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.
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
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...
THE FOLLOWING IS CODED IN C
Write a function that sets each element in an array to the sum
of the corresponding elements in two other arrays.
That is, if array 1 has the values 2,4, 5, and 8 and array 2 has
the values 1, 0, 4, and 6, the function assigns array 3 the values
3, 4, 9, and 14.
The function should take three array names and an array size as
arguments.
Test the function in a...