2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
There are 11 numbers on cards.
6 cards contain even numbers.
Answer: p(even) = 6/11
There is only one card with a 7. After the first card is picked and returned, there are 11 cards in the bag again.
p(even then 7) = p(even) * p(7) = 6/11 * 1/11 = 6/121
Answer: p(even then 7) = 6/121
Answer: 10+30=40 :)
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).
Step-by-step explanation:
Your assignment probably gave you numbers, like (3,4) or (-5,6). They are graphed on the graph. the first number is where the y axis is and the y axis goes _____ on the coordinate plane. Then he second number is the x axis and that goes up and down like an l. To figure out what the points are you go first in the hose and up the stairs. Put your finger on the dot and count the lines it takes DOWN or UP to get to the middle line. If you ad a negative number you count up to the middle line and positives you count down. Write that number down like this (your 1st number here, Now go back to your point and and count how many lines to get to the middle line that goes up and down otherwise known as your y axis. You either count left or right to get to this line. Count the line it takes to get to that centered line. If you have to count t the right to get this number, mark it as negative. If you count to the left its positive. Now you answer should look like this just replaced with numbers instead of words. (First number here, Second number here) Good luck on your assignment!
