Find the slope of the tangent line to the polar curve r = cos(30) at 0 = 7. Enter as an integer or fraction in lowest terms. Slope =

Q: Evaluate (2x – y) dx + (x + 9y) dy. C: x-axis from (o, 0) to (0, -9) and (0, -9) to (9, -9)

A: We will evaluate the given integral as shown below

Q: Find a particular solution to the DE: y"+ 3y' – 4y = e* xe B. Yp = C. Yp = x²e* D. y, = xe-x E. None…

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Q: The exact area of the region enclosed by f(x) = -(x+ 2)(x-2) and g(x) = (r+ 2)(x- 2) is given by…

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Q: Let C be the curve represented by the equations x = 5t, y = t", (0 < t < 1). In each part, evaluate…

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Q: Determine the following Laplace transforms: (i) mathcal L \ cos^ 2 3t\ .

A: Given

Q: If f(x) is continuous on the interval [a, b] and a <c < b, | f(x) dæ is equal to then

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Q: 00 1 dx x(Inx)2

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Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) logg (x) lim In(x) X00

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Q: The Trapezoidal Rule ou e id b oblw Jeot en f (x) dx = h +f(x1) + f(x2) + ..+ f(xn-1) +f(xn)) b-a…

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Q: dy Then find the slope of the curve at the given point dx Differentiate implicitly to find…

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Q: Suppose that Po is invested in a savings account in which interest is compounded continuously at 6…

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. = x²…

A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…

Q: A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10…

A: In the given question first, we will form a figure using the given information   And we will use the…

Q: The function f(x) = 2x – 27x2 + 48x +1 has one local minimum and one local maximum. Use a graph of…

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Q: A company that produces cell phones has a cost function of C = 17x² – 444x + 18816, where C is the…

A: Given query is to find the number of units to minimize the cost.

Q: Determine the range of f(x,y)=tan 2+x +y

A: Here the value of x2+x2+y3 can vary from -∞ to ∞. The possible values of tan-1x2+x2+y3 is…

Q: 3 Dax has a banner that is 7 feet long and 5 feet wide. He wants to make a new banner that has the…

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Determine an equation of the line tangent to the curve Y = 5x-4 at the point with x- coordinate 4.

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Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = e"i+etj K(t)

A: We have to find k(t)=?

Q: Assume the annual rate of change in the national debt of a country (in billions of dollars per year)…

A: Solve for debt equation by integrating the given equation.

Q: Solve the following differential equation (6х' — у +3)dx + (Зу* — х- 2)dy

A: Here, i am providing the handwritten solution

Q: Find the area of the region bounded by the curves x=y3 and y=x2.

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Q: 4), (-5, -7/4) 1) Yes 2) No

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Q: Given the Total Cost function, TC = 10 + 5Q?, find the marginal cost function, MC when Q = 10. [2]

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Q: Find the area of the specified region. sec e Inside the dircle r 3 and to the right of the line r =…

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Q: Confirm that the force field F(, y) = 2xy°i + 3x²y°j is conservative in some open connected region…

A: If force field is conservative then it is independent of path.

Q: uppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. "rove that dy…

A: Given F(x,y,z)=0

Q: Ben is a fisherman with a boat in Rhyl harbour. This is part of a graph of the depth of water at the…

A: According to guidelines,  we must answer only three of the multipart questions given. Please…

Q: | (1– 2r)dr

A: Given:∫01(1-2x)dx = ∫011dx- ∫012xdx                     ∫fx±gxdx=∫fxdx±∫gxdx…

Q: Confirm that the force field F = xy'i+ x²yj is conservative in some open connected region containing…

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Q: General Directions: Follow the directions given for each section. Write your solutions and final…

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Q: Find the surface area of the portion of the cone z=ax +y within the cylinder x+y =1.

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Q: 7. When a vehicle is said to be travelling at -35 km/h, what does this infer?

A: We can explain the answer in the following steps.

Q: Evaluate the definite integral. sin(3t)dt

A: I=∫0π3 sin(3t) dt  =-cos(3t)30π3  =-13 cos3π3-cos0

Q: A street light is mounted at the top of a 15 ft tall pole. A man 6 ft tall walks away from the pole…

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Q: Chain rule and impicity differentiotion Sappose that Forsy,z) =0 defines z ds d Funetion OF x and…

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Q: To rationalize the denominator of 45 what value should the numerator and denominator be multiplied…

A: We can answer the question as below.

Q: Use the Divergence Theorem to calculate the surface integral F• ds; that is, calculate the flux of F…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: First we will draw graph for function.

Q: 2. Find the absolute minimum and the absolute maximum of the function f(x) = x - 4r +5 on the…

A: Steps to find the absolute maximum and minimum of a function f(x) on [a,b].  : Find the critical…

Q: Find the Cartesian coordinates of the given point. (8, 0) 1) (0, 8) 2) (-8, 0) 3) (8, 0) 4) (0, -8)

A: Given problem:- Find the Cartesian coordinates of the given point.   (8,0)

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: a) Graph the function f(x) = 2x -5x+3 b) Draw a tangent line to the graph at the point whose…

A: Given the function is  f(x) = 2x2-5x+3

Q: The following figure provides the plot of f(1). -4- 3. 2- 3. -2 -1 2-

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: /1 5/2 Find the length of the curve r (t) = ( t,4t,25t ) for 0<t <1.

A: Use the parameterization of curve for finding the length of curve .

Q: undamental set of solutions of a homogeneous linear nth-order differential equati mprises(Choose…

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Q: Use a finite approximation to estimate the area under the graph of the given function on the stated…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: We use the concept of derivatives to find the absolute minimum and absolute Maxima

Q: Find the antiderivative of f(x) = 2 csc2 a given that f () = 1. 4.

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