Answer:
Step-by-step explanation:
(a)
or, via symmetry
____________
(b)
By the chain rule:
For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that
Differentiating with respect to theta
2/3 is the slope
____________
(c)
"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3
A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time
</span><span />
Answer:
30 :75
Step-by-step explanation:
Answer:
not statistically significant at ∝ = 0.05
Step-by-step explanation:
Sample size( n ) = 61
Average for student leader graduates to finish degree ( x') = 4.97 years
std = 1.23
Average for student body = 4.56 years
<u>Determine if the difference between the student leaders and the entire student population is statistically significant at alpha</u>
H0( null hypothesis ) : u = 4.56
Ha : u ≠ 4.56
using test statistic
test statistic ; t = ( x' - u ) / std√ n
= ( 4.97 - 4.56 ) / 1.23 √ 61
= 2.60
let ∝ = 0.05 , critical value = -2.60 + 2.60
Hence we wont fail to accept H0
This shows that the difference between the student leaders and the entire student population is not statistically significant at ∝ = 0.05
The given polynomial expressed as partial fraction is 5x^3 + 9/x
<h3>Polynomial function and partial fractions</h3>
Polynomial function are function that have a leading degree of 3. Given the expression below;
f(x) = (5x^4+9)/x
Applying partial fraction
Since the part fraction means separating the fraction into two parts, hence;
f(x) = 5x^4/x + 9/x
Simplify
Since there is value of x at both numerator and denominator, it will cancel out to have
f(x) = 5x^3 + 9/x
From the result, we can see that p(x) = 5x^3 and k = 9
Hence the given polynomial expressed as partial fraction is 5x^3 + 9/x
Learn more on polynomial here: brainly.com/question/2833285
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