A. 4 (is the only factor for expression -48xyz -24xy +40)
Answer:
y = ⅓ x² - 3
Step-by-step explanation:
---------------
Answer:
.
Step-by-step explanation:
The equation of a circle of radius 
centered at 
is:
.
.
Differentiate implicitly with respect to 
to find the slope of tangents to this circle.
![\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E%7B2%7D%20%2B%20y%5E%7B2%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B25%5D)
.
Apply the power rule and the chain rule. Treat 
as a function of , 
.
.
.
That is:
.
Solve this equation for 
:
.
The slope of the tangent to this circle at point 
will thus equal
.
Apply the slope-point of a line in a cartesian plane:
, where
is the gradient of this line, and
are the coordinates of a point on that line.
For the tangent line in this question:
,
.
The equation of this tangent line will thus be:
.
That simplifies to
.
Answer:
The flag of Switzerland is square.
Step-by-step explanation:
Only Switzerland has a flag that is square.
The measurements can be anything convenient. The aspect ratio (height to width) is 1 : 1.
When the flag is displayed next to a rectangular flag, it should have the same area as the rectangular flag. (This will mean the Swiss flag side length is the geometric mean of the rectangular flag dimensions.)
_____
Sometimes, the measurements of the flag are chosen to go with the height of the flagpole. The US flag is customarily displayed on a pole 3-4 times as long as the flag is long. That is, the diagonal of the flag is about 0.28 to 0.38 times the pole height.* I could not find comparable information about the Swiss flag.
____
* The diagonal is of interest when the flag is hanging down along the pole, not flying in the wind.
