Numerade

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Find the indefinite integral and check the result by differentiation. (Remember the constant of integration.) $\int (3 \text{ (sec}(\theta))^{2} - 2 \sin(\theta)) \,d\theta$ $3 \tan(\theta) + 2 \cos(\theta) + C$

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What is the value of the 8-bit binary quantity 10101000 if it is interpreted a. as an unsigned integer, and b. as a signed integer represented in sign/magnitude notation?

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Part E The focal length ____________ when the index of refraction of the lens is increased and ____________ when the radius of curvature of the lens is increased. decreases / decreases increases / increases increases / decreases decreases / increases

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Exercise 13.5 Let $x, y \in \mathbb{R}^n$. What implications (i.e., $(a) \implies (b)$ or $(b) \implies (a)$) are valid between the following statements? If you claim an implication is true, then you need to prove is. If you are convinced a statement is false, then provide a counterexample. (a) $(x, y) = 0$, (b) For every $\lambda \in \mathbb{R}$ it follows that $||x|| \le ||x + \lambda y||$.

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21. The equilibrium mixture at 1000 K for the reaction CO$_2$(g) + H$_2$(g) $\rightleftharpoons$ CO(g) + H$_2$O(g) contains 0.276 M H$_2$(g), 0.276 M CO$_2$(g), 0.224 M CO(g), and 0.224 M H$_2$O(g). Determine: A. The equilibrium constant, K$_p$. Keep your answers to 3 significant figures. 0.659 $K_p = \frac{(0.224)^2}{(0.276)^2}$ $K_p = 0.659$ B. $\Delta G^{\circ}_{rxn}$ at 1000 K. Keep your answers to 3 significant figures. kJ/mol

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1. Generate 2 cycles of a discrete sinusoidal sequence by sampling a 20 Hz, unity amplitude, continuous time sinusoid at fs=1000 Hz cycles/sample with n=0:99 (N=100): $\text{Signal}(n) = \sin \left(2 \cdot \pi \cdot \frac{f}{f_s} \cdot n\right)$ Plot the discrete signal sequence Signal(n) versus n. 2. Generate 100 samples of a Gaussian noise sequence: $\text{Noise}(n) = 0.5 \cdot \text{randn}(1,100)$ Plot the discrete noise sequence Noise(n) versus n. 3. Add the noise to the signal to generate the noisy sinusoid: $\text{X}(n) = \text{signal}(n) + \text{noise}(n)$ Plot the noisy sinusoidal sequence X(n) versus n. 4. Filter the noisy sinusoid X(n) using the following: $\text{y}(n) = (1/2) \cdot [x(n) + x(n-1)]$ Plot the filtered sequence Y(n) versus n. 5. Filter the noisy sinusoid in (b) using the following: $\text{y}(n) = (1/3) \cdot [x(n) + x(n-1) + x(n-2)]$ Plot the filtered sequence Y(n) versus n. 6. Filter the noisy sinusoid in (b) using the following: $\text{y}(n) = (1/4) \cdot [x(n) + x(n-1) + x(n-2) + x(n-3)$ Plot the filtered sequence Y(n) versus n. 7. Compare and explain your filtered results from 4, 5, and 6.

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Find the HCF of $x^3 - y^3$, $x^6 - y^6$ and $x^4 + x^2y^2 + y^4$.

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18. If an event will never happen then the probability is A. 1 B. 1/2 C. 1/3 D. 0 19. All the possible outcomes that can occur when a coin is tossed twice are listed in the box. What is the probability of having a head? A. 1/4 B. 1/2 HH TH TT HT C. 3/4 D. 1 20. In a 2000-ticket draw for an educational prize, your name was written on 58 tickets. What is the probability that you will get the prize? A. 2.9% B. 5.8% C. 29% D. 58%

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The total cost of paint brush sets purchased for the art class is made up of a $125 fee and $15 for each paint brush set purchased. There is a linear relationship between the total cost and the number of paint brush sets purchased. What type of variation is this relationship, and what is its initial value? direct variation, $15 direct variation, $125 partial variation, $15 partial variation, $125

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2-30. Approximately 3 out of every 25 Americans live in California. About 3 out of every 50 Americans live in New York, and about 2 out of every 25 Americans live in Texas. c. About what percentage of Americans do not live in California, New York, or Texas?

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