For each of the following data sets, write a system of equations
to determine the coefficients...
For each of the following data sets, write a system of equations
to determine the coefficients of the natural cubic spline passing
through the given points.
x| 3 4 6
------------------
y| 10 15 35
Solutions
Expert Solution
now using matrices algebra we
can find the coefficients easily.
For each of the following data sets, write a system of equations
to determine the coefficients of the natural cubic spline passing
through the given points.
x| 2 4 7
-------------
y| 2 8 12
Determine the form of a particular solution to the following
differential equations (do not evaluate coefficients).
(a)y′′ −4y′ = x+1+ xe^(2x) + e^(4x) + e^(4x)sin4x
Solve the following linear equations with constant coefficients,
using characteristic equations and undetermined coefficients as
needed.
y''+4y'-12y=x+e^2x y(0)=1,y'(0)=2
Write down descriptions for each of the following sets:● Three different countably infinite subsets of the real
numbers.● Three different uncountably infinite subsets of the real
numbers.● One uncountably infinite proper super set of the real
numbers.
Determine if each of the following sets of vectors U is a
subspace of the specified vector space, and if so, describe the set
geometrically:
(a) U ⊆ R2, where U = {〈x1,x2〉 : x1 = 0}
(b) U ⊆ R2, where U = {〈x1,x2〉 : x1x2 = 0}
(c) U⊆R3,whereU={〈x1,x2,x3〉:〈1,2,3〉·〈x1,x2,x3〉=0}
(d) U ⊆ R3, where U = {〈x1,x2,x3〉 : 〈1,2,2〉 · 〈x1,x2,x3〉 = 0
and
〈1, 3, 0〉 · 〈x1, x2, x3〉 = 0}
Use MATLAB to determine the intersection point for the sets of equations shown below. Use the backslash when possible.Graph the equations with different colors, and plot the intersection point with a red star marker. If the equations do not intersect, graph them anyway.
Include a legend:
a) -4x1 + 2x2 = 10 b)-4x1+2x2^3 = 10
x1 + x2 = -8 x1+ x2 = -8
Question 2: For each of the following data sets, classify into
the following, and give a brief explanation for each choice:
i. Quantitative or Qualitative
ii. Discrete or Continuous
iii. Nominal, Ordinal, Interval, or Ratio
a) Low temperature on the day of the winter solstice at a
certain location, in °C, over 20 consecutive years.
b) Number of years, out of the last 20 years, when the low
temperature on the day of the winter solstice was below 0 °C,...
Determine which of the following sets of data satisfy the first
law of thermodynamics? (Recall that E = total energy = U + KE +
PE)
a. W = 50 kJ Q = 170 kJ DeltaE = 120 kJ
b. W = 100 Btu Q = -110 Btu DeltaE = -210 Btu
c. W = 250 kJ Q = -110 kJ DeltaE = -100 Wh
d. W = 44 kPa-m3 Q = -84 kPa-m3 DelatE = 40 kN-m
Consider the following system of equations for all
problems.
The following system of equations is designed to determine
concentrations (the c’s in g/m3) in a series of coupled reactors as
a function of the amount of mass input to each reactor (the
right-hand sides in g/day).
8?1 − 4?2 − 2?3 = 2000
−3?1 + 18?2 − 6?3 = 1400
−4?1 − 2?2 + 12?3 = 3000
Calculate and interpret the condition number. Use the
row-sum norm. Scale the coefficient...
In questions below determine whether each of the following sets
is countable or uncountable.
For those that are countably infinite exhibit a one-to-one
correspondence between the set of positive integers and
that set.
1) The set of positive rational numbers that can be written with
denominators less than 3.
2) The set of irrational numbers between sqrt(2) and π/2.