Answer:
x - 8y - z = 1
Step-by-step explanation:
Data provided according to the question is as follows
f(x,y) = z = ln(x - 8y)
Now the equation for the tangent plane to the surface
For z = f (x,y) at the point P 
is
Now the partial derivatives of f are
= 1
Now
= -8
So, the tangent equation is
Now after solving this, the following equation arise
z = x - 9 - 8y + 8
z = x - 8y - 1
Therefore
x - 8y - z = 1
Answer:
Step-by-step explanation:
All those words, when the math is so much clearer!
x = (9±√(9^2-4*1*5))/2 = (9±√101)/2
*Given
Money of Phoebe - 3 times as much as Andy
Money of Andy - 2 times as much as Polly
Total money of Phoebe, - £270
Andy and Polly
*Solution
Let
B - Phoebe's money
A - Andy's money
L - Polly's money
1. The money of the Phoebe, Andy, and Polly, when added together would total £270. Thus,
B + A + L = £270 (EQUATION 1)
2. Phoebe has three times as much money as Andy and this is expressed as
B = 3A
3. Andy has twice as much money as Polly and this is expressed as
A = 2L (EQUATION 2)
4. This means that Phoebe has ____ as much money as Polly,
B = 3A
B = 3 x (2L)
B = 6L (EQUATION 3)
This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.
5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,
6L + 2L + L = £270
9L = £270
L = £30
So, Polly has £30.
6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.
A = 2L
A = 2(£30)
A = £60
Andy has £60
B = 6L
B = 6(£30)
B = £180
Phoebe has £180
Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
Each exterior angle = 360 / 40 = 9 degrees. So each interior angle = 180 - 9
= 171 degrees.
