4. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?

Q: Solve the initial value problem with 1> 0 and y(1) = 0. 17 +2°y = ²

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Q: 3. Find two positive numbers whose product is 100 and whose sum is a minimum.

A: given product of two number is 100. let two numbers are x and y

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A: Let radius of cylindrical tank =r m and height of cylindrical tank =h m

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Q: g(t) = t t - 1 on [3, 5]

A: First find critical points by g'( t ) = 0 Given function g( t ) = tt - 1

Q: 3. Sketch a graph of a continuous function f(x) with the following properties: o f(x) is increasing…

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Q: 3. Water flows onto a flat surface at a rate of 5cm³/s forming a circular puddle 10mm deep. How fast…

A: to determine how fast is the radius growing when the radius is: (A) 1 cm (B) 10 cm (C) 100 cm

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Q: DITIONAL TOPICS IN TRIGONOMETRY Solving a triangle with the law of sines: Problem type 1 Consider a…

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Q: This is similar to Section 6.1 Proble For f(x,y)=-2x8y8: (a) Determine fx(x,y). Answer: (b)…

A: according to bartleby policy we do only first part. please re-post other parts in next question…

Q: Evaluate the iterated integral. y-z Sª √² √²³² √²-² (²2x JO (2x - y) dx dy dz

A: I=∫04∫0z2∫0y-z2x-ydxdydz

Q: 1. Calculate the following limits. If the limit ends up being ± ∞o, I as,'` which it is lim x->0 ( =…

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Q: Suppose that the derivative of a certain polynomial g(x) is g'(x) = 3x² + 12x + 15. On which…

A: The derivative of a certain polynomial gx is g'x=3x2+12x+15

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Q: Consider the function f(x) = 12x5 + 15x4 - 240x³ + 1. f(x) has inflection points at (reading from…

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Q: Use the explicit formula, b Š a 4 S (3x² - 2x+5) dx -2 n Σ f(a+k¹b-a)) (b=a] n f(x) dx = limfa+k-…

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Q: Determine whether the following series converges or diverges. n=1 n 6 + Inn (-1)"-

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Q: Determine the radius of convergence and interval of convergence of each power series. ∞ xn Σ(-1)",…

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Q: 4 a) Three non-zero vectors are coplanar if (a x b) c = 0. Explain how/why this test for coplanar…

A: a→=0,k,4,b→=3,0,2,c→=k,3,6

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A: length of the flagpole=60 ft.

Q: Determine if the following statement is true or false. The points P₁ (3, 0, 1), P₂(3, -6, -3), P3(4,…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 12x - 2 on the interval [1,5], how many va…

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Q: 1. Suppose f is a function satisfying the following conditions: lim f(x)→ ∞, lim f(x)→-∞, lim f(x) =…

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Q: Integral practice Tom's dog Max runs across the yard along the path y = 5. If the temperature of…

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Q: The function w() is graphed below. Find the value of each of the following integrals based on the…

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Q: Find the radian measure of the angle with the given degree measure. 285⁰ 1.58T X rad

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Q: Find the most general antiderivative of the function: f(x)= 5x² - 4x² + 3x x²

A: Given: f(x)=5x3-4x2+3xx2 We are required to find: Most general antiderivative of f(x)

Q: A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t),…

A: As s( t ) = position of the particle a( t ) = acceleration of the particle a( t ) = d2sdt2v( t ) =…

Q: 4. f(x) = x² + 2 5. f(x) = 3x² + 2x - 3 6. f(x) = -4x³ - 2

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Q: (i) the interval(s) on which the function f is strictly increasing or strictly decreasing.

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Q: Consider the following function and closed interval. f(x) = x³ - 3x + 6, [-2, 2] Is f continuous on…

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Q: When estimating distances from a table of velocity data, it is not necessary that the time intervals…

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Q: Use a geometric series to represent each of the following functions as a power series about x = 0.…

A: (a) To find: The power series representation for f(x) and interval of convergence. Given…

Q: Express the lengths a, b, c, and d in the figure only in terms of the trigonometric ratios of 0. The…

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Q: Ray is installing an eavestrough. He needs the eavestrough to drop 1 in. for every 50 in. length so…

A: ray is installing an eavestrough. He needs the eavestrough to drop 1 in for every 50 in length

Q: this is incorrect

A: Given that, the triple integral    ∭Ex+y-5zdV,  where  E = x,y,z | -2≤y≤0, 0≤x≤y, 0≤z≤x+y2

Q: Consider the integral (5y + 5x) dA where R is the parallelogram bounded by the lines 5y + 5x = 0 5y…

A: Given the integral: ∫∫R5y+2xdA where R is the parallelogram boundedby the lines 5y+5x=0, 5y+5x=25,…

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Q: Use the Remainder Theorem and synthetic division to find the value of f(x) where x is 5. f(x) = x³ -…

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Q: Find the interval(s) 2 3x f(x) = is concave up. 4 7 where 3 X² - 2x² − 3x + 2 -

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Q: Consider the following descriptions of the vertical motion of an object subject only to the…

A: it is given that,  the gravity of the earth is g=-9.8 m/s2