 # Upper-Level Maths Questions & Answers

Recent questions in Upper Level Math Meera Sunker 2022-05-20

### 1a.  Show from first principles, i.e., by using the definition of linear independence,that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrixA with associated eigenvector v = u + iw, then the two real solutionsY(t) = eat(u cos bt − wsin bt)andZ(t) = eat(u sin bt + wcos bt)are linearly independent solutions of ˙X = AX. 1b. Use (a) to solve the system (see image)  Meera Sunker 2022-05-20

### Reduce the system(D2 + 1)[x] − 2D[y] = 2t(2D − 1)[x] + (D − 2)[y] = 7.to an equivalent triangular system of the formP1(D)[y] = f1(t)P2(D)[x] + P3(D)[y] = f2(t)and solve. omar aljaradi 2022-05-09

### Identify each of the following statements as true or false in relation to confidence intervals (CIs). Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.    TrueFalseA 95% CI is a numerical interval within which we are 95% confident that the true mean μ$\mu$ lies.  A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯¯¯$\overline{x}$ lies.  The true mean μ$\mu$ is always inside the corresponding confidence interval.  For a sample size n=29$n=29$, the number of degrees of freedom is n=30$n=30$.  If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not$not$ contain the true mean 𝜇. Niraj Prajapati 2022-04-15

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### Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m Jane 2022-03-26

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### The solid lies between the Planes perpendicular to the x axis at X=-1amd X=1. Cross-sections perpendicular to the x axis between between these planes are circular disk with the diameters run from the semicircle y =-root(1-x*2)to the semi circle y=root(1-x*2).Find a formula for the area of cross section A(x) Cheyanne Leigh 2021-10-05 Answered

### The table shows the number of students in a school's beginning and advanced orchestra classes. The student pay a fee for instruction books: $5 for brass,$5 for woodwinds, and $8 for strings. Find the amount each class will spend on books. $\begin{array}{|ccc|}\hline & Advanced& Beginning\\ Brass& 12& 28\\ Strings& 22& 25\\ Woodwinds& 18& 30\\ \hline\end{array}$ Anish Buchanan 2021-10-05 Answered ### The following definition is discussed in advanced mathematics courses. Evaluate $f\left(-34\right)$, $-\sqrt{2}$, and $f\left(\pi \right)$. aortiH 2021-10-04 Answered ### Assume that all the distributions are normal, average is always taken to be the arithmetic mean xˉ or μ. A college Physical Education Department offered an Advanced First Air course last semester. The scores on the comprehensive final exam were normally distributed, and the the z scores for some of the students are shown below: Robert, 1.11 Juan, 1.66 Susan, –1.9 Joel, 0.00 Jan, –0.65 Linda, 1.46 (c) Which of these students scored below the mean? necessaryh 2021-10-01 Answered ### The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: Robert, 1.10 Juan, 1.70 Susan, -2.00 Joel, 0.00 Jan, -0.80 Linda, 1.60 If the mean score was μ=150 with standard deviation σ=20, what was the final exam score for each student? lwfrgin 2021-09-30 Answered ### One reason for the increase in the life span over the years has been the advances in medical technology. The average life span for American women from Email-trough 2007 is given by $W\left(t\right)=49.9+17.1\mathrm{ln}t\left(1\le t\right)$ where W(t) is measured in years and t is measured in 20-year intervals, with t=1 corresponding to the beginning of 1907. a. Show that W is increasing on (1, 6). b. What can you say about the concavity of the graph of W on the interval (1, 6)? ddaeeric 2021-09-30 Answered ### The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if$ $\underset{n\to \mathrm{\infty }}{lim}\frac{{a}_{2n}}{{a}_{n}}<1/2$ then $\sum {a}_{n}$ converges, while if $\underset{n\to \mathrm{\infty }}{lim}\frac{{a}_{2n+1}}{{a}_{n}}>1/2$ then $\sum {a}_{n}$  diverges. Let ${a}_{n}=\frac{{n}^{\mathrm{ln}n}}{{\left(\mathrm{ln}n\right)}^{n}}$. Show that $\frac{{a}_{2n}}{{a}_{n}}\to 0$ as $n\to \mathrm{\infty }$ Brittney Lord 2021-09-30 Answered

### Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a female whose current age is x years old is $f\left(x\right)=0.0069502x2-1.6357x+93.76\left(60\le x\le 75\right)$ years. What is the life expectancy of a female whose current age is 65? Whose current age is 75? Ayaana Buck 2021-09-26 Answered

### Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function $f\left(t\right)=-0.00447{t}^{3}+0.09864{t}^{2}+0.05192t+0.8\left(0\le t\le 15\right)$ gives the number of surgeries (in millions) performed in physicians' offices in year t, with t=0 corresponding to the beginning of 1986. a. Plot the graph of f in the viewing window [0,15] $×$ [0,10]. b. Prove that f is increasing on the interval [0, 15]. tricotasu 2021-09-25 Answered

### Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was $\overline{x}=5.35\mathrm{mg}$ . $\mathrm{dl}.$ The distribution of uric acid in healthy adult males can be assumed to be normal, with $\sigma =1.85\mathrm{mg}$. $\mathrm{dl}$ .Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error?

In the majority of cases, students dealing with upper-level Math questions will have to solve not only numerical problems or equations but also verbal tasks. The answers that are provided below free of charge will help you to find solutions to your questions that are dealing with more advanced Maths problems. Remember that one must look into analysis and evaluation of original instructions, which is why upper-level Maths requires more thinking as you study questions and see how the answers have originated. The trick is to see similarities in solutions that are being provided as it always helps.