9514 1404 393
Answer:
(8.49; 225°)
Step-by-step explanation:
The angle is a 3rd-quadrant angle. The reference angle will be ...
arctan(-6/-6) = 45°
In the 3rd quadrant, the angle is 45° +180° = 225°.
The magnitude of the vector to the point is its distance from the origin:
√((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49
The polar coordinates can be written as (8.49; 225°).
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<em>Additional comment</em>
My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.
Answer:
24 and 48
Today, the son is 24 years old, and the father is 48 years old.
Step-by-step explanation:
(x - 10) + (2x - 10) = 52
3x + 20 = 52
3x = 72
x = 24
The father is 2 times his son's age.
2x
= 2(24)
= 48
So, the son is 24 and the father is 48.
10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.
The probability of type II error will decrease if the level of significance of a hypothesis test is raised from 0.005 to 0.2.
<h3 /><h3>What is a type II error?</h3>
A type II error occurs when a false null hypothesis is not rejected or a true alternative hypothesis is mistakenly rejected.
It is denoted by 'β'. The power of the hypothesis is given by '1 - β'.
<h3>How the type II error is related to the significance level?</h3>
The relation between type II error and the significance level(α):
- The higher values of significance level make it easier to reject the null hypothesis. So, the probability of type II error decreases.
- The lower values of significance level make it fail to reject a false null hypothesis. So, the probability of type II error increases.
- Thus, if the significance level increases, the type II error decreases and vice-versa.
From this, it is known that when the significance level of the given hypothesis test is raised from 0.005 to 0.2, the probability of type II error will decrease.
Learn more about type II error of a hypothesis test here:
brainly.com/question/15221256
#SPJ4
Answer:
90
Step-by-step explanation:
y^2 + 5y + 6 =
(7)^2 + 5(7) + 6 =
49 + 35 + 6 =
84 + 6 =
90
Dy/dx = d/dx 6cosx^2
= 12cosx d/dx cosx
= 12cosx (-sinx)
= -12cosxsinx
