This is the answer to the question
Answer:
d = 25t
Step-by-step explanation:
pick tow points on the line, the easier for me is (0,0) and (2,50). The equation options are given in slope intercept form such as y = mx + b; where m is the slope and be is where the line intercepts the y-axis. We can see that "b" is zero because the line intercepts the y-axis at 0 (b = 0).
to find the slope you use the two points for the m
m =
=
= 25 is the slope
Therefore the equation should d = 25t
I am not sure how you would approach this using the chain rule, but I can use the quotient rule.
The derivative of cos(u)=-sin(u)
The derivative of sin(u)=cos(u)
The quotient rule states:
[f'(x)g(x)-f(x)g'(x)] / [g(x)]^2
f'(x)= -sin(x)
g(x)= [1+sin(x)]
f(x)= cos(x)
g'(x)= cos(x)
Plug in:
[-sin(x)*[1+sin(x)] - [cos(x)*cos(x)] / (1+sin(x))^2
Simplify by distributing
-sin(x) - sin^2(x) - [cos(x)*cos(x)] / (1+sin(x))^2
Multiply the cos(x)*cos(x)
-sin(x) - sin^2(x) - cos^2(x) / (1+sin(x))^2
That is the answer or the answer could be simplified further by pulling out the negative.
- [sin(x)+sin^2(x)+cos^2(x)] / (1+sin(x))^2
Answer: ![(11.44,\ 17.4)](https://tex.z-dn.net/?f=%2811.44%2C%5C%2017.4%29)
Step-by-step explanation:
The confidence interval for population mean is given by :-
![\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Given : Sample size : ![n=36](https://tex.z-dn.net/?f=n%3D36)
Sample mean : ![\ovreline{x}=14.42](https://tex.z-dn.net/?f=%5Covreline%7Bx%7D%3D14.42)
Standard deviation : ![\sigma=6.95](https://tex.z-dn.net/?f=%5Csigma%3D6.95)
Significance level : ![\alpha=1-0.99=0.01](https://tex.z-dn.net/?f=%5Calpha%3D1-0.99%3D0.01)
Critical value : ![z_{\alpha/2}=z_{0.005}=2.576](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.005%7D%3D2.576)
Now, the 99% confidence interval for the mean percent body fat in all men aged 20 to 29 will be :-
![14.42\pm (2.576)\dfrac{6.95}{\sqrt{36}}\\\\\approx14.42\pm2.98\\\\=(14.42-2.98,\ 14.42+2.98)=(11.44,\ 17.4)](https://tex.z-dn.net/?f=14.42%5Cpm%20%282.576%29%5Cdfrac%7B6.95%7D%7B%5Csqrt%7B36%7D%7D%5C%5C%5C%5C%5Capprox14.42%5Cpm2.98%5C%5C%5C%5C%3D%2814.42-2.98%2C%5C%2014.42%2B2.98%29%3D%2811.44%2C%5C%2017.4%29)
Answer:
7 years
Step-by-step explanation: