Numerade

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a rover is circling on icy planet, with mass 899 kg and coefficient of static friction 0.120. The speed is 4.2x10^-2. Will it make the radial turn of 10.0cm?

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Q1 (20 marks): A ball is thrown vertically downward with a speed of $ 5 \mathrm{~m} / \mathrm{s} $ from the roof of a building. It hits the ground after 3 . Calculate: (a) the height of the building; (b) the velocity of the ball when it hits the ground.

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A total charge 3.2 ✕ 10−6 C is distributed uniformly throughout a cubical volume whose edges are 7.0 cm long. Do the same calculation for cubes whose edges are 14.0 cm long and 3.0 cm long.

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Find all values of $\lambda$ (the Greek letter lambda) for which the homogeneous linear system has nontrivial solutions. (Enter your answers as a comma-separated list.) $(\lambda - 6)x + y = 0\ \(x + (\lambda - 6)y = 0$

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If the demand for golf is price-inelastic and your local public golf course increases the greens fees for using the course, you expect:

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Tiny Toads LLC sells birthday cakes for $50 each. Fixed costs of production are $15. The average variable costs are $15 for one birthday cake, $20 for two units, $25 for the three units, $31¼ for four units, and $40 for five units. (a) In the form of a table, calculate total revenue, marginal revenue, total cost, average variable cost, average fixed cost, average total cost, and marginal cost for each output level (one to five units). (b) What is the profit-maximizing quantity of output? (c) On one diagram, sketch the total revenue and total cost curves. (d) On another diagram, sketch the marginal revenue, marginal cost, average variable cost, average total cost, and average fixed cost curves.

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You are a genetic counselor, and your patient has been diagnosed with the autosomal recessive disorder known as "Gaucher's Disease". Individuals with this disease have trouble breaking down certain lipids. Your patient is expecting a child. Her husband has been screened, and it is determined that he is a carrier of Gaucher's disease. Please answer the following question using this information. Group of answer choices: - There is a higher probability that her son inherits the condition than a daughter. - More than one of these answers is correct. - The gene is found on the X chromosome. - The dominant allele is the normal allele.

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The function f(x,y) = xy(1 - 6x - 10y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that we mean that $(x, y)$ comes before $(z, w)$ if $x < z$ or if $x = z$ and $y < w$. First point of type ? Second point of type ? Third point of type ? Fourth point of type ?

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2. Given the following sequence determine the sum of the first 50 terms 1, 3, 5, 7,...

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2. In this problem, you'll look at the differential equation $\frac{dy}{dt} = e^{-t-y}$. (a) Which of the following is the slope field of the differential equation? Explain how you eliminated the other choices. (i) (iii) (ii) (iv) (b) On the slope field you picked in (a), sketch the solution curve satisfying y(0) = 1. (c) Use separation of variables to find the general solution of the differential equation. (d) Find the solution of the differential equation which satisfies the initial condition y(0) = 1. You may want to use a graphing calculator or computer to check that your solution matches your sketch from (b). (e) Check that your answer to (d) is correct by plugging it in to the original differential equation.

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michael h.