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1. Find the specific gravity of the oil in the tank shown, where $h_1 = 0.1$ m, $h_2 = 1.5$ m, and $h_3 = 1.4$ m. The pressure reading of gage A is 35 kPa and that of gage B is 46 kPa. Also find the gage pressure at the bottom of the tank. What is the gage pressure at the bottom of the tank in mm of water? [10] Hint: Density of air is small, and pressure can be assumed constant throughout the air column. Fluid transmit pressure that is pressure at B is the pressure due to oil and air pressure.
Doing, attempting, or offering to do any of the following related to an interest in real estate: advertise, buy, appraise, rent, sell, auction, lease, or exchange.
Suppose Shen comes into a large sum of money and decides to lend it out to earn interest on it. He realizes, however, that even if he could evaluate whether a borrower is creditworthy before making a loan, he cannot ensure that his borrower will use the money as promised. He therefore deposits his money in a local bank, a financial intermediary. Because financial intermediaries can track customers' uses of money more easily than Shen can and take action quickly in cases where borrowers use the money irresponsibly, this is an example of how financial intermediaries can help solve the problem of:
Q4. Sequences and summations 1. Find $\sum_{k=10}^{20} k^2(k-3)$ 2. Use the mathematical induction to show that if n is a positive integer, then $1 + 2 + \dots + n = n(n+1)/2$ Q5. Matrices 1. Find the matrix multiplication of A and B, where $\begin{bmatrix} 1 & 0 & 4 \\ 2 & 1 & 1 \\ 3 & 1 & 0 \\ 0 & 2 & 2 \end{bmatrix} A = \begin{bmatrix} 2 & 4 \\ 1 & 1 \\ 3 & 0 \end{bmatrix} B = $ 2. Find inverse matrix $\begin{bmatrix} 7 & -8 & 5 \\ -4 & 5 & -3 \\ 1 & -1 & 1 \end{bmatrix}$
(b) Let $l$, $m$, $n$ be nonnegative integers. Show that the number of solutions to the equation $x_1 + x_2 + \dots + x_n = m$, where $x_i$ are nonnegative integers satisfying $x_i < l$ for every $1 \le i \le n$, is given by $$\sum_{d=0}^n (-1)^d \binom{n}{d} \binom{m - dl + n - 1}{n - 1}.$$ (c) Use the previous part to deduce that for any $l$, $m$, $n$: $$\sum_{d=0}^n (-1)^d \binom{n}{d} \binom{(n - d)l}{n - 1} = 0.$$
Each time a basketball player attempts a shot, it is a 2-point shot with probability \alpha and a 3-point shot with probability $1 - \alpha$ for $0 \le \alpha \le 1$. The probability that she makes the 2-point shot is 0.5. The probability that she makes the 3-point shot is 0.4. Compute the standard deviation of the points she scores per shot, as a function of $\alpha$. What are the maximum and minimum values of the standard deviation, and at what values of $\alpha$ are they attained?
Solve 17 and 18 please. 17. Consider the DE y + by + cy = 0. If y is a solution of the equation, what conditions must be placed on b and c so that lim y as y approaches 0? 18. Suppose the solution to an IVP whose characteristic equation has roots 1.2 = i is given by y = Ae^(cosx) + Be^(sinx). (1) Determine the conditions that R and A must satisfy in order to write y in the form y = Re^(cosx). (2) (Hint: Start by expanding 2, and then compare it to (1).)
Solve the simply supported beam problem if the initial conditions are $u(x, 0) = \sin(\frac{\pi x}{L})$ $u_t(x, 0) = \sin(\frac{\pi x}{L})$ Compare the solution if instead of a beam you had a vibrating string.
a bond is selling for 1200 and pays coupon of 0.08 what is the current yiels