As part of a liability defence (see the Wikipedia page on
Liebeck v. McDonald's for a similar case), lawyers at Tim Hortons
have hired you to determine the temperature of a cup of Tim
Horton's coffee when it was initially poured. However, you only
have measurements of the coffee's temperature taken after it has
been purchased. According to Newton's Law of Cooling, an object
that is warmer than a fixed environmental temperature will cool
over time according to the following relationship:
T(t)=E+(Tinit−E)e−ktT(t)=E+(Tinit−E)e−kt
where EE is the constant environmental temperature, and TT is the
temperature of the object at time tt. The object has initial
temperature TinitTinit.
Below you are given a data set measured from a purchased cup of
coffee. The external temperature of the room is 2020 °C. The
temperature of the coffee TiTi is given for several titi, where
titi is the time in minutes since the coffee was poured.
Transform the solution T(t)T(t) by putting the exponential term on
one side and everything else on the other and taking natural logs
of both sides to get:
ln(T(t)−E)=ln(Tinit−E)−kt.ln(T(t)−E)=ln(Tinit−E)−kt.
Now transform the data below in the same way so that you can use
linear least squares to estimate the unknown parameters TinitTinit
and kk. Fit the transformed data to a line yi=b+axiyi=b+axi, i.e.,
find the values of aa and bb which minimize
f(a,b)=∑i=1((yi)−(b+axi))2f(a,b)=∑i=1((yi)−(b+axi))2:
| t_i (in minutes) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| T_i (in °C) | 86.1914 | 84.3832 | 88.5955 | 86.5824 | 86.7775 | 79.0971 | 80.4190 | 75.3221 | 74.7302 |
Use the computed coefficients aa and bb to calculate the
following quantities:
What was the initial temperature TinitTinit of the coffee when it
was poured? °C
What is the time constant kk? /min
In: Advanced Math
In Trites v Renin Corp. the court held that there is no constructive dismissal where a temporary layoff has been rolled out in accordance with Ontario’s Employment Standards Act. Subsequent cases in Ontario have
|
a
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confirmed this
principle
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b
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confirmed this principle but only
as long as the employer acted reasonably and in good faith in
placing the employee on temporary layoff
|
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c
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overturned this principle by findng
that a temporary layoff may constitute constructive dismissal even
where the employer complies with the requirements of Ontario’s
Employment Standards Act
|
|
d
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overturned this principle in some
cases while confirming it in others, depending on the specific
facts of the case
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In: Accounting
A snake of proper length 100 cm is moving at speed v = 0.6c to the right across the table. A mischievous boy, wishing to tease the snake, holds two hatchets 100 cm apart and plans to bounce them simultaneously on the table so that the left hatchet lands immediately behind the snake’s tail 1 .
The boy argues as follows: “The snake is moving with v = 0.6c, therefore, its length measured in my frame is 100cm γ = 80 cm. This implies that the right hatchet will fall 20 cm in front of the snake, and the snake will be unharmed”. On the other hand, the snake argues “the hatchets are approaching me at 0.6c, and the distance between them is 80 cm. Since I am 100 cm long, I will be cut in pieces when they fall” (it’s a very smart snake).
Use Lorentz transformation to resolve this apparent paradox. In other words, resolve it quantitatively, not just with a qualitative argument about non-simultaneity.
Please show work quantitatively, thanks!
In: Physics
A man pushing a crate of mass
m = 92.0 kg
at a speed of
v = 0.845 m/s
encounters a rough horizontal surface of length
ℓ = 0.65 m
as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.351 and he exerts a constant horizontal force of 288 N on the crate.
A man pushes a crate labeled m, which moves with a velocity vector v to the right, on a horizontal surface. The horizontal surface is textured from the right edge of the crate to a horizontal distance ℓ from the right edge of the crate.
(a) Find the magnitude and direction of the net force on the crate while it is on the rough surface.
| magnitude | N |
| direction | ---Select--- same as the motion of the crate opposite as the motion of the crate |
(b) Find the net work done on the crate while it is on the rough
surface.
J
(c) Find the speed of the crate when it reaches the end of the
rough surface.
m/s
In: Physics
Q1
A potential difference of 13 V is found to produce a current of 0.45 A in a 3.1 m length of wire with a uniform radius of 0.36 cm. Find the following values for the wire: (a) the resistance (b) the resistivity
In: Physics
In: Physics
Define a subspace of a vector space V . Take the set of vectors
in Rn such that th
coordinates add up to 0. I that a subspace. What about the set
whose coordinates add
up to 1. Explain your answers.
In: Math
We have potential of
V (x) = ( 0, 0 ≤ x ≤ a.
∞, elsewhere.
a) Find the ground state energy and the first and second excited states, if an electron is enclosed in this potential of size a = 0.100 nm.
b) Find the ground state energy and the first and second excited states, if a 1 g metal sphere is enclosed in this potential of size a = 10.0 cm.
c) Are the quantum effects important for both systems? Explain why or why not.
d) Use the uncertainty principle to estimate the velocities of the electron and the metal sphere.
In: Physics
In †he 1973 case of Roe V. Wade, it was found that the negative right to abortion only created an obligation to noninterference. In this light, do we curtly have a negative right to health care? Explain your answer.
In: Nursing
A 1.0 toaster and a 2.0 lamp are connected in parallel with the
110-V supply of your house. (Ignore the fact that the
voltage is AC rather than DC.)
(a) Draw a schematic of the circuit.
(b) For each of the three components in the circuit, find the
current
passing through it and the voltage drop across it.
(c) Suppose they were instead hooked up in series. Draw a
schematic
and calculate the same things.
In: Physics