First you have to multiply -8 to (-4x-1)
which is, -12x+8
then there is -9x you have to add like terms
-12x-9x+8
-21x+8 is your final answer
Answer:
If is positive, then the parabola opens upward, so the function decreases on and increases on . But if is negative, then just the reverse
Answer:
He spends $298
Step-by-step explanation:
He has 16 curtains
16*2=32
That answer is how many he needs
Now multiply that by the price
32 curtains for $29
32*29=928
The answer is $928
Answer: -1/2, -0.22, 0, 12%, 0.56
Step-by-step explanation:
-1/2 is equal to -0.50, making it the number with the least value.
-0.22 is closer to 0 than -0.50, meaning it is greater then -0.50 and less than 0.
0 is between the negative and positive numbers, giving it the spot that it has.
12% is equivalent to 0.12, meaning it is more than 0, and less than 0.56, which is the greatest number.
0.56 has more value than any other number in the problem, meaning it goes last in the order.
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).
