Many of today’s mathematicians use computers to test cases that are either too time-consuming or involve too many variables to test manually, allowing the exploration of theoretical issues that were impossible to test a generation ago.
Answer: Option A
<u>Explanation:</u>
One of the most useful inventions in scientific world are the computers. We can use different programming language and create programs in them. These programs help other to solve difficult problems. Most of the theoretical problems in science can be solved by using these programming features in computer within a specific time limit.
Otherwise, earlier mathematician used to take months to solve a complex mathematical problem manually, but now with the inclusion of computers, the mathematician can solve the problems containing more number of variables or other theoretical issues.
Answer:
The change in the charge on the positve plate when the Teflon is inserted is +2.5 nC.
Explanation:
- It can be showed that the capacitance of a parallel-plate capacitor, can be expresssed as follows:

- Where ε, is the dielectric constant of the material that fills the space between plates.
- When this space is filled with air, ε= ε₀ = 8,85*10⁻¹² F/m.
- At the same time, the capacitance of a capacitor, by definition, is as follows:

- If we insert a Teflon slab, in such a way that fills completely the gap between the plates, all other parameters being equal, if ε = 2*ε₀, this means that C₂ = 2* C₁. = 50 pF
- As V₂=V₁ (due to the capacitor remains connected to the same battery) the charge must be the double, so Q₂ = 2* Q₁ = 5 nC.
- So, the change in the charge of the positive plate is +2.5 nC.
Answer:
For the first blank, the answer is decreases. For the second blank, the answer is increases. And finally for the third blank, the answer is decreases.
Explanation:
For the first blank, the answer is decreases. For the second blank, the answer is increases. And finally for the third blank, the answer is decreases.
When a liquid is cooled, the kinetic energy of the particles decreases. The force of attraction between the particles increases, the space between the particles decreases, and the matter changes its state to solid.
Answer:
17 °C
Explanation:
From specific Heat capacity.
Q = cm(t₂-t₁)................. Equation 1
Where Q = Heat absorb by the metal block, c = specific heat capacity of the metal block, m = mass of the metal block, t₂ = final temperature, t₁ = Initial temperature.
make t₁ the subject of the equation
t₁ = t₂-(Q/cm)............... Equation 2
Given: t₂ = 22 °C, Q = 5000 J, m = 4 kg, c = 250 J/kg.°c
Substitute into equation 2
t₁ = 22-[5000/(4×250)
t₁ = 22-(5000/1000)
t₁ = 22-5
t₁ = 17 °C
As Potential energy =mgh
m= 0.95kg
h=3 meter
g = 9.8 m/sec^2. ( acceleration due to gravity)
So P.E =(0.95)(9.8)(3)kgm^2/s^2
P.E =27.93 joules