Find a vector equation of a plane having x-intercept 4, y-intercept -1 and a z-intercept of 5. Write in the form: [x,y,z] = [a,b,c] + ....

Q: Let f(x) be a continuous and differentiable function such that f(3)=7 and 2 < f'(x) < 4 for all x.…

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Q: a. AOR: y = 0 b. AOR: x=0 c. AOR : x = 2

A: Since you posted multiple subparts, I need to solve only first three subparts.

Q: Calculate the linear combination. 5(i +2j) - 3(2j+ k) + 7(2k − i) = (x, y, z) (Give your answers as…

A: To calculate the following linear combination. 5i+2j-32j+k+72k-i=x, y, z where,  x=?y=?z=?

Q: Find a polynomial f(x) with leading coefficient 1 such that the equation f(x) = 0 has the given…

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Q: 10. Given = [10,4] and = [12, 13], find the projection of u on v. -

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Q: Verify that the indicated function is an explicit solution of t y" - 4y' + 20y = 0; y = e²x cos 4x…

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Q: consider the region bounded by the parabolas: y=x² + 4x + 3 and Find y = - x² + 2x + 3 the area of…

A: The region bounded by the parabolasy=x2+4x+3 and y=-x2+2x+3

Q: Find the general antiderivative. Use c as the constant of integration. x 9 dx

A: ∫exex+9dx

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)4e¯x dy…

A: ey+12e-y dx + ex+14e-x dy = 0

Q: Find the rate of change of ƒ (x, y, z) = 6xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: 1 The equation of the line that goes through the point (7, 9) and has slope can be written in the…

A: The equation of a straight line passing through the point x1,y1 and having slope m is given by…

Q: Evaluate the line integral JC 2xyz dx + x²z dy + x²y dz where C is an oriented simple curve…

A: We have, integral 2xyz dx + x²z dy + x²y dz where C is an oriented simple curve connecting (1, 2, 4)…

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L-1100 feet apart. As the…

A: The given image of the problem is: L=1100  feetA=50°B=35°

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) =…

A: we have given velocity function v(t)=5t-9

Q: Two cars approach an intersection at right angles, one traveling north at 60 km/h and the other…

A: We have to find the rate at which distance between the cars is changing.

Q: Calculate S3, S4, and S5 and then find the sum for the telescoping series where S is the partial sum…

A: Given: S=∑n=2∞ 1n+1-1n+2 To find the S3,S4,S5,S.

Q: Find the partial derivatives of the function fz(x, y) fy(x, y) f(x, y) 2x +9y 5x – 2y

A: given function is f(x,y)=2x+9y5x-2y

Q: Compare the functions f(x) = x³ and g(x) = ex by graphing both functions in several viewing…

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Q: Find the length of the curve. = (4t, r(t) = 4t, t2, 6 0 ≤t ≤1.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find all values of m so that the function y = emx is a solution of the given differential equation.…

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Q: In Exercises 39-42, find dy/dx. - Sv V2+cos³ t dt 39. y = 40. y = -7x² [T²³v 2 V2+cos³ t dt

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Q: (a) Show that (b) Solve the equation -1 cos(2 tan ¹x): = (d) Find the general solution to cos 7x…

A: Note : As per our Guidelines , we can solve first part as your all parts not too small . Please…

Q: Answer with "true or false". In addition, if the answer is wrong, correct the statement.     If…

A: Given f(x)=xex, then we have to check f'(x)=x2ex that whether this statement is true of false.

Q: Use the equations to find дz дх дz ду || || дz дх дz дх OF дх ƏF дz and and əz ду дz ду x2 - y2 + z²…

A: Given: ∂z∂x=-∂F∂x∂F∂z and ∂z∂y=-∂F∂y∂F∂zx2-y2+z2-8z=9 We are required to find: ∂z∂x and ∂z∂y

Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

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Q: The following graph of the function f satisfies limf(x) = -1. In the following exercises, determine…

A: Given :- The graph of the function f satisfies with limx→3f(x)=-1 To find :- A value of δ&gt;0 That…

Q: Suppose that f(x) is differentiable function Such that f'(2) = 8 f (2) = 4, if then what is the…

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Q: Calculate the linear combination. (Give an exact answer.) X = y = 6(4j+2k) - 4(2i + 7k) = (x, y, z)…

A: The vector is given by 64j+2k-42i+7k = x, y, z To determine: The values of x, y, and z.

Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

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Q: Find a Cartesian equation relating and y corresponding to the parametric equations Write your answer…

A: x=3sin6t ,y=6cos6t

Q: A jumbo jet maintains a constant airspeed of 500 miles per hour (mi/hr) headed due north. The jet…

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Q: ons, use your work (a) to help you the generar (Recall that general antiderivative of a function…

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Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: Determine whether a given series converges or diverges.

A: Given: ∑n=1∞2n3-19n+1 We are required to find: Whether the given series converges or diverges.

Q: Express the limit as a definite integral on the given interval. 2 lim Σ 19(x;*)3 – 5xi]Δx, [2,7] i =…

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Q: The Equilibrium Price is $19 is wrong

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Q: If the slope of the tangent line to the graph of www y=f(x) at x=a is m (a) = 2a-3, and f(1)=5, then…

A: We have,   m(a) = 2a -3     f(1) = 5

Q: Without a calculator work out the value of 5632–1402 1128 – 1 10 4 Please share your mettrod.

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Q: A function fhas a slant asymptote y = mx + b (m‡0) if lim [f(x) - mx + b] = 0 and/or lim [x)-mx + b]…

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Q: ƒ(x) = x + 1 X

A: fx=x+1x

Q: Construct an equation that has an absolute maximum of 5 when graphed. Please show steps.

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Q: Use the Integral Test to determine whether the infinite series is convergent. To perform the…

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Q: 12-0 dt = + C

A: We know that the integral of x^n dx = x^(n+1)/(n+1)

Q: A manufacturer has been selling 1150 television sets a week at $420 each. A market survey indicates…

A: Given :- At $420, A manufacturer sold number of televisions are 1150. And at $21 rebate offered to a…

Q: (c) Given equation r²+(2-1)² = 4 in the cylindrical coordinates. (1) Express the equation in…

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Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

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Q: If an+1 an then the series Σ an n=1 is divergent Select one: True O False 4n+5 4n+7

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Q: Evaluate the definite integral. [° ( Z - ²3/) dx J₁ X

A: ∫16x6-9xdx

Q: f(t) = t sin(at) 14. f(t) nat

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Q: Find the indefinite integral sin(√) da by using the substitution u = √ and then using integration by…

A: Use the u-subsituation method