What type of conic section is represented by the parametric equations below? X=3cos(t)-1 y=3sin(t)+4
1 answer:
Answer:
Circle
Step-by-step explanation:
Examples of conic sections are the circle, the ellipse, the parabola and the hyperbola. Parametric equations are used to express the x and y variables in terms of a less complicated manner using a third variable (t or θ).
The parametric equation for a circle with an equation is given by:
where r is the radius of the circle and (h, k) is the center of the circle.
A conic section with a parametric equations X=3cos(t)-1, y=3sin(t)+4 is a circle with center at (-1, 4) and radius of 3. The equation of the circle is:
(x + 1)² + (y - 4)² = 3²
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Answer:
Step-by-step explanation:
Hello!
To see if driving heavy equipment on wet soil compresses it causing harm to future crops, the penetrability of two types of soil were measured:
Sample 1: Compressed soil
X₁: penetrability of a plot with compressed soil.
n₁= 20 plots
X[bar]₁= 2.90
S₁= 0.14
Sample 2: Intermediate soil
X₂: penetrability of a plot with intermediate soil.
n₂= 20 (with outlier) n₂= 19 plots (without outlier)
X[bar]₂= 3.34 (with outlier) X[bar]₂= 2.29 (without outlier)
S₂= 0.32 (with outlier) S₂= 0.24 (without outlier)
Outlier: 4.26
Assuming all conditions are met and ignoring the outlier in the second sample, you have to construct a 99% CI for the difference between the average penetration in the compressed soil and the intermediate soil. To do so, you have to use a t-statistic for two independent samples:
Parámeter of interest: μ₁-μ₂
Interval:
[(X[bar]₁-X[bar]₂)±*Sa
]
[(2.90-2.29)±2.715*0.20]
[0.436; 0.784]
I hope this helps!