Use a scalar projection (NOT A FORMULA- unless you derive that formula as part of your solution) to find the shortest distance from the point (1,−2,5) to the plane given by −2x+6y−z=18  . Please give a detailed solution

Q: 6x Find the derivative of h(x) = 2 h'(x) = 36log, (x) 6

A: Topic:- application of derivatives

Q: For the given cost function C(x) = 12100 + 300x + x² find: = a) The cost at the production level…

A: We are allowed to solve the first three subparts of the question. If you need the rest of the…

Q: Given the function below 3 25 g(x) = X x+1 Which of the following leads to the solution of the…

A: Topic = Function

Q: Find the general solution to 3y''+xy'+y=0 in the form of a power series around the ordinary point…

A: Note: this x0=0 is an ordinary solution. Let us assume that:y=∑n=0∞Cn(x-0)n…

Q: Find the transform of the given function by use of a table. f(t)=e-4 4 A F(s) = 5(₁-4) 1 s+4 B F(s)…

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Q: Given the table of values for f(t), is f(t) increasing or decreasing? It f(t) 1 10 O increasing O…

A: To determine whether the given function is increasing or decreasing.

Q: Given the function (fog)(x) == and g(x)=3+√√x, which of the following is the expression for /(x+2) ?…

A: Topic = Function

Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, 1, -3) and the direction in…

A: Please see the below picture for detailed solution.

Q: S Using the integration by parts method, 10x ex dx =

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Q: Show that (csc(x)) = -csc(x) cot(x). d dx d dx -(csc(x)) H = = d dx sin²(x) 1 sin(x) 1 = -csc(x)…

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Q: Here is a bivariate data set. Find the regression equation for the response variable y. X y 35.8…

A: Given that a bivariate data set. Here we have to find the regression equation for the response…

Q: The following table shows retail sales in drug stores in billions of dollars in the U.S. for years…

A: NOTE: Refresh your page if you can't see any equations. . from the graph, we can see that the given…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. IRL -144 yz dx dz dy =

A: I am attaching image so that you understand each and every step.

Q: Find the derivative of: 7 sin² (8x³). Hint: sin²(x) = [sin(x)]²...so use the chain rule (twice!).…

A: Given: fx=7sin28x8   As we know that; The Power law: ddxxn=nxn-1 Apply the Chain rule: fgx'=f'gx·g'x…

Q: Find the absolute maximum and absolute minimum of the function f(x) Provide your answer below: •…

A: Let's find absolute maximum and minimum value.

Q: Evaluate the following integral

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Q: Find the points on the curve y = x³ + 3x² - 9x + 9 where the tangent is horizontal. (x, y) = smaller…

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Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (-3, -4) and the direction in…

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Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The objective of the question is determine the gradient at  a point and directional derivative at a…

Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 12 s² + 16 Your answer should be…

A: To find the inverse Laplace transform L-1Fs of the given function.Fs=12s2+16

Q: Determine the area of the region bounded by two the curves f(x)=x²-18x + 28 and g(x) = 9x + 14.

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Q: sec²0-tan²0+ tan0 sec = sine + cos 0

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Q: Q1 Consider the plane curve defined by the parametric equations x = 2 + 2 cos² (t), y = 3+ sin(2t)…

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Q: Using the integration by parts method, / -13x e ¹+13e ¹+C 13e ¹ + C O 13x e¹ O-13c e 13e+C O 13r e 2…

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Q: Find the critical numbers of the function f(x) graph. x = X = X = is ✔ Select an answer Local Max…

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Q: The area under the curve y= 7x bounded by the lines x = 8 and x = 17 above the x-axis is = Square…

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Q: 100 Determine, with full justification, if $19 da converges.

A: We have to find the following conditions according to the given information

Q: (x - 1) If 1 / ² ) = = √ Ada² + √ dx [ B (x − 3)(x + 7) - 3 - then A+B = Bdx x +7'

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Q: Q3 Calculate the area of the shaded region in the given figure y Focus point Parabola curve P- 2p 8p…

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Q: Let f(x) = 4 sec (3x) f'(x) =

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Q: Find the derivative y'(x) implicitly for the equation y' (x)= 4-2y 4x +3 y 2x + 1³.

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Q: Find the derivative of the function. 14 logg(t) t g' (t) = g(t) =

A: Topic = Derivative

Q: Determine the set of x-values where f(x) 2 + 4x is continuous, using interval notation. 1 X-

A: Topic- Function and continuity of it We are given, f(x)=2x-1+4xA rational function is continuous on…

Q: Find the critical numbers of the function. h(t) = 3/4 - 2¹/4

A: Topic = Derivative

Q: 1.y = 3x cos=-9sin 2y=2csc(1-3x) tan 2x 3.y=1-cot 2x

A: According to our guidelines we can solve first 3 questions please upload remaining…

Q: Find the derivative of the function below. h(x) = x tan (8/x) + 1 dh

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 25 m/s, its height…

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Q: Find the linearization L(x,y,z) of the function f(x,y,z) at the given points. f(x,y,z)= ex+cos (y+z)…

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Q: Evaluate the limit: lim 02 does not exist lim √(0+1)²-1. Q→-2 0 1 0

A: Put Q= -2

Q: Use the power series method to solve the given initial-value problem. (Format your final answer as…

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Q: on given by P(q) = -0.02q² +5q-31, where and produced, and P(q) is the total profit, in of…

A: Here profit function is given to us.

Q: If two integers have opposite parity, then their product is even. Direct proof.

A: Topic = Algebra

Q: Consider the function f(x) 72x² + 10, The absolute maximum of f(x) (on the given interval) is at X =…

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Q: Suppose that the length 7, width w, and perimeter P of a rectangle are differentiable functions of…

A: Topic = Derivative

Q: Find all of the following for the function y = x¹ ex a. x-intercept(s) b. y-intercept(s) C.…

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Q: A particle moves along the x-axis so that its velocity at time 0 7 or (₂) Submit Answer U ∞ > [₂]…

A: slope of velocity vs time graph represent acceleration  and where  slope is positive indicate that…

Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: Find the derivative y'(x) implicitly for the equation y' (x)= 9x+8 V = 2x + 1³.

A: The given equation 9x+8y=2x+y3 We have to find the derivative using implicit derivative.

Q: The area under the curve y Square Units 5x bounded by the lines x = 9 and x = 26 above the x axis is

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