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2 answers:
Answer: See below.
Step-by-step explanation:
Let's go number by number.
Rational pretty much means you can put it into a fraction of whole numbers.
The first number is -81,572.
- This number is <u>rational</u> because it can be put into a fraction (
) that is made up of whole numbers.
The second number is .
- This number is <u>irrational</u> because it cannot be put into a fraction of whole numbers.
- Keep in mind that most squareroots are irrational. Especially those that don't equal a whole number.
The third number is 5.636336333
- There is a pattern so the number is <u>rational</u>.
- Usually a pattrn means it can be put into a fraction.
The fourth number is . This equals 4 if you solve it out.
- Since we just get 4, that certainly can be put into a fraction of whole numbers, so this is <u>rational.</u>
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Answer: The volume of the grapefruit is approximately 8 times as great as the volume of the lime.
Step-by-step explanation:
You need to use the formula for calculate the volume of a sphere. This is:
Where "r" is the radius.
<u>Volume of the grapefruit</u>
You know that its diameter is 16 centimeters.
Since the radius is half the diameter, you get that its volume is:
<u> Volume of the lime</u>
According to the information given in the exercise, the diameter of the lime is 8 centimeters.
As it was explained above, the radius is half the diameter. Knowing that, you get that volume of the lime is the shown below:
In order to find approximately how many times as great is the volume of theat grapefruit as the volume of that lime, you need to divide the volumes calculated above. Then:
Answer:
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).
Step-by-step explanation:
The correct statement is described below:
Find the absolute maximum and minimum values of the function below:
,
Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.
First, we obtain the first derivative of the function and equalize it to zero:
(Eq. 1)
As we can see, only a solution is a valid critical value. That is:
Second, we determine the second derivative formula and evaluate it at the only critical point:
(Eq. 2)
x = 6
(Absolute minimum)
Third, we evaluate the function at each extreme of the given interval and the critical point as well:
x = 2
x = 6
x = 12
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).