y - 3
g(y) = ------------------
y^2 - 3y + 9
To find the c. v., we must differentiate this function g(y) and set the derivative equal to zero:
(y^2 - 3y + 9)(1) - (y - 3)(2y - 3)
g '(y) = --------------------------------------------
(y^2 - 3y + 9)^2
Note carefully: The denom. has no real roots, so division by zero is not going to be an issue here.
Simplifying the denominator of the derivative,
(y^2 - 3y + 9)(1) - (y - 3)(2y - 3) => y^2 - 3y + 9 - [2y^2 - 3y - 6y + 9], or
-y^2 + 6y
Setting this result = to 0 produces the equation y(-y + 6) = 0, so
y = 0 and y = 6. These are your critical values. You may or may not have max or min at one or the other.
Answer:
y= 15
Step-by-step explanation:
Y= Kxz
y=6 x=1/2 z=6
15= K (1/2) (6)
15= K (3)
K= 5
SO
y= (5) (1/2) (6)
Y= 15
Answer:
The factorization of 
is 
Step-by-step explanation:
This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form 
or 
. It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of by using the <em>sum and difference of cubes </em>factorization.
1.) We calculate the cubic root of each term in the equation , and the exponent of the letter x is divided by 3.
![\sqrt[3]{729x^{15}} =9x^{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B729x%5E%7B15%7D%7D%20%3D9x%5E%7B5%7D)
then ![\sqrt[3]{10^{3}} =10](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B10%5E%7B3%7D%7D%20%3D10)
So, we got that
which has the form of which means is a <em>sum of cubes.</em>
<em>Sum of cubes</em>
with 
y 
2.) Solving the sum of cubes.
.
The time it takes for a certain object or person, in this case Georgia, to travel from one place to another is the quotient of the distance and speed. Such that the given above can be best represented by the equation below,
42 minutes = (7/8 + 5/6 + x) / 1/18
The value of x from the equation is approximately 0.625 miles.
