Simplify sqrt of 4x^6
1 answer:
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Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,
The option B is the correct option.
Given information-
The given expression in the problem is,
Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.
Suppose<em> </em><em>x</em> is a number with power <em>a. </em>The power is power of the power of number <em>x. </em>Then by the power rule of the exponents,
Using the power rule of the exponents given expression can be written as,
Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,
Hence the expression which is equal to the given expression is,
The option B is the correct option.
Learn more about the power rule of exponents here;
Answer:
<em>Maximum value of f=2.41</em>
Step-by-step explanation:
<u>Lagrange Multipliers</u>
It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.
Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.
for some scalar called the Lagrange multiplier.
For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is
The gradient of f is
Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in .
We have
Let's compute the partial derivatives
The Lagrange condition leads to
Operating and simplifying
Replacing the value of in the two first equations, we get
From the first equation
Replacing into the second
Or, equivalently
Squaring
To solve, we use the restriction h
Multiplying by 100
Replacing the above condition
Solving for x
We compute the values of y by solving
For
And for
Finally, we get z using the other restriction
Or:
The first solution yields to
And the second solution gives us
Complete first solution:
Replacing into f, we get
f(x,y,z)=-0.4
Complete second solution:
Replacing into f, we get
f(x,y,z)=2.4
The second solution maximizes f to 2.4