What is the value of this expression when x = -1 and Y = 2? 4x^3 × y^2
2 answers:
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<h2>Dimension of box is 2 m x 2 m x 1.33 m</h2>
Step-by-step explanation:
Let a be base side and h be the height.
Volume of box, V = a²h
The sides of the box will cost $3 per m² and the base will cost $4 per m². Cost for making is $48.
That is
4a² + 3 x 4 x a x h = 48
4a² + 12 a x h = 48
a² + 3 ah = 12
So volume is
At maximum volume we have derivative is zero,
Negative side is not possible, hence side of square base is 2m.
Substituting in a² + 3 ah = 12
2² + 3 x 2 x h = 12
h = 1.33 m
Dimension of box is 2 m x 2 m x 1.33 m
First we must understand how to write a logarithmic function:
In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:
Next, we need to understand basic logarithm rules.
1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:
log(a^2) = 2log(a)
2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:
log(ab) = log(a) + log(b)
3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:
log(a/b) = log(a) - log(b)
Now we can use these rules to solve the problem.
![log(r)=log( \sqrt[3]{ \frac{A^2B}{C} } )](https://tex.z-dn.net/?f=log%28r%29%3Dlog%28%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7BA%5E2B%7D%7BC%7D%20%7D%20%29)
We can rewrite the cube root as:
Now we can move the one-third to the front:
Now we can split up the logarithm:
Finally, we can move the exponent to the front of the log of A:
Distribute the one-third to get the answer:
The answer is (4).
In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:
Next, we need to understand basic logarithm rules.
1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:
log(a^2) = 2log(a)
2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:
log(ab) = log(a) + log(b)
3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:
log(a/b) = log(a) - log(b)
Now we can use these rules to solve the problem.
We can rewrite the cube root as:
Now we can move the one-third to the front:
Now we can split up the logarithm:
Finally, we can move the exponent to the front of the log of A:
Distribute the one-third to get the answer:
The answer is (4).