<span>the correct answer is
D) 1000 kilometers </span>
Let's assume
boiling point is y
altitude is x
we are given
This relationship between altitude and boiling point is linear
At an altitude of 1000 feet, water boils at 210°F
so, first point is (1000,210)
so, x1=1000 , y1=210
At an altitude of 3000 feet, water boils at 206°F
so, second point is (3000,206)
so, x2=3000,y2=206
now, we can find slope
now, we can plug values
now, we can use point slope form of line
so, we can plug it
so, point slope form of line is
now, we can plug x=8000
and then we can solve for y
So,
the boiling point of water at an altitude of 8000 feet is 196°F..........Answer
Answer:
The shape of the pebbles is a result of weathering and deposition.
Step-by-step explanation:
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
