There is a 57% they will both be black.
8+6=14
8÷14=.571 move decimal point 2 to the right
This problem can be solved using the formula for interest which is: F = P (1 + i)^n where:
F = future value
P = principal value
i = interest per year
n = interest period
Since we are already provided with the values of each, direct substitution should be done. This is shown below:
F = P(1 + i)^n
F = 125000(1 + 0.035)^10
F = 176324.85
Therefore, the value of the house after 10 years will be $176,324.85
Wow, Lagrange multipliers in high school!
As a rule with these Lagrange multiplier problems, when the problem is symmetrical with respect to interchange of the variables, the solution almost always ends up with all the variables equal -- what else could it be?
We want to maximize the area of a rectangle with sides x and y subject to the perimeter being constant.
(i)
The area of a rectangle is just the product of its sides:
A = f(x,y) = xy
(ii)
The perimeter of a rectangle is the sum of its sides:
P = g(x,y) = x + x + y + y = 2x+2y
(iii)
Usually I like to form the objective function E=f-λg before I take the derivatives. I usually use a lambda not a gamma for the multiplier.
Let's do what they ask. They want the gradient ∇f(x, y)
∇f(x, y) = (y, x)
(iv)
λ∇g(x, y) = (2λ, 2λ)
(v)
I'm not sure what γ=1/2y is about; I'll solve it like I know how and see where we are.
There it is. We get
y = 2λ
so we also find
x = 2λ
(vi)
We have y=x=2λ so we've shown the variables are equal, i.e. our rectangle is a square. We can solve for λ using our constraint:
P = 2x+2y = 8λ
λ=P/8
so as expected we have a square with side length P/4:
x=y=2λ=P/4
Answer:
( -6 , 4 ) , ( -5 , 6 ) , (-3 , 6 ) , (-1 , 4 )
Answer5 people and 7 dogs
Step-by-step explanation: