Numerade

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Evaluate the definite integral. (Assume a > 0.) a^1/2 x^3sqrt( a^2 − x^4) dx0

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1. Given two matrices A and B, prove that (assuming A-¹ and B-¹ exist), (AB)-1 = B-1A-1. 2. Consider the matrices below. Establish which of them can be inverted (i.e., the inverse exists) and calculate the inverses: A1 = $$\begin{bmatrix} 1 & 2 \\ 2 & -1 \end{bmatrix}$$ A2 = $$\begin{bmatrix} 3 & 0 \\ 0 & 1 \end{bmatrix}$$ A3 = $$\begin{bmatrix} 1 & 1 \\ 2 & 3 \end{bmatrix}$$ A4 = $$\begin{bmatrix} 1 & -4 & 2 \\ 0 & 2 & -1 \\ 0 & 0 & 5 \end{bmatrix}$$ A5 = $$\begin{bmatrix} -2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix}$$ A6 = $$\begin{bmatrix} 1 & -1 & 3 \\ 1 & 1 & 2 \\ 2 & 0 & 7 \end{bmatrix}$$

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What is the major product of the following reaction? 1) HCl (1 eqv) 2) HBr (1 eqv) + enantiomer Br Cl Cl Br + enantiomer (E/Z mixture) Br Cl H Cl + enantiomer Br H

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2 Find the simple interest owed for the loan. $4,200 at 6% for 1 year # ( 80 F3 $ 4 a F4 R 07 5⁰0 % 5 V 9 F5 T G 6 MacBook Air B F6 Y H & 7 K D N * 00 8 J H In one year at 6%, deposit of $4,200 earns $ in simple interest. DII F8 M ( 9 K DD F9 O V O J F10 command P Time Remaining: 01:11:55 A. **** F11 33 { option 11 + = 21 ? F12 } Next 1

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Telencephalon Third ventricle Mesencephalon Diencephalon Metencephalon Myelencephalon Spinal cord Central canal Lateral Optic Fourth ventricle vesicle Future cerebral ventricle aqueduct

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Find the ordinary points for the following second-order linear equations: 1. Hermite Differential Equation: y" - 2xy' + 2py = 0 2. Laguerre's Differential Equations: xy" + (1-x)y' + py = 0 3. Chebyshev's equation: (1-x²)y" - xy + p²y = 0 4. Airy's Equation: y" + p²xy = 0

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Question 14 Using sigma notation, write the following expression as an infinite series: $1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + ...$ A. $\sum_{n=0}^{\infty} \frac{n^2 + 1}{n^2}$ B. $\sum_{n=1}^{\infty} \frac{n^2 + 1}{n^2}$ C. $\sum_{n=1}^{\infty} \frac{3}{4} (-1)^n$ D. $\sum_{n=0}^{\infty} \frac{3}{4} (-1)^n$

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2. We add a Leap Day on February 29, almost every four years. The leap day is an extra day and we add it to the shortest month of the year, February. There are three criteria to identify leap years: The year can be evenly divided by 4, is a leap year, unless: The year can be evenly divided by 100, it is NOT a leap year, unless: The year is also evenly divisible by 400. Then it is a leap year. This means that in the Gregorian calendar, the years 2000 and 2400 are leap years, while 1800, 1900, 2100, 2200, 2300 and 2500 are NOT leap years. Your task is to write a program to input an integer variable. Write a function to verify whether the integer is a leap year or not. The function should return True/False. Example: Input: 1900 Output: False Input: 1992 Output: True

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QUESTION 8 The mortgage lender says that you must pay PMI and the rate is $100 a month. When you take into account your monthly mortgage payment and add PMI, property taxes, homeowners insurance and the HOA fee, what is your total monthly payment? A. $863.86 B. $977.56 C. $1,161.78 D. $2,134.55

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Question 8 Figure Q8 shows a section of a steel component on which a Delta strain gauge rosette has been attached. The Young's modulus (E) for the material is 200 GPa and the shear modulus (G) is 80 GPa. The strain gauge readings from the rosette are: $\epsilon_a = 40 \mu$, $\epsilon_b = 980 \mu$, $\epsilon_c = 330 \mu$, (a) Determine the principal strains and their orientations relative to the x direction, either by calculation or by a Mohr's strain circle construction, you are NOT required to do both. (b) Hence determine the principal stresses. (12 marks) (8 marks) Z 94 60° 00660 a x

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lori g.