Compute the gradient of
.

Set this equal to the zero vector and solve for the critical points.








The last case has no real solution, so we can ignore it.
Now,


so we have two critical points (0, 0) and (2, 2).
Compute the Hessian matrix (i.e. Jacobian of the gradient).

Check the sign of the determinant of the Hessian at each of the critical points.

which indicates a saddle point at (0, 0);

We also have
, which together indicate a local minimum at (2, 2).
Answer:
The slope is 9/8, and the y-intercept is -10/3
Step-by-step explanation:
y = mx + b
in this case:
m = 9/8
b = -10/3
and the m in the equation is the slope while the b is the y-intercept
Emma:
Number of hours = 4
Total cost = 18
Where x is the cost per hour n and y is the flat fee
18 = 4x + y
Louise:
number of hours = 7
total cost = 25.50
25.50 = 7x + y
We have the system of equation:
18 = 4x + y
25.50 = 7x + y
Solve the first equation for y
18-4x = y
y = 18-4x
Replace y on the second equation; and solve for x
25.50 = 7x + (18-4x)
25.50 = 7x + 18 -4x
25.50 = 3x + 18
25.50 - 18 = 3x
7.5 = 3x
7.5/3 = x
2.5 = x
a. Cost per hour = $2.5
Now, replace x on any equation and solve for y
18 = 4x + y
18 = 4 (2.5) + y
18 = 10 +y
18 - 10 = y
8 = y
b. Flat fee = $8
c. Use the equation:
Cost = flat fee + cost per hourx (number of hour)
Cost = 8 + 2.5 (2)
Cost = 8 + 5 = $13
<span>2p + q = 1
9p + 3q + 3 = 0
q = 1 - 2p
replace </span>q = 1 - 2p into 9p + 3q + 3 = 0
9p + 3(1 - 2p) + 3 = 0
9p + 3 - 6p + 3 = 0
3p + 6 =0
3p = -6
p = -2
q = 1 - 2p
q = 1 -2(-2)
q = 1 + 4
q = 5
(-2 , 5)
answer
<span>{(-2, 5)} first one</span>
Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .
<u>Step-by-step explanation:</u>
Here we have , Leanne runs a lap in 12 minutes. Kory runs a lap in 9 minutes. We need to find out that If they both start running at 10 am, at what time will they both cross the start together again . Let's find out:
Kory runs a lap in 9 minutes and , Leanne in 12 minutes , in order to find at what time will they both cross the start together again we will find LCM of 9 & 12 :
⇒ 
⇒ 
So ,LCM of 9 & 12 is 36 .That means Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .
In clear way , Kory will run race as :
1st lap = 9 minutes
2nd lap = 18 minutes
3rd lap = 27 minutes
4th lap = 36 minutes , i.e. at 10:36 am he'll complete his 4th lap
For , Leanne
1st lap = 12 minutes
2nd lap = 24 minutes
3rd lap = 36 minutes i.e. at 10:36 am he'll complete his 3rd lap .
This means Kory & Leanne will meet at 10:36 am completing there 4th and 3rd lap respectively .