Step-by-step explanation:
Please refer to the attachment
Find the unknown length y in the following pair of similar triangles.
1 answer:
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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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I tried I hope this helps in any kind of way
Hello.
We have:
- A point that the line passes through
- The slope of the line
Plug the values into the Point-Slope Formula:
I hope it helps.
Have a nice day.