Answer:
African
Explanation:
The African Institute for Mathematical Sciences (AIMS) is an educational and research institute located in Muizenberg, South Africa. It was founded in 2003. Through the Next Einstein Initiative aims to establish 15 more institutes in the African continent. The founder of AIMS is Neil Turok. AIMS has collaborations with various European Universities.
Explanation:
According to Newton's second law of motion, the rate of change of momentum is directly proportional to the applied unbalanced force. The mathematical expression is given by:
![F=\dfrac{d(mv)}{dt}](https://tex.z-dn.net/?f=F%3D%5Cdfrac%7Bd%28mv%29%7D%7Bdt%7D)
Where
F is the applied force
m is the mass of the object
v is the velocity with which it is moving
![F=m\dfrac{dv}{dt}](https://tex.z-dn.net/?f=F%3Dm%5Cdfrac%7Bdv%7D%7Bdt%7D)
Momentum of a particle is given by the product of mass and velocity as :
![p=mv](https://tex.z-dn.net/?f=p%3Dmv)
Hence, this is the required solution.
Answer: Both masses are 0.285 m apart
Explanation:
According to the law of Universal Gravitation:
Where:
is the gravitational force between the masses
is the gravitational constant
is the mass of the first object
is the mass of the second object
is the distance between the objects
Isolating
:
![d=\sqrt{\frac{Gm_{1}m_{2}}{F}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%5Cfrac%7BGm_%7B1%7Dm_%7B2%7D%7D%7BF%7D%7D)
![d=\sqrt{\frac{(6.674x10^{-11}\frac{m^{3}}{kgs^{2}})(5 kg)(7.5 kg)}{3.07(10)^{-8} N}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%5Cfrac%7B%286.674x10%5E%7B-11%7D%5Cfrac%7Bm%5E%7B3%7D%7D%7Bkgs%5E%7B2%7D%7D%29%285%20kg%29%287.5%20kg%29%7D%7B3.07%2810%29%5E%7B-8%7D%20N%7D%7D)
This is the distance between both objects
The equivalent resistance of several resistors connected in series is
the sum of their individual values.
Four 75-ohm resistors connected in series are electrically equivalent
to a single resistor of 300 ohms.
The battery voltage doesn't matter. In fact, it doesn't matter whether the
resistors are anywhere near a battery or not. They could just as well still
be in the little Radio Shack envelope on the top shelf of the storage room.
If they're connected in series, then they're still electrically equivalent to a
single 300-ohm resistor.
The lowest and highest wavelengths of this part of the electromagnetic spectrum are:
![\lambda_1 = 200 nm=200 \cdot 10^{-9} m](https://tex.z-dn.net/?f=%5Clambda_1%20%3D%20200%20nm%3D200%20%5Ccdot%2010%5E%7B-9%7D%20m)
![\lambda_2 = 400 nm=400 \cdot 10^{-9} m](https://tex.z-dn.net/?f=%5Clambda_2%20%3D%20400%20nm%3D400%20%5Ccdot%2010%5E%7B-9%7D%20m)
The frequency and the wavelenght of an electromagnetic wave are related by
![f= \frac{c}{\lambda}](https://tex.z-dn.net/?f=f%3D%20%5Cfrac%7Bc%7D%7B%5Clambda%7D%20)
where c is the speed of light and f the frequency. By using this equation, we can find the frequencies that corresponds to the lowest and highest wavelengths of this part of the spectrum:
![f_1 = \frac{c}{\lambda_1}= \frac{3 \cdot 10^8 m/s}{200 \cdot 10^{-9} m}=1.5 \cdot 10^{15}Hz](https://tex.z-dn.net/?f=f_1%20%3D%20%20%5Cfrac%7Bc%7D%7B%5Clambda_1%7D%3D%20%5Cfrac%7B3%20%5Ccdot%2010%5E8%20m%2Fs%7D%7B200%20%5Ccdot%2010%5E%7B-9%7D%20m%7D%3D1.5%20%5Ccdot%2010%5E%7B15%7DHz%20%20)
![f_2 = \frac{c}{\lambda_2}= \frac{3 \cdot 10^8 m/s}{400 \cdot 10^{-9} m}=7.5 \cdot 10^{14}Hz](https://tex.z-dn.net/?f=f_2%20%3D%20%20%5Cfrac%7Bc%7D%7B%5Clambda_2%7D%3D%20%5Cfrac%7B3%20%5Ccdot%2010%5E8%20m%2Fs%7D%7B400%20%5Ccdot%2010%5E%7B-9%7D%20m%7D%3D7.5%20%5Ccdot%2010%5E%7B14%7DHz%20%20)
So, the highest frequency associated with this part of the spectrum is the one corresponding to the lowest wavelength: