Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7 - 2t y=t z = 9+t

Q: Find the general solution of the given higher-order differential equation. y"" - 7y" + 8y' + 16y = 0…

A: Given the following differential equation:

Q: Calculate the indicated Riemann sum S3 for the function f(x)=x²-9x-52. Partition [0,6] into three…

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Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

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Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: Find curl (62 i + 7x j + 2y k). curl (62 i + 7x j + 2y k) = (i )k )i + (i )j + ( i

A: Here we have to find the curl.

Q: Express the following function in terms of unit step function and hence find their Laplace…

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Q: Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse…

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 e-{2}- L²s² + n²π² 2_2

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Q: Find the curvature and the radius of curvature at the stated point. ㅠ r(t) = 11 cos(t)i + 10 sin(t)j…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

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Q: 768 on the interval [-20, -10]. Find the H plute extrema for the function on the given interval.…

A: * As per policy only first question is answered. Please refer to the image below

Q: Find the curvature and the radius of curvature at the point t = 0. et cos(t), y et sin(t), z = 9et K…

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Q: The volume of a right circular cone of radius x and height y is given by V volume of the cone is 247…

A: To find dydx

Q: Evaluate the integral [(4x + 15y)da + (6x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

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Q: Find the solution of the given initial value problem. ty' + 2y = sint, y(7) = 5, t > 0 y = cos(t)…

A: As we know that; The standard of the First order linear differential equation is: dydt+Py=Q Where, P…

Q: Which among the following vectors is parallel to V = ? i.) A = ii.) B = iii.)

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = e sin(t), z =…

A: Basic calculation of vector is required

Q: Question Find the linear approximation L(x) of the function f(x) (Enter an exact answer.) Provide…

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Q: Find the value of b for which the differential equation (ye5ay + x) dx + (bxe5y) dy = 0 is exact,…

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Q: Determine the vector field of F. F(x, y) = yi-xj X X

A: Solution: F(x,y) = yi - xj We can sketch it by looking at a small number of vectors to get a general…

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: 2.) √ √9-4x² dx x² Solution: Case I let u = asino 2x = 3 sine x = 3 sino 2 dx = ² coso do 2 so, by…

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Given function is x9 - 9x

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: The given function is: fx=x9-9x  Analyze and sketch a graph of the function. Find any intercept,…

Q: For an arithmetic sequence, a17 a1 = the sum of the first 65 terms= > Next Question - 47. If the…

A: It is given that, a17=47 and common difference(d)=5 a1=? Sum of the first 65 terms=?

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

A: here the given differential equation  (6 -20y +e-5x)dx -4dy = 0 this can be written as  dy/dx +(5)y…

Q: If a rock is dropped from a height of 237 ft, its poistion t seconds after it is dropped until it…

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Q: Evaluate the following integral. Sx² e 19x dx --- 2 Let u=x. Use the integration by parts formula to…

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Q: Screenshot (1603) p Find the solution of the given initial value problem in explicit form. ³(²-) =…

A: Let's find general solution of diffrential equation.

Q: Which are the foci of the ellipse represented by 25x² + 16y² = 400?

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Q: f(t) = (t + 1)³

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Q: Find the domain of the vector-valued function. r(t) = n(t) 0 (-∞, +∞0) O (1, + ∞ ) O (0, +∞ ) O [1,…

A: Find the domain for all three components and then take intersection of those.

Q: Solve the system using Cramer's Rule. 2x + 5y = -25 -x+3y=-4 Find the determinant D (denominator).…

A: Please refer to the image below

Q: An automobile company is ready to introduce a new line of cars through a national sales campaign.…

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Q: sider the following function. y = 6x In(x) y'(x). () = dy"(x). x) =

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Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). O True…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-tj² L{f(t)}…

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Q: What is the symmetric equation of the line that is normal to the plane x + y + z = 9 at the point…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Evaluate the limit ALGEBRAICALLY (by simplifying), NOT just by graphing: lim h→0 (6 + h)² - 36 h

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Q: Applying Lagrange Multiplier, what is the minimum value of f(x, y) = x² + y2 where x > 0 and y> 0…

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Q: Find the area of the region bounded by the following curve. The limiçon r= 6-4 cos 0

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Q: given 8x+5w+xw+2x2+0.3w2, find the optimum point

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Q: Screenshot (16 Find the solution of the given initial value problem in explicit form. 1 y' = (1 -…

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: Sketch a graph of the polar equation. 3 2+3 cos 0

A: The given polar curve r=32cosθ

Q: Liv F and curl F if F(x, y, z) = xºi - 2j+yzk. F= F=

A: Topic:- application of derivatives

Q: r = graph (8-2) i+ 10tj O It is a line in 2-space through the point (-2, 10) and parallel to the…

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Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s))} = f(t)g(t). True False

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Q: 1 *{{37² +3=6} S

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