three intersection points of the lines are the three vertices of the triangle)
- for general FORMULA, let the coordinates of three vertices of a triangle PQR be P(a,b) , Q(c,d) , R(e,f)
- then the coordinates of the centroid( let say , G) of the triangle is given by
G =
- therefore , the exact coordinates of the centroid =
this point is marked as G in the graph uploaded.
This is a 30-60-90 triangle and we can apply rules to easily identify the hypotenuse of this triangle, which is denoted by <em>x</em>.
The length of the longer side of the triangle is given in the problem. To solve the hypotenuse of this triangle, let's solve first for the length of the shorter side of the triangle.
The shorter side can be solved by just dividing the length of the longer side by the square root of 3. Hence, we have
Since we already have the values for the length of the shorter side and longer side, we can solve for the hypotenuse using the Pythagorean theorem.
Hence, the value of hypotenuse for this right triangle is
Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder
Area of the base of the cylinder =
Area of the cylinder 'wall' = width × length =
×
=×
=
Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.
Surface area of cone is given by
where 
is the slanted height of the cone
SA of cone =
Hence total painted surface area is
Area of the base of the cylinder =
Area of the cylinder 'wall' = width × length =
Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.
Surface area of cone is given by
SA of cone =
Hence total painted surface area is