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Recently Asked Advanced Mathematics Questions

• Q 1 : We consider the following first order differential equation x' + A(t)r - B(t)r* = 0 with k an integer greater or equal to 2. a) Setting y = 2¹-k prove that (1) is transformed into y' + (1 − k)A(t)y − (1-k)B(t) = 0 b) Use this result to solve r x = -x³. (1) See Answer
• Q 2 : (2) If ABCD is a parallelogram such that ABD = 30, Show that DM >AM where M is the point of the intersection of the two diagonals of the parallelogram. See Answer
• Q 3 : (1) If ABCD is a quadrilateral such that AC BD. Show that the quadri-lateral PQRS is a rhombus where P,Q, R and S are the midpoints of the sides of the quadrilateral ABCD. See Answer
• Q 4 : Determine the points of intersection between the circle, x2 +y2 = 3, and the hyperbola, xy = 1. As shown in the plot, there are four roots. However, it is enough to find only one root because the others can be deduced from symmetry. a) Solve the system of equations using the Successive Substitution method,starting with the initial guess xo = 0.5 and yo = 1.5. Show two complete iterations. b) Solve the system of equations using Newton-Raphson method, starting with the initial guess xo= -0.5 and yo =-1.5. Show two complete iterations. Evaluate &s for the second iteration. c) Solve the system of nonlinear equations by calling the MATLAB function newtmult. Yoursolution should achieve an accuracy of 6 significant figures. Report the solution, number ofiterations and errors. See Answer
• Q 5 : Use eigenvalues and eigenvectors to find the general solution of the following system of differential equations \mathrm{d} / \mathrm{dt} \times(\mathrm{t})=-\mathrm{x}(\mathrm{t}) \quad \mathrm{d} / \mathrm{dt} \mathrm{y}(\mathrm{t})=-4 \mathrm{x}(\mathrm{t})+4 \mathrm{y}(\mathrm{t}) \text { First find the eigenvalues } \lambda_{1}, \lambda_{2} \text { and the corresponding eigenvectors } V_{-} 1, V_{-} 2 \text { of the matrix of coefficients. } \text { Write the eigenvalues in ascending order (that is, } \lambda_{1} \leq \lambda_{2} \text { ): } Write the eigenvectors in their simplest form, without simplifying any fractions that might appear and one of components is 11 or –1–1: See Answer
• Q 6 : a) The gcd(-12, 22) is. b) The gcd(188, -56) is c) The gcd(-546, - 428) is . Are 13, 67, 124 pairwise relative prime? O Yes O No Are 3, 52, 31 pairwise relative prime? O Yes O No See Answer
• Q 7 : 10. (15 points total)Small hard particles are found in the molten glass from which glass bottles are made. On average 20 particles are found in 100 kg of molten glass. The distribution of these particle sis Poisson. If a bottle made of this glass contains one or more such particles it has to be discarded. Bottles of mass 1 kg are made using this glass. What is the probability that a randomly chosen bottle needs to be discarded? (b) (5 points) Using the expression above for the probability that a randomly chosen bottle is defective, determine the probability that in a randomly chosen batch of 10 bottles, 4out of the 10 are defective? (c) (5 points) Suppose you randomly sample the bottles one by one, what is the probability that the first defective bottle found is the 5th sample? See Answer
• Q 8 : \text { We consider the matrix } A=\begin{array}{ccc} -1 & 0 & 0 \\ -1 & 2 & 0 \\ 0 & 4 & B \end{array} \text { Write the eigenvalues of } A \text { in ascending order (that is, } \lambda_{1} \leq \lambda_{2} \leq \lambda_{3} \text { ): } \text { (ii) Write the corresponding eigenvectors }\left(\vec{\nabla}_{1} \text { corresponds to } \lambda_{1}, \vec{V}_{2} \text { corresponds to } \lambda_{2}, \vec{\nabla}_{3} \text { corresponds to } \lambda_{3}\right. \text { ) } in their simplest form, such as the components indicated below are 1. Do not simplify any fractions that mightappear in your answers. (iii) Write the diagonalisation transformation X such that X^{-1} A X=\begin{array}{ccc} \lambda_{1} & 0 & 0 \\ 0 & \lambda_{2} & 0 \\ 0 & 0 & \lambda_{3} \end{array} and such that X has the following components equal to 1, x21 = X22=X33=1: See Answer
• Q 9 : 9. Find the radius of convergence of each of the following power series: \text { (a) } \sum n^{3} z^{n}, \text { (b) } \sum \frac{2^{n}}{n !} z^{n} \text { (c) } \sum \frac{2^{n}}{n^{2}} z^{n} \text {, } \text { (d) } \sum \frac{n^{3}}{3^{n}} z^{n} See Answer
• Q 10 : D. Suppose that the coefficients of the power series sigma a z are integers, infinitely many of which are distinct from zero. Prove that the radius of convergence is at most 1. See Answer
• Q 11 : This practical includes a number methods that you would expect an accredited lab to employ as part of their quality control system. Give two examples. Describe how they give confidence to the validity of the data. See Answer
• Q 12 : 1)do you think provide the more valid data? With reference to the sample preparation methods employed in the practical, and how the portable XRF instrument works why do Present a basic statistical analysis on the XRF data. Which of the particle size fractions you think this might be? See Answer
• Q 13 : From the ICP data which of the two wavelengths measured for iron do you think give the most valid results and why? See Answer
• Q 14 : Exercise 7. Give an example of a set Ø + ACQ that that is both open and closed-in Q. Justify your answer. See Answer
• Q 15 : Assess the ICP data. Describe the main methodological controls on the values reported. See Answer
• Q 16 : Describe one additional QC methodology and explain how it might be used here. An example might be that demonstrated in validating the ICP data from the Birmingham canal dredging study. See Answer
• Q 17 : Exercise 10. Let (X,d) be a metric space and let A, B be two closed subsets of X such that AUB and A n B are connected. Prove that A is connected. See Answer
• Q 18 : 3. Find the exponential Fourier series of the waveform and draw the frequency spectrum See Answer
• Q 19 : 4. Plot amplitude and phase spectra for figure in question 2. See Answer
• Q 20 : 5. Find the trigonometric and exponential FS of waveform given below See Answer

Popular Subjects for Advanced Mathematics

• Symbolic Logic
• Abstract Algebra
• Advanced Mathematics
• Basic Mathematics
• Complex Analysis
• Differential Equations
• Integration
• Linear Algebra

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A great tool to help students learn new things, prepare for tests, and master subjects like math, chemistry, and physics. Unlike traditional tutoring services, our app doesn't just hand out answers - it guides students through each problem with detailed step-by-step explanations and solutions, empowering them to understand and solve similar problems on their own. Here's how our app helps you learn: Comprehensive help with homework. Whether you're solving algebraic equations or balancing chemical reactions, our app will give you the support you need to solve even the most challenging problems. Our application will help you cope with even the most complex tasks! Easy organization: With the ability to save completed tasks and questions in the app's file directory, students can easily return to their work to review, share it with classmates, or print it for reference. Cooperative Learning: Need more help? AI Homework Helper facilitates group learning by allowing users to work on math problems with friends, classmates and others, creating a collaborative learning environment. For those looking for unlimited access to our premium features, we offer a subscription service: Your iTunes account will be charged upon confirmation of purchase. Subscriptions are automatically billed according to the selected plan. Manage your subscription and turn off auto-renewal in Settings to maintain control of your membership. Subscriptions with a free trial period will transition to a paid subscription upon renewal. At AI Homework Helper we believe in empowering students to become confident and independent learners. Try our app today and discover the difference it can make in your academic journey. Privacy Policy: https://docs.google.com/document/d/1_5xd-bfOv8_3y3huQ64q0-NcKNFlpJT6aLiqrel15VI/edit Terms of Use: https://docs.google.com/document/d/1ceeWBb2GMjoYEs9gEVAnEIYgN1T0G7F-DCNWoiSrvYU/edit

Ratings and Reviews

App privacy.

The developer, YASIN YUZGULEC , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

Data Not Collected

The developer does not collect any data from this app.

Privacy practices may vary, for example, based on the features you use or your age. Learn More

Information

• Homework Helper: AI Math Solve $6.99
• App Support
• Privacy Policy

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