Answer:
Torque, 
Explanation:
It is given that,
Force acting on the particle, 
Position of the particle,
We need to find the torque on the particle about the origin. It is equal to the cross product of position and the force. Its formula is given by :
The cross product of vectors is given by :

or

So, the torque on the particle about the origin
. Hence, this is the required solution.
Electromagnetic radiation are represented in waves. Each type of wave has a certain shape and length. The distance between two peaks in a wave is called the wavelength. This value is equal to the speed of light divided by the frequency.
Wavelength = c/f
Wavelength = 3x10^8 / <span>5.42x10^15
</span><span>Wavelength = 5.54 x 10^-8 m = 55.35 nm</span>
Answer:
a) > x<-c(1,2,3,4,5)
> y<-c(1.9,3.5,3.7,5.1,6)
> linearmodel<-lm(y~x)
And the output is given by:
> linearmodel
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
1.10 0.98
b) 
And if we compare this with the general model 
We see that the slope is m= 0.98 and the intercept b = 1.10
Explanation:
Part a
For this case we have the following data:
x: 1,2,3,4,5
y: 1.9,3.5,3.7,5.1, 6
For this case we can use the following R code:
> x<-c(1,2,3,4,5)
> y<-c(1.9,3.5,3.7,5.1,6)
> linearmodel<-lm(y~x)
And the output is given by:
> linearmodel
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
1.10 0.98
Part b
For this case we have the following trend equation given:

And if we compare this with the general model 
We see that the slope is m= 0.98 and the intercept b = 1.10
The correct answer is B: a set of dimensions
Answer:
The maximum error is 
Explanation:
From the question we are told that
The length is 
The radius is 
The pressure is 
The rate is 
The viscosity is 
The error in the viscosity is mathematically represented as

Where 
and 
and 
So
![\Delta \eta = \frac{\pi}{8} [ |\frac{r^4}{v} | * \Delta P + | \frac{4 * P * r^3}{v} |* \Delta r + |-\frac{P* r^4}{v^2} |* \Delta v]](https://tex.z-dn.net/?f=%5CDelta%20%20%5Ceta%20%20%3D%20%5Cfrac%7B%5Cpi%7D%7B8%7D%20%5B%20%7C%5Cfrac%7Br%5E4%7D%7Bv%7D%20%20%7C%20%2A%20%20%5CDelta%20%20P%20%20%20%2B%20%20%20%20%7C%20%5Cfrac%7B4%20%2A%20%20P%20%2A%20r%5E3%7D%7Bv%7D%20%20%7C%2A%20%20%5CDelta%20%20r%20%2B%20%20%7C-%5Cfrac%7BP%2A%20r%5E4%7D%7Bv%5E2%7D%20%20%7C%2A%20%20%5CDelta%20%20v%5D)
substituting values
![\Delta \eta = \frac{\pi}{8} [ |\frac{(0.002)^4}{0.5*10^{-9}} | * 1750 + | \frac{4 * 4 *10^{5} * (0.002)^3}{0.5*10^{-9}} |* 0.0002 + |-\frac{ 4*10^{5}* (0.002)^4}{(0.5*10^{-9})^2} |* 0 ]](https://tex.z-dn.net/?f=%5CDelta%20%20%5Ceta%20%20%3D%20%5Cfrac%7B%5Cpi%7D%7B8%7D%20%5B%20%7C%5Cfrac%7B%280.002%29%5E4%7D%7B0.5%2A10%5E%7B-9%7D%7D%20%20%7C%20%2A%20%201750%20%20%20%2B%20%20%20%20%7C%20%5Cfrac%7B4%20%2A%20%204%20%2A10%5E%7B5%7D%20%2A%20%280.002%29%5E3%7D%7B0.5%2A10%5E%7B-9%7D%7D%20%20%7C%2A%20%200.0002%20%2B%20%20%7C-%5Cfrac%7B%204%2A10%5E%7B5%7D%2A%20%280.002%29%5E4%7D%7B%280.5%2A10%5E%7B-9%7D%29%5E2%7D%20%20%7C%2A%20%200%20%5D)
![\Delta \eta = \frac{\pi}{8} [56 + 5120 ]](https://tex.z-dn.net/?f=%5CDelta%20%20%5Ceta%20%20%3D%20%5Cfrac%7B%5Cpi%7D%7B8%7D%20%5B56%20%20%2B%20%205120%20%5D)

