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worty [1.4K]
3 years ago
6

Describe 2 ways that an exterior angle of a triangle is related to one or more or the interior angles

Mathematics
1 answer:
shtirl [24]3 years ago
8 0
The 2 angles at a vertex are supplementary (one interior and one exterior) the exterior angle is = the the sum of the 2 remote interior angles..
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Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont
Neko [114]

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:

f(x) = x^{3}-9\cdot x^{2}+ 3, 2 \leq x \leq 12

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:

f'(x) = 3\cdot x^{2}-18\cdot x

3\cdot x^{2}-18\cdot x = 0

3\cdot x \cdot (x-6) = 0 (Eq. 1)

As we can see, only a solution is a valid critical value. That is: x = 6

Second, we determine the second derivative formula and evaluate it at the only critical point:

f''(x) = 6\cdot x -18 (Eq. 2)

x = 6

f''(6) = 6\cdot (6)-18

f''(6) =18 (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

f(2) = 2^{3}-9\cdot (2)^{2}+3

f(2) = -25

x = 6

f(6) = 6^{3}-9\cdot (6)^{2}+3

f(6) = -105

x = 12

f(12) = 12^{3}-9\cdot (12)^{2}+3

f(12) = 435

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

6 0
3 years ago
Which condition is MOST likely to be true of an observational study on human subjects?
vodomira [7]
A because all of the other ones are weong
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3 years ago
At 10:00 AM Han and Tyler
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3 years ago
If the circumference of a circle is divided by the length of its diameter. whats the result
Mnenie [13.5K]

Answer:

3.14 or π  (It's the same thing)

Step-by-step explanation:

If you divide the circumference by its diameter, the constant ratio is called Pi

8 0
3 years ago
Find the volume: A cone with a diameter of 16cm and a height of 16cm.
soldier1979 [14.2K]
<h2><em>The formula for a cone is in the attachment below. Substitute Pie for 3.14.</em></h2><h2><em>3.14 x 8 x 8 x 16/3 = 1071.78667. You can round this up and you get 1072.33.</em></h2><h2><em></em></h2><h2><em>Final Answer: 1072.33cm^3</em></h2><h2><em>Hope this helps and have a nice day! o/</em></h2>

6 0
3 years ago
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