Answer:
Nina practiced the viola for 11.25 hours last week.
Step-by-step explanation:
Juan practiced the violin for 9 hours last week. For each 3 hours that he practices the violin, he practices 2.5 hours of cello. So
3h violin - 2.5h cello
9h violin - xh cello
He practiced 7.5 hours of cello, the same as Nina.
For every 3 hours Nina spends practicing the viola she practices the cello for 2 hours. So:
3h viola - 2h cello
xh viola - 7.5h cello
Nina practiced the viola for 11.25 hours last week.
Therefore the maximum value of function f(x,y,z)= =1/27
And the minimum value is 0
<h3>What is function?</h3>function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.
Here,
The function is given as:
f(x,y,z)=
=1
=>-1=0
Using Lagrange multiplies, we have:
L(x,y,z,λ)=f(x,y,z) +λ(0)
Substitute f(x,y,z)= and
-1=0
Differentiate
L(x)=+2λx
L(y)=+2λy
L(z)=+2λz
L(λ)=-1
Equating to 0
+2λx =0
+2λy = 0
+2λz = 0
-1 = 0
Factorize the above expressions
+2λx =0
2x(+λ)=0
2x=0 and (+λ)=0
x=0 and = -λ
+2λy = 0
2y(+λ)=0
2y=0 and (+λ)=0
y=0 and = -λ
+2λz = 0
2z(+λ)=0
2z=0 and (+λ)=0
z=0 and = -λ
So we have ,
x=0 and = -λ
y=0 and = -λ
z=0 and = -λ
The above expression becomes
x=y=z=0
This means that,
=1
x= ±1/
So,
y= ±1/
z= ±1/
The critic points are
x=y=z=±1/
x=y=z=0
Therefore the maximum value of function f(x,y,z)= =1/27
And the minimum value is 0
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