Numerade

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\lim_(x->2)((x-1)(x 4))/(\root(3)(2x^(2))) 1. $$ \lim_{x \to 2} \frac{(x-1)(x+4)}{\sqrt[3]{2x^2}} $$

BEST MATCH

(14 pts) A merry-go-round is a solid cylinder platform with the mass M=100kg, radius r=1.50m, and a frictionless axle at the center. Two students with masses m_(1)=70.0kg and m_(2)=65.0kg are standing at the rim of the platform. The platform is initially at rest. A third student, standing on the ground, applies a constant force tangential to the rim, spinning it up with an angular acceleration of 0.450ra(d)/(s^(2)). (e) (4 pts) The two students on the platform move towards the center of the platform. What is the angular speed of the platform when they are at the center?

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During the prior year, SDIC purchased 10% of the common shares of Twin Cones (TC), a producer of dipped ice cream cones, for $200,000. The shares of TC are not publicly traded, and the purchase price was established as five times net income of $40,000. The past fiscal year has proved to be a challenge for TC due to increased competition, commodity price inflation, and an inability to raise prices due to limits on consumer discretionary spending. TC’s most recent financial statements report reveals net income of $27,500.

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Knowing that y is a function of x, and that f = y2x , find the expression for a) @f@x , and b) dfdx

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Texts: A pair of parallel metal plates are separated by a distance d of 1.5 mm. At one particular time, the lower plate Vi is held at a potential of 100 V, while the upper plate Vu is held at 25 V. a. What is the electric field between the plates? b. If a proton were placed in the electric field, what would be the magnitude and direction of its acceleration? c. If the proton were replaced by an electron, how would the electron's acceleration differ from the proton's? Please give a qualitative answer to this question, no calculation needed.

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The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t^2 - 2t - 24, 1 \leq t \leq 7 (a) Find the displacement. -234/3 m (b) Find the distance traveled by the particle during the given time interval. 101 m

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B. A MIMO multivariable control system is given by its state-space realization: $x = \begin{bmatrix} 1 \\ 0 \end{bmatrix} \begin{bmatrix} 1 & 1 \\ 0 & 2 \end{bmatrix} x + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \begin{bmatrix} 0 \\ 1 \end{bmatrix} u = Ax + Bu$ Let a state feedback gain, randomly chosen, to be $K_1 = \begin{bmatrix} 1 \\ 0 \end{bmatrix} \begin{bmatrix} 0 \\ 1 \end{bmatrix}$ and a pre-compensating matrix, randomly chosen, be $V = \begin{bmatrix} 1 \\ 1 \end{bmatrix}$. Find a state feedback gain K to place the eigenvalues of $A_{cl}$ at the desired location given by $\lambda^* = -1 \pm j$.

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Temperature (°C) Problem 2 (1.0 pt max). The hafnium-vanadium (Hf-V) phase diagram is shown below (see next page). It has only single-phase regions labeled, for two hafnium-rich solid solutions (marked \alphaHf and \betaHf), an intermetallic compound HfV$_2$-based solid solution (HfV$_2$), and a vanadium-rich solid solution (V). 2200 \betaHf 2000 1800 1600 1400 HfV$_2$ V 1200 \alphaHf 1000 0 20 40 60 80 100 (Hf) Composition (wt% V) (V) The phase transformations that occur in this system are two eutectics, one eutectoid, three congruent meltings, and one allotropic transformation for pure hafnium. Complet parts (a)-(b) below. (a) Label all phase fields on the phase diagram. (b) For each phase transformation, estimate the temperature and write the reaction that occurs upon cooling, including approximate compositions of all phases. Example for part (b): Allotropic transformation for pure hafnium occurs at $T \approx$ 1670°C according to the reaction \betaHf (0 wt% V) \alphaHf (0 wt% V) cooling heating 1

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6. (12 points) 90% of the students own lap top computers at a certain large university. Suppose 9 students are chosen at random. (a) What is the probability that exactly 7 of them own a lap top computer? (b) What is the probability that at least 8 of them own a lap top computer?

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Example 2.3 Let the following image be given. egin{array}{|c|c|c|c|} hline 3 & 2 & 8 & 2 \ hline 5 & 1 & 7 & 1 \ hline 9 & 1 & 6 & 1 \ hline 8 & 0 & 5 & 2 \ hline end{array} 1. Determine the threshold for image binarization using the Otsu method. Show intermediate results. 2. Perform image thresholding.

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celia o.