At time t=0, a particle is located at the point (2.9.2). It travels in a straight line to the point (9,8,4), has speed 6 at (2.9.2) and constant acceleration 7i-j+2k.

Q: Find the directional derivative of f at the point P in the direction of a. a=i-j f(x, y) = 7x³ —…

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Q: Find the area of the following triangle T. The vertices of T are A(6,7,3), B(8,17,4), and C(6,8,3).

A: Here we have to find the area of triangle.

Q: . To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared)…

A: We have to determine drug dosages, doctors estimate a person's body surface area  We have to…

Q: Find the general solution of the given differential equation. x²y + x(x + 2)y = ex y(x) = Give the…

A: Solution: The given differential equation x2y'+x(x+2)y=ex

Q: 7(4) = X

A: given parametrized curve is r(t)→ = t , arc tant , -t then we have to find the unit tangent vector…

Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

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Q: For what function f and number a is the limit lim the value of f'(a)? 5t² - 8t+3 t-1 1. f(t) = 5t² -…

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Q: Find parametric equations for the line through the point Po(5,4,-7) that is parallel to the line…

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Q: Use a finite sum to estimate the average value off on the given interval by partitioning the…

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Q: xp zp ^p rəх JJJ, 6. . In z

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: lim h - 0 /49+h-7/h

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Q: It is known that g(x) dx = e5, f² g (x) dx = 4, and f g (x) dx = 12. Find S2 9 (x) dx. O e5 16

A: Given ∫17g( x )dx = e5∫12g( x )dx = 4 ∫79g( x )dx = 12∫29g( x )dx = ?

Q: Find the limit or indicate that it does not exist. + [ (251) 10 (20₁1)₁ + ( a ) ] lim sin COS tan…

A: Topic = Limits

Q: Evaluate the integral [(2to7¹²) i + (20−ºt) j+ (5) k]dt

A: We have to evaluate the given integral.

Q: Find an equation for the line that is tangent to the curve y = 2x³ - 2x at the point (1,0). The…

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Q: Find an equation of the plane. The plane that passes through the point (-2, 3, 3) and contains the…

A: Given: Plane passes through point (-2, 3, 3) and it contains two lines x+y-z = 3 and 4x-y+5z = 2  To…

Q: z = -2x³ - 3y4 + 6xy² + 1166

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Q: (t − 1)y'+ln(t – 6)y = 4t, y(10) = 3 Find the interval in which the solution of the initial value…

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Q: 9. A marble moves along a straight path and its position at time t, in seconds, is given by s(t) =…

A: given  s(t)=5t-2t2we know v(t)=d dt(s(t))dtndt=ntn-1

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: A continuous annuity with withdrawal rate N = $2,000/year and interest rate r = 2% is funded by an…

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Q: dx ly dt dy 11 -e²x+3y Y sin² (t)y² = e-9 sin² (3t) cos² (3t)

A: (a) given D.E is dydx=x2ye2x+3y⇒dydx=x2ye2xe3y⇒(y e-3y) dy = (x2e2x)dxon integration both side…

Q: The equation r(t) = cos(2t) i+sin(2t) j, t20 describes the motion of a particle moving along the…

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Q: Suppose that a teacher agrees to pay a student 10¢ for every problem in this chapter that the…

A: solution of this problem is given below

Q: For the vectors u = (-9,0,5) and v= (1,4,-4), calculate proj,u and scalvu.

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Q: 7. A pond initially contains 1,000,000 gal of water and an unknown mount of an undesirable chemical.…

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Q: Find the area of the surface generated when the given curve is rotated about the x-axis. y = 2√x on…

A: given  y=2x  on 48,99formula for surface area is  S=∫ab2πy1+(y')2dxdxndx=nxn-1∫xndx=xn+1n+1+c

Q: 1. ƒ (x) = 10x² + 6x f 7

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Q: The buyer for a retail store located in a shopping mall has convinced himself that if he prices…

A: The Profit function is given as , Px=-x2+39x-210 where the price of a personal fan is $x.

Q: Differentiate the function L(x) = -3e¹(cscx + 5cotx). Answer

A: Topic = Derivative

Q: Solve the IVP for y(x): 5 dy dx +=y=7y³, y(1) = 1 X y(x) = =

A: dydx+5xy=7y3given  y(1)=11y3dydx+5x×1y2=7

Q: cot x cosa simplifies to f(x) - sinx where f(x) I

A: Given;  1) cotx cosx 2) cosx cot2x +cosx.

Q: Can we make the matrix F = J₁ J₂ = J3 -1 = [3] 7 5 = J4= F [44] -1 2 -2 1 [24] -2 49 Answer: Yes,…

A: Here we have to choose the correct option.

Q: Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some…

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Q: Ive the initial value problem for r as a vector function of t dr ferential equation: dt 3t i-5t j-…

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Q: Evaluate the integral C arc y= = x² from (0, 0) to (1,1). NOTE: Enter the exact answer. (6.x+6y)dx +…

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Q: Determine the right end behavior of y = - 13x + +3x². + 1x4 As x → ∞0, Oy → +∞ y → -∞ Oy → -13 Oy -…

A: y=-13x+13x2+14x4if degree is even and leading coefficient is positive than as x→-∞, f(x)→∞ as x→∞,…

Q: 1 Find the slope of the tangent to the curve f(x): at the point where x = 9 4 √x The slope of the…

A: The slope of the tangent to the curve y= f(x) at x = k  is  f '(k).

Q: Find the first and second derivatives. 6 dr ds 1 3 4s 4 5s

A: Given  r = 1/(4s3) - 6/(5s4)

Q: Problem 1 x JI√ ار कर X dydx

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Q: Let ƒ : R² →→→ R be defined by f(x, y) = (x² + y²) ³. Find f(x, y). Note: the partial derivative at…

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Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y=x² and…

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Q: Reputable scientists know that the average surface temperature of the world has been rising…

A: Given :T=0.02t+15.0

Q: It takes 1600 J of work to stretch a spring from its natural length of 1 m to a length of 3 m. Find…

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Q: Describe the steps you would follow to find the limits of integration that express a double integral…

A: The steps to find the limits of integration that express a double integral over a nonrectangular…

Q: QUESTION 10 Given a system model what is/are the dominant system characteristic root(s)? d³x d²x dt…

A: Please see the below picture for detailed solution.

Q: Let f(x) = -5 sin(x) cos(x). df dx d² f dx²

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Q: 3 State the intervals on which the given function is increasing, decreasing, or constant. 25 20 15-…

A: Given query is to find the interval where function increasing and decreasing.

Q: Suppose that the sales at Borders bookstores went from 6868 million dollars in 1992 to 402 million…

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