Thermally Challenged
Volume will not change
When undergoing an isochoric process
Prevents Floating By Forcing "0" Value
What is a pull-down resistor?
When your binomial distribution involves a sample size of n = 2400 coin tosses, you use this theorem to approximate the distribution as a smooth, continuous Normal curve instead.
What is the Central Limit Theorem?
you use this formula to find the centripetal acceleration of a particle traveling at speed v around a curve with a radius of R.
a_c = v^2 / R
You are driving a motor with a 24 Volt peak PWM signal. If your pulse ON time is 2 milliseconds and your period is 8 milliseconds, this is the average voltage delivered to the motor.
Duty = (on-time) / (period) ->(2ms) / (8ms) = 0.25
V_(mean) = V_(peak) * duty
24 * 0.25 = 6
this formula relates the pressure, volume, mass, and temperature of an ideal gas.
P V = m R T
evaluating this expression
= V_r / 2^n
should be done to calculate what for what?
the smallest possible analogue voltage step (the resolution) output of a DAC
To differentiate a fraction like
f(x) = (2x^2 - x + 1) / (x^2 - 2x + 2)
you use this rule
(u'v - uv') / v^2
What is the Quotient Rule?
In constrained rectilinear motion, if Mass A is connected to Mass B via a doubled-back cable around a moving pulley, and Mass A moves downward by a distance of ΔA, Mass A's acceleration will be exactly this multiple of Mass B's acceleration.
What is twice (or 2 times)?
If your system needs to access exactly 536,870,912 addresses, you will need exactly this many parallel wires for your address bus.
2^29 = 536,870,912
:.
29 wires
To find the heat flux emitted by a real, non-blackbody surface, you multiply the Stefan-Boltzmann constant by the temperature to the 4th power, and by this specific radiative property of the material, denoted by 𝞮
What is emissivity?
q = epsilon * sigma * T^4
for what equation is the following true?
"always round down"
D = (V_i / V_r) * 2^n
also "ADC digital output equation"
when computing the following you may use this rule to differentiate the numerator and denominator until it makes sense.
\lim_{x \to 0} (\sin(x) / (\cos(x) - 1))
What is L'Hôpital's Rule?
Calum is pushing his canoe across a 50-meter-wide river. If his push speed is 2 m/s straight across, and the river is flowing downstream at a speed of 5 m/s, it will take him exactly this many seconds to reach the opposite bank.
25 Seconds
A Geiger counter detects radioactive particles with a tiny probability of 1/10000. If 30000 particles are emitted during observation, your mean rate of occurrence is:
\lambda = 3
Using the Poisson distribution formula:
P(X = k) = (\lambda^k e^{-\lambda}) / k!
the probability of registering exactly zero particles is e raised to this power.
What is -3?or approx 0.05
\lambda = 30000 * (1/10000) = 3 -> (3^0 * e^{-3}) / 0!
Since 3^0 = 1 and 0! = 1, the answer is exactly:
e^{-3}
Fluid in a piston-cylinder is at an initial pressure of 20 bar and a volume of 0.05㎥. If it expands according to the relation PV2 = Constant until the volume doubles to 0.1 m3, your final pressure will drop to this value.
5 bar
P_1 V_1^2 = P_2 V_2^2
20 * (0.05)^2 = P_2(0.1)^2 -> 20 * 0.0025 = P_2 * 0.01
0.05 = P_2 * 0.01
When drawing which graph would you use this equation?
period = 1/f
I2C, SPI and PWM
You're evaluating ball bearings with a mean diameter
\mu = 6.00 mm
and a standard deviation
\sigma = 0.02 mm
If your machine's upper tolerance limit is exactly 6.06 mm (+1%), your normalized z-score for this limit is exactly this integer.
What is z = 3?
z = (X - \mu) / \sigma -> z = (6.06 - 6.00) / 0.02 -> z = 0.06 / 0.02 = 3
A frictionless spherical cow is dragged by a tornado. The cow rotates in the xy-plane at a fixed radius of 500 meters from the center, sweeping through an angle at a rate of 10 degrees per second. This is the magnitude of the cow's velocity relative to the tornado.
\omega = (10/180) * \pi \approx 0.1745 rads^-1
The relative velocity magnitude is
v = \omega * r --> 0.1745 * 500 = 87.25 ms^-1
While an isolated system blocks both energy and mass transfer, a closed system only blocks the transfer of this across its boundary.
What is Mass?
From a thermodynamic perspective, these two common household devices are functionally identical
What are a heat pump and a refrigerator?
you multiply the peak voltage by this formula
duty cycle =
(on-time)/(period)
To find the derivative of the deeply upsetting function
f(x) = \sin(x)^{\cos(x)}
you must first do what
Use Logarithmic Differentiation
To determine how much kinetic energy is lost when two supermarket trolleys slam into each other, you use this dimensionless parameter.
e
(What is coefficient of restitution?)
Yes
Will You Pass These Exams?