Answer:
The required vector parametric equation is given as:
r(t) = <3cost, 3sint>
For 0 ≤ t ≤ 2π
Step-by-step explanation:
Given that
f(x, y) = <2y, -sin(y)>
Since C is a cirlce centered at the origin (0, 0), with radius r = 3, it takes the form
(x - 0)² + (y - 0)² = r²
Which is
x² + y² = 9
Because
cos²β + sin²β = 1
and we want to find a vector parametric equations r(t) for the circle C that starts at the point (3, 0), we can write
x = 3cosβ
y = 3sinβ
So that
x² + y² = 3²cos²β + 3²sin²β
= 9(cos²β + sin²β) = 9
That is
x² + y² = 9
The vector parametric equation r(t) is therefore given as
r(t) = <x(t), y(t)>
= <3cost, 3sint>
For 0 ≤ t ≤ 2π
Answer:
5 = 9 + 6
Step-by-step explanation:
You have to take out the "|"
8x-1 ≤ 2x+11
8x-2x ≤ 11+1
6x ≤ 12
X ≤ 12/6
X ≤ 2
Answer:
The 95% confidence interval for the concentration in whitefish found in Yellowknife Bay is (0.2698 mg/kg, 0.3702 mg/kg).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 8 - 1 = 7
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.3246
The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.32 - 0.0502 = 0.2698 mg/kg
The upper end of the interval is the sample mean added to M. So it is 0.32 + 0.0502 = 0.3702 mg/kg
The 95% confidence interval for the concentration in whitefish found in Yellowknife Bay is (0.2698 mg/kg, 0.3702 mg/kg).