The value of (27/8)-2/3 is..
Exact Form: 65/24
Decimal Form: 2.7083...…
Mixed Number Form: 2 17/24
I'm not sure which one is the scale size so i'll solve for both...
Ratio is 2cm:4m
0.02m:4m or 2cm:400cm also work as ratios
400cm/2cm=200 (so the scale is 200X smaller than the original)
Option 1::
If the scale of the item is:
l=12cm and w=6cm
then we can solve for the actual size by multiplying the values by 200
l=12cm*200=2400cm or 24m
w=6cm*200=1200cm or 12m
Option 2::
If the original item has a length of 12m and a width of 6m then:
l=12m and w=6m
We can find the scale length by dividing by 200
l=12m/200=.06m or 6cm
w=6m/200=0.03m or 3cm
Answer: sqrt(2)/2 which is choice D
======================================================
Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
------------
Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
Given that B is the midpoint of line AC and line BC is congruent to line DE.
The following statements and reasons, proves that line AB is congruent to line DE.
Statement Reasons
1. B is the midpoint of line AC Given
2. Line AB is congruent to line BC. Midpoint of a line segment
3. Line BC is congruent to line DE Given
4. Line AB is congruent to line DE Transitive property
We want to find

, for

.
Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:

.
Thus,
![y'=[(x^2+2)^3]'[(x^3+3)^2]+[(x^3+3)^2]'[(x^2+2)^3]\\\\ =3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3](https://tex.z-dn.net/?f=y%27%3D%5B%28x%5E2%2B2%29%5E3%5D%27%5B%28x%5E3%2B3%29%5E2%5D%2B%5B%28x%5E3%2B3%29%5E2%5D%27%5B%28x%5E2%2B2%29%5E3%5D%5C%5C%5C%5C%20%3D3%28x%5E2%2B2%29%5E2%28x%5E3%2B3%29%5E2%2B2%28x%5E3%2B3%29%28x%5E2%2B2%29%5E3)
Answer: A)

.