Answer: 100
Step-by-step explanation:
Question:
Find the point (,) on the curve that is closest to the point (3,0).
[To do this, first find the distance function between (,) and (3,0) and minimize it.]
Answer:
Step-by-step explanation:
can be represented as:
Substitute for
So, next:
Calculate the distance between and
Distance is calculated as:
So:
Evaluate all exponents
Rewrite as:
Differentiate using chain rule:
Let
So:
Chain Rule:
Substitute:
Next, is to minimize (by equating d' to 0)
Cross Multiply
Solve for x
Substitute in
Split
Rationalize
Hence:
4x+2y<=16
3x+3y<=15
2x+y<=8
x+y<=5
3x+2y->maximize profit
X Y profit
1 4 11
2 3 12
3 2 13
4 0 12
3 1 11
3 2 13
2 3 12
1 4 11
0 5 10
Farmer need to make 3 Apple pies and 2 apple cobblers
Farmer will use 16 cups of apples and 15 cups of flour
profit of farmer will be $13
An asymptote is a vertical horizontal or oblique line to which the graph of a function progressively approaches without ever touching it.
To answer this question we observe the graph. All the values of x and y must be identified for which the graph of the function tends to infinity.
It is observed that these values are:
x = -1
x = 3
y = 0
The first two corresponds to the equations of a vertical line. The third corresponds to horizontal line, the axis of x. It can be seen that although the graph of the function is very close to these values, it never "touches" them