Answer with Step-by-step explanation:
Relationship between rotation and reflection:
In reflection, the pre-image gets flips across the same line.
whereas in rotation, the pre-image get spin around a point.
Rotations can be represented as two reflections i.e. the composition of reflections over two intersecting lines is always equal to rotation of that object.
In rotation, the object will get turned, this is turning some degree either clockwise or anti-clockwise.
Hence, rotation requires spinning and reflection requires flipping.
Answer:
see the explanation
Step-by-step explanation:
we know that
A gross is equal to 120 ones or ten dozen
what is 15 tens - 1 gross
we know that
15 tens means ----> That you are adding 10, 15 times or multiplying 10 by 15, which gives you
1 gross means ---> That you are adding 10, 12 times or multiplying 10 by 12
which gives you
so
The algebraic expression of 15 tens - 1 gross is equal to
Convert to word expression
3 tens
Answer:
The dimensions of the box that minimize the materials used is
Step-by-step explanation:
Given : An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft³.
To find : The dimensions of the box that minimize the materials used ?
Solution :
An open top box is to be built with a rectangular base whose length is twice its width.
Here, width = w
Length = 2w
Height = h
The volume of the box V=36 ft³
i.e.
The equation form when top is open,
Substitute the value of h,
Derivate w.r.t 'w',
For critical point put it to zero,
Derivate the function again w.r.t 'w',
For w=3,
So, it is minimum at w=3.
Now, the dimensions of the box is
Width = 3 ft.
Length = 2(3)= 6 ft
Height =
Therefore, the dimensions of the box that minimize the materials used is