Find the area of the triangle having vertices at (−2,3,1),(1,2,3) and (3,−1,2)

Q: x° 16x6 -24x3 +9 dx

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Q: Enclosing an Area Patricia wishes to have a rectangular garden in her backyard. She has 64 ft of…

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Q: Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder.…

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Q: 1. Find the absolute extrema, if any, of the following functions on the given interval. (a) f(x) = 4…

A: Given:     a) fx=4-3x ; (-1,2]           dydx=ddx4-3x                   f'x=-3   There in no…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. -…

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Q: dt 4. Solve the initial-value problem dx = -2x – 2y dt dy = -2x + y, dt where the initial condition…

A: To find the solution of the given system of differential equations.

Q: The area of the finite region enclosed by the curves y = 3x and y 27 - a is given by the definite…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, Po(3, - 3,…

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Q: I. Evaluate each of the following iterated integrals. clnx Si S, So yezdzdxdy

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Q: 3x + 5 dx, ] (x + 1)(x – 3)²

A: ∫3x+5x+1x-32dx

Q: 2. of the image graph in terms of x? y 2-3 C. y= 2(1-x+2|- 3) D. y= (1-2x+ 2|-3) A. y= -|2x +2|- 3…

A: Consider the graph

Q: sin 3x cos“ 3xdx

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Q: y – 2. Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and a = -1, 2…

A: x-12=2-y=z implies L1 : x-12=y-2-1=z-01x=-1, y-23=z-12 implies  L2 : x+10=y-23=z-12If lines L1 and…

Q: Given the function f (x) = %3D x - 4 Find the interval where f (x) is increasing or decreasi

A: Given: f(x)=xx-4

Q: Water flows into a conical container at a rate of 7 cm's The radius of the container is 5 cm and the…

A: We have to find rate of change of Radius.

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: Determine any critical point(s) for the function f(x)=  -3 / x2 - 9

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Q: sin x ferentiate y = (x² + 1)°

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Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

A: The given equation is: y2-12y-16x-28=0⇒y2-12y+36=16x+28+36⇒(y-6)2=16x+64⇒4(4)(x+4)=(y-6)2 which is…

Q: (vi) S 16-x 2+15 dx. u=

A: The objective of the question is evaluate the indefinite integral.

Q: 27T 3. x y2 and x + y = 2 is revolved about y = 1. (Answer: C. u.) 2

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Q: ppose a compa headsets, the cost and revenue functions (both in dollars) are given by C(x) = 32,000…

A: Profit = revenue - cost Px=130x-0.001x2-32000+60x=-0.001x2+70x-32000

Q: Basic Catalus 1. f(x)- f(xth) = 5 (x +h) - Sx - 3 lim 5(x+h)-3- [5x-3] = lim 56 +5h -3 - 5% +½ h-70…

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Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

A: As asked we can answer the question with out all explanation in the following steps

Q: 6y dx dy

A: x limit  x=y2and y is from 0 to 1 Option B

Q: following integration can be solved by using the     technique, where in the first application of…

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Q: 15. Determine the coordinate of point C, which lies on the y-axis, if it is equidistant from point A…

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Q: 1. Find the area bounded by the parabolas y= 4x and y'+12x = 36

A: Topic:- application of integration

Q: Q5: S x dx ajconverges to 1 bjconverges to cconverges to- 4. d)diverges 25-2

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Q: Given the demand function D(p)=150/p Find the Elasticity of Demand at a price of $38

A: Given, Given the demand function Q=150/p At p=38 Q=150/38 Q=75/19 We know that price Elasticity of…

Q: dx - メ+イ

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Q: V9 – x² x2

A: Given: I=∫9-x2x2dx   ...1   As we know that; The trigonometric identities; 1). sin2x+cos2x=1 2).…

Q: 1. Evaluate the following integrals. | (csc 0)(1 + sin² 0 + sin 0 cot? 0) de а.

A: Given ∫(cscθ)(1+sin2θ+sinθcot2θ) dθTo evaluate the integral:

Q: Let R be the finite region enclosed by the curve y = 6x(3 – 2x) and the x-axis. Let V be the volume…

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Q: Evaluate the improper (i) (2 – 2)-i dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A particle started to move from the origin along a curve with velocity given by the function Cos T…

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Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms of r.

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Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms ofr.

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Q: In Exercises, the given vectors form a basis for a subspace W of R' or R'. Apply the Gram-Schmidt…

A: The given vectors of ℝ3 are: x1=110, x2=342

Q: dx 2+

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Q: 24 – 49 dy 2+ 49 с.

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Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

A: use the equation given and find the region to be integral

Q: Use the substitution u = 6x? + 1 to convert the integral fo xeoz+1 dx to an integral of the form L…

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Q: Assuming that out of 200 documents, 40 documents are relevant. A search engine returns 30 documents,…

A: We have to calculate the recall percentage.

Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: 6. (D2 – 6D + 8)y = e2x + sinx %3D

A: The given differential equation is: D2-6D+8y=e2x+sinx   So, the auxiliary equation is: m2-6m+8=0

Q: 1. Find the inverse of the matrix 6 12 3 3 A. 10 10 C. 30 30 3. 10 7. 3. 30 10 30 152/5 D.…

A: Solution is done in step 2

Q: Write true if the statement is correct and false if the statement is incorrect. = V3x + 2 Given the…

A: As asked we can answer the question true or false with out explanation as below.

Q: Solve fæ² In(æ) dæ using Integration by Parts. Use u In(x) and v = x². Ansuw or:

A: The detailed solution is given below thank you

Q: In what instance does the Chain Rule of differentiation applicable? Explain briefly.

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