If f(x)=2x² +5√(x-2), complete the following statement:

1 answer:

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By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

<h3>How to determine the domain of a function with radical components</h3>

Domain is the set of x-values such that the value of the function exists. By algebra we know that the domain of polynomials is the set of all <em>real</em> numbers, whereas the domain of <em>radical</em> functions is the set of x-values such that y ≥ 0. If we know that f(x) = 2 · x² + 5 · √(x - 2), then the domain is restricted by the <em>radical</em> component and defined by x ≥ 2.

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

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Dr.Lamb is mixing a solution for his next patient. He has a cylindrical test tube which is 4 inches across on the inside. The de

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Answer: There are 34.35 liters left in the test tube.

Step-by-step explanation:

Since we have given that

Depth of the tube = 9 inches

Circumference of base=4 inches

As we know the formula of circumference ,

$Circumference=2\pi r\\\\4=2\times \frac{22}{7}\times r\\\\4\times{7}{22\times 2}=r\\\\\frac{7}{11}=r$

Now, we need to find the volume of tube is given by

$\text{ Volume of test tube }=\pi r^2h\\\\\text{ Volume of test tube }=\frac{22}{7}\times \frac{7}{11}\times \frac{7}{11}\times 9\\\\\text{ Volume of test tube }=\frac{126}{11}=11.45\ inches^3$