Solve the initial value problem for r as a vector function of t. dr Differential equation: Initial condition: r(t) =i+j+k = - 7t i - 3t j - 7t k dt r(0) = 2i + 3j+5k

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Q: Evaluate the indefinite integral: 52+3r2 S de (r³+1³)³ = +C

A: NOTE: Refresh your page if you can't see any equations. . ...................(1) substitute  take…

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Q: For the demand function q = D(p) = 425-p, find the following. a) The elasticity b) The elasticity at…

A: The given demand function is: q=Dp=425-p (a) To find the elasticity.

Q: Consider the function below. (If an answer does not exist, enter DNE.) f(0) = 2 cos(0) + cos²(0),…

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Q: A piece of wire of length L is bent into the shape of a rectangle. Which dimensions produce the…

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

Q: B. x² + 3xy-5y² = 5 at (2, 1) C. xy² + y = 14 at (3,2)

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Q: 5 8 (OT-7) dt ||

A: SOLUTION-

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Q: The half-life of phosphorus-32 is approximately 24.3 days. Step 1 of 3: Determine a so that A(t) =…

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Q: (c) Find a parametrization for the tangent line to c(t) at to = 47. (Enter your answer as a…

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Q: 2. On a certain planet's moon, the acceleration due to gravity is 2.3 m/sec. If a rock is dropped…

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Q: Express the vector - 6i- 2j-9k as a product of its length and direction. - 6i-2j-9k= 11 -[A-0-8] i+…

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Q: Given that 2x - 1 - (x − 2)(x+3) A x - 2 + B x + 3

A: NOTE: Refresh your page if you can't see any equations. . use partial fraction

Q: ӘР Find and дх w = exy. ӘР when x = 0, y = 2 if P = √u² + v2 + w², u = xey, v = yex, and ду

A: Given x=0y=2P=u2+v2+w2u=xeyv=yexw=exy

Q: If f(x) = 4x² + 2, find the following. f(4 + √2) f(4) + f(√2) f(4x) f(3 - x) f(x +h)-f(x)

A: SOLUTION-

Q: Evaluate the integral or show that it is diverg -6 Y

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Q: ind the f(x) = 4x + 4 cot (1) TT 7T 2 over the interval 4 4 The absolute minimum value: The absolute…

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Q: Determine the derivative of f(x) = 2.72²+3 Select the correct answer below: O (8x)72x²+3 O (8x In…

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Q: Use the given graph of f(x) = √√√x to find a number & such that if |x - 4| < 8 then 8= y 2.4 2 1.6 ?…

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Q: y" + 4y = -12 cos 2x - 4 sin 2

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

Q: Question Consider the price-demand equation given by P = Provide your answer below: 8 5 1 2,500 -x.…

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Q: 2. Apply the Integral Test to determine if the series converges or diverges: +00 4 -2 n ln(n)

A: find the  convergence of series  ∑n=2∞ 4nlnn

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A: Distance between two points   ( x1 , y1)  and ( x2 , y2) is given as d=(x2-x1)2+(y2-y1)2

Q: 3 1 (a-2ja dalim dx = (x 2)² s-20 = = || - lim s 2 lim s 2 f 1 (x - 2)² S 1 dx + lim + lim t-20 +…

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Q: D is a region in the 2nd quadrant that is inside a circle with equation x² + y² = 16 and outside the…

A: The given region is bounded by the equations x2+y2=16 and x2+y-22=4 in second quadrant as shown…

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A: The function is given by fx = x2-2x-8 To evaluate: the x-intercepts of the function fx and the value…

Q: 1. A homogeneous function is one such that f(tx, ty) = ta f(x, y) for some a. (a) Show that f(x, y)…

A: We have to find out one part

Q: Find the second derivative. f"(x): 11 f(x) = 7e-x-3e-7x

A: Given query is to find the Indicated derivative.

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A: The tangent line to a curve y=f(x) is horizontal if y'=0.

Q: Given f(2)=3e²-3 df dz Question Help: Message instructor

A: Find the derivative

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Q: The position vector for a particle moving on a helix is c(t) = (4 cos(t), 4 sin(t), t²). (a) Find…

A: NOTE: Refresh your page if you can't see any equations. . the given value of t is

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: let I=    limt→2t2-8t3-3t+72 put  t=2

Q: researcher at a coat manufacturer finds that the marginal cost at a production level of 400 coats is…

A: Given query is to find the correct interpretation of the statment.

Q: Use Newton's method to find an approximate solution of In (x) = 6 -x. Start with x = 8 and find x2.…

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

Q: QUESTION 3 Find the second order partial derivative Y (x,z) XZ of the function Y = Y (x,z)=- XZ Y…

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Q: Determine which, if any, of the following f(x) = 9² +9, 32x+3, g(x) h(x) = = 27 (95),

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Q: -x Write the expression 4 in the form 2 for a suitable constant k. Determine k. Give your answer as…

A: The expression is given by 4-x To determine: The expression in the form 2kx. Formula Used: amn =…

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Q: Question What is the first derivative of s(x) = (6²)5? Select the correct answer below: O s'(x) =…

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Q: Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of…

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Q: The following graph shows a rough approximation of historical and projected median home prices for a…

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Q: A linearised graph of y against x² is given below and the line passes through the origin and (5,6).…

A: Let Equation of linear graph fx=a+bxHere At x we use x2 So fx2=a+bx2

Q: Let f(x) = -4 ln(6x)

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Q: Consider the following function. (If an answer does not exist, enter DNE.) f(x)=√x² + 3-X (a) Find…

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Q: Find the derivative of f(x) = ¹07.5 f'(x) = Question Help: Video Message instructor

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Q: Consider the function f(x) = 2 − 6x², - 4 ≤ x ≤ 1. The absolute maximum value is 2 and this occurs…

A: for critical points    f'(x)=0                   dxndx=nxn-1…

Q: 6. Consider the function (a) (b) y = 1+ log₂ (x - 1). Graph the function Label at least 3 points on…

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