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carlos jones

carlos j.

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Let $F(x) = \int_0^x \frac{3-t}{t^2+16} dt$ for $-\infty < x < +\infty$ (a) Find the value of $x$ where $F$ obtains its maximum value. $x = 3$ (b) Find the intervals over which $F$ is only increasing or decreasing. Use interval notation using U for union and enter "none" if no interval. Intervals where $F$ is increasing: Intervals where $F$ is decreasing: (c) Find open intervals over which $F$ is only concave up or concave down. Use interval notation using U for union and enter "none" if no interval. Intervals where $F$ is concave up: none Intervals where $F$ is concave down: $(-\infty, +\infty)$

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Question 5 of 5 [CO3] [20 marks] Find the value of $v_z$ and $v_y$ using superposition theorem.

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the center of the circle is ( 2 , 6 ) (2,6), and the radius r is the square root of 45. Sketch the circle from the previous problem, and label its center and four points on the circle along with their coordinates.

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Steel cylinders 10mm in diameter are annealed by heating to 1000 K and then slowly cooling to 400 K in an air environment for which $T_\infty$ = 325 K and $h$=20 W/m$^2$ K. Assuming the properties of the steel to be $k$= 40 W/m K, $\rho$=7800 kg/m$^3$, and $c$=600 J/kg K, estimate the time required for the cooling process.

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a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. \(f(x) = \frac{6}{4x + 1}\), a = -1 a. f'(x) =

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5. A firm produces widgets with production function: $q = 2\sqrt{KL}$. In the short run, the firm's amount of capital is fixed at $K = 100$. The rental rate is $v = 1$ and the wage for L is $w = 4$. (a) Find the firm's short-run total cost curve (SRTC), short-run average cost curve (SRAC), and the short-run marginal cost (SMC) function. (b) Graph the firm's SAC and SMC using the following levels of production: $q = 25$ and $q = 100$. (c) Find the firm's total cost curve as a function of $q$, $w$, $v$, and $K_1$. (d) What level of K should be chosen to minimize total cost (note: K will be a function of $q$, $w$, $v$)? (e) Use the above results to calculate the long-run total cost of production.

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Evaluate \(\iiint x^3 y z^3 \, dx \, dy \, dz\) taken over the space \(x \ge 0, y \ge 0, z \ge 0\) and \(\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} \le 1\).

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2. a glass of water - always - meals - drink - after - We 3. a bottle of bir pletok - evening - father - My - drinks - every 4. Zaenab - What - to - drink - like - does 5. likes - Mrs. Rohaya - kerak telor - eat - to 6. usually - tea - Mumun - drinks - sugar - without tolong susunin kata kata nya dong

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Question 10 (2 points) Listen Which of the following statements about the visual system are accurate? (Select all that apply) Light striking a retinal molecule eventually leads to the closing of ligand gated $Na^+$ channels Both rods and cones can detect colors Rods are active in low light, and cones are active in bright light Photoreceptors are depolarized in the dark

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