Numerade

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WHICH OF THE FOLLOWING ARE POLICY INSTRUMENTS AVAILABLE TO THE CENTRAL BANK AS IT TRIES TO ACHIEVE ITS MACROECONOMIC GOALS? I. GOVERNMENT EXPENDITURES ON GOODS AND SERVICES AND TAXES II. THE GOVERNMENT BUDGET DEFICIT OR SURPLUS III. CHANGES IN THE DISCOUNT RATE a. I and II b. III only c. II only d. II and III

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To find the area of the triangle, we can use the formula: Area = (1/2) * a * b * sin(C) First, we need to convert the angle C from degrees and minutes to just degrees. To do this, we use the formula: C = 83 + 24/60 = 83.4 degrees Now we can use the formula for the area: Area = (1/2) * 4 * 9 * sin(83.4) Area ≈ (1/2) * 4 * 9 * 0.9962 Area ≈ 17.93 Rounded to the nearest hundredth, the area of the triangle is 17.93 square units.

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The price of gas per gallon 40 years before was $1.28 which increased to $4.17now. Use this information to answer the following questions Question 1 a) Which of the following is/are true? Select all that apply. The purchasing power increases over time with inflation The purchasing power decreases over time with inflation The purchasing power remains constant over time with inflation Inflation/deflation compounds over time 3 pts Question 2 9 pts b) What has the average annual rate of inflation for gas per gallon been for the last 40 years? Round of to the nearest integer. If your answer is 15.1%, enter 15.

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First use the formula $A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \ -c & a \end{bmatrix}$ for the general $2 \times 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$ to find $A^{-1}$. Then use $A^{-1}$ to solve the system $Ax = b$. $A = \begin{bmatrix} 5 & 6 \ 4 & 5 \end{bmatrix}$; $b = \begin{bmatrix} -16 \ -14 \end{bmatrix}$ Find $A^{-1}$. $A^{-1} = \[\]$ Solve the system. $x = \[\]$

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A matrix, A ? Rnxn, such that A = AT is called a symmetric matrix. Let A be diagonalizable, i.e., A has an eigen-decomposition, A = VDV-1. In other words, a symmetric matrix has orthogonal eigenvectors, i.e., VVT = I, and column-wise we can write $v_i^T v_j = \begin{cases} 1, & i = j; \\ 0, & i \neq j. \end{cases}$ (1) (b) Let $A = \begin{bmatrix} 5 & 4 \\ 4 & 3 \end{bmatrix}$. Show that its eigenvectors are orthogonal. (Compute the eigenvectors and show that they satisfy Eq. (1)). Plot the eigenvectors and show that they are 90° apart.

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The following derivation proves the logical equivalence $(p \lor \neg q) \land (\neg p \lor \neg q) \equiv \neg q$. Supply a reason for each step. $(p \lor \neg q) \land (\neg p \lor \neg q) \equiv (\neg q \lor p) \land (\neg q \lor \neg p)$ $\equiv \neg q \lor (p \land \neg p)$ $\equiv \neg q \lor c$ $\equiv \neg q$

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(a) Using Figure 1 below, if the power captured by the wind is 15kW, compute the output power. Gears Generator Transformer Power Output 95% 95% 96% 98% Figure 1 A Wind Turbine System

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21 $F = 4F_0$ $m_2 = m_0$ $m_1 = 2m_0$ 2b b b

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When insulin is secreted, what happens? Tissue stores of glucose are depleted. Glucose is taken up by the cells. The blood glucose level rises. • The liver breaks down glycogen. • Adipose tissue breaks down fat.

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Consider a causal linear time-invariant system whose system function is $H(z) = \frac{1 - \frac{3}{10}z^{-1} + \frac{1}{3}z^{-2}}{(1 - \frac{4}{5}z^{-1} + \frac{2}{3}z^{-2})(1 + \frac{1}{5}z^{-1})} = \frac{\frac{1}{2}}{1 - \frac{4}{5}z^{-1} + \frac{2}{3}z^{-2}} + \frac{\frac{1}{2}}{1 + \frac{1}{5}z^{-1}}$ Draw the signal flow graphs for implementations of the system in each of the following forms: • Direct form I • Direct form II • Cascade form using first- and second-order direct form II sections • Parallel form using first- and second-order direct form II sections

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steven m.