Numerade

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Problem 3. The formal derivative $D: P^n(\mathbb{R}) \rightarrow P^{n-1}(\mathbb{R})$ given by $D\left(\sum_{i=0}^{n-1} \alpha_{i} x^{i}\right)=\sum_{i=0}^{n-2}(i+1) \alpha_{i+1} x^{i}$ is a linear map. Find a basis of $P_4(\mathbb{R})$ and a basis of $P_3(\mathbb{R})$ such that the matrix of D with respect to these bases is $\left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$.

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IN tax year 2023 if my agi is 42918, filing status is HOH, having 2 dependents who lived with me all year and are under the age of 17. what would my earned income tax credit be?

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QUESTION 4 (20 Marks) Figure Q4 shows the Turning Moment Diagram of a wind turbine torque generator operating at a constant speed of 1800 rpm. A flywheel with a mass inertia 80 $kgm^2$ is installed on the system to limit the energy fluctuation. Determine i. The power generated by the wind turbine ii. Energy fluctuation in one cycle iii. Maximum and minimum speed of the flywheel and when it occurs. T (kNm) 3.0 2.0 1.0 0 10 20 30 40 50 60 →t(s) Figure Q4 / Rajah S4

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Which of the following file organizations uses a key field to arrange records in a sorted order? a. Sorted files b. Indexed files c. Heap files d. Hashed files

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The energy required to increase the speed of a certain car from 19 m/sm/s to 26 m/sm/s is 200 kJkJ.

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light enters a liquid of refractive index 2.0. in this liquid its speed will be

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Compared with European Americans, Asian Americans have a. longer life expectancy. b. lower infant mortality. c. lower cardiovascular mortality. d. All of the above

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t^2 + 10t + 100\nLet f(t) = \frac{t^2 + 10t + 100}{t^2 + 20t + 100} give the amount of oxygen in a lake t days after organic waste has been poured into it. At what time t is the amount of oxygen at its lowest?

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A dark ink is continuously injected into a flow field by means of a needle probe extending into the middle of a field. A photograph, taken at any instant in time shows a line starting at the needle tip and extending downstream in the flow field. This line is called a _____. ? a. streakline ? b. pathline ? c. streamline ? d. timeline As a very light feather is carried about by air, time-lapse video captures the changing location of the feather. An imaginary line connecting each subsequent location of the feather is called a _____. ? a. streamline ? b. pathline ? c. timeline ? d. streakline The term "curl" and "angular velocity" have the same meaning. Select one: ? True ? False

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Question 8 2 p Write a C++ assignment statement that sets the integer variable myScore equal to zero. (*Note: Type your answer in the text box below.) < Previous No new data to save. Last checked at 1:21am

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sarah l.