Advance Math question and answers for August 14, 2023
- Q Given f(x) = sin^2(x) and g(x) = sin^4(x) (give exact answersfor all parts): a) Plot the functions on the x-interval [0, ?].Find the volume when the region enclosed by the...
- Q (2) More inclusion-exclusion counting: How many bit strings oflength 15 have bits 1, 2, and 3 equal to 101, or have bits 12, 13,14, and 15 equal to 1001 or...
- Q It was estimated that in 2013, the Greenland Ice Sheet and itsoutlying ice caps were losing mass at a rate of about -393 Gt/y(gigatonnes per year).1 Suppose that in 2023,...
- Q For each system described below say as much as possible abouteach system’s solutionset. Note which theorems you are using to reach yourconclusions.(a) A consistent system of 8 equations in 5...
- Q Define error function and complementary error function,mathematically. Explain how these functions can be tabulated.
- Q Use LU decomposition to solve the following system of equations(show your work). Do not use a pivoting strategy, and check yourresults by using the matrix inverse to show that [A][A]-1=...
- Q Using a power series methodology, obtain the general solution(form u = c1u1 + c2u2 + f(x)) to the equation u” + 4u = x.
- Q A voltage of 10 sin(3t) volts is impressed on a series circuitcontaining a 20? resistor, 10^-3 H inductor and a 1?F capacitor.Obtain expressions for the charge q on the capacitor...
- Q Scenario 7.2 - Gulab GreatnessHistorical demand for gulab jamun from a sweet stall on CommercialRoad is as displayed in the table.MonthDemand (orders)January66,753February67,686March68,641April68,979May69,278June69,577July69,602August70,348September70,806October71,011November71,819December72,752What is the trend component of Holt's model for...
- Q Consider a general system of linear equations with m equationsin n variables, called system I. Let system II be the systemobtained from system I by multiplying equation i by a...
- Q Consider the initial value problemy? = 18x ? 3y, y(0) = 2(a) Solve it as a linear 1st order ODE with the method of theintegrating factor.(b) Solve it using a...
- Q Example 3.5: Again let X = Y = R. Define g by g(x) = x2. Thegraph of this function has the familiar parabolic shape as inFigure 3.1(b). Then for example,...
- Q 10. A student has to take eight hours of classes a week. M-F.They want to have fewer hours on Friday than on Thursday. In howmany ways can they do this?...
- Q Two chemicals A and B are combined to form a chemical C. Therate of the reaction is proportional to the product of theinstantaneous amounts of A and B not converted...
- Q Discrete MathematicsA tree contains 1 vertex of degree 2, 1 vertex of degree 3, 1vertex of degree 4, 11 leaves and the remaining vertices havedegree 3.Find the total number of...
- Q Let P(n) := ” If n^3 is odd then n is also odd.” I.e., if ?k ?Z, n3 = 2k + 1, ?b ? Z, n = 2b + 1a)...
- Q How many eight-digit positive integers have the sum of digitsbeing even?
- Q Here are mass spectrometric signals for methane in H2:CH2 (Vol %) 0 0.062 0.122 0.245 0.486 0.971 1.921Signal (mV) 9.1 47.5 95.6 193.8 387.5 812.5 1671.9a) Subtract blank value from...
- Q 1. (14) List the elements for each of the following sets:(1) P({a, b, c}) (Note: P refers to power set)(2) P{a, b}) - P({a, c})(3) P(Æ)(4) {x Î ?: (x...
- Q For a binary FSK system, s1(t)=A cos (?0+?)t and s2(t)=A cos(?0-?)t are defined.a) Prove that the above signals are orthogonal if ?T=n?, where T isthe bit interval and n is...
- Q A manufacturer of animal feed makes two grades of food. Each bagof high grade feed contains 10kg of wheat brand and 5kg of maize,while each bag of low-grade feed contains...
- Q Without using a calculator, find the cube root of 2, correct to1 decimal place.
- Q *(1)(a) Find a formula for the intersection of a cone {(x,y,z):x^2+y^2=z^2} with a plane {(x,y,z): z=c}.(b) Find a formula for the intersection of a cone {(x,y,z):x^2+y^2=z^2} with a plane {(x,y,z):...
- Q a)Select all solutions of (d^2/dx^2)y(x)+64y(x)=0.y(x)=3cos(8x)y(x)=3cos(4x)y(x)=C1sin(8x)+C2cos(8x)y(x)=?4sin(8x)y(x)=C2cos(8x)b)Select all solutions of (d^2/dx^2)y(x)+36y(x)=0.y(x)=C2cos(3x)y(x)=C1sin(3x)y(x)=3cos(3x)y(x)=3cos(6x)y(x)=3sin(3x)+8cos(3x)
- Q 3. The Bay City Parks and Recreation Department has received afederal grant of $600,000 to expand its public recreationfacilities. City council representatives have demanded fourdifferent types of facilities—gymnasiums, athletic fields,...
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