Write an equation for the line through the point (1,3) parallel to the line y = x + 10. Oy=z O y = 1/2 Oy = 1/2+1/ 0y=1/2-1 Oy=2x+5

Q: 2) x² + y² - 16x + 18y +96= 0

A: Here we havw to convert standard form,  2) x2+y2-16x+18y+96=0

Q: B-Find the center of mass of the region bounded above by the half circle y = √ Na²-x² and below by…

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: 4x² + 4y² = 4y - 8x + 5?

A: equation can be written as 4x2+4y2-4y+8x-5=0 ⇒x2+y2-y+2x-54=0 Recall: if the general circle equation…

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A: Use the definition of domain of function

Q: 1) x² + y² + 18x - 26y +246 = 0 3) x² + y² + 16x +10y + 80 = 0 5) x² + y² - 22x+26y +254 = 0 7) x² +…

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Q: Evaluate (2a³y +9y³)dA, D is the region bounded by y 33522 a. 5 Ob. 4811 5 C. None of the choices.…

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A: Given problem:- A manufacturer is planning to sell a total of 300 machines to both foreign and…

Q: Determine the value of k for which Assume that k is a positive number. k k 1/² 2/² | = 4 2k = 0

A: Given determinant of the 2 by 2 matrix is 0

Q: y" − 3y' + 2y = 4e²t ; y(0) = −3, y '(0) = 5 —e2t4e2t + et 7 7 (1+t)4e²t - 7et 8e2t - 7et -e²t 4te²t…

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Q: Discuss the relationship between the number of solutions of the following system and the constant k.…

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Q: HA-[-2]. If = O A-¹ O A-¹ = O A-¹ = O A-¹, 24 = find A-¹. 3 = 6 -4] [4-2] 6 -5]

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Q: Determine the absolute extrema of the function ?(?) = sqrt of x - 9 on the interval [9,45]

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Q: Find Vf at the given point. f(x,y,z) = x² + y² -32² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+ (8)j + (-30)k…

A: Topic = Derivative

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given problem:- Find parametric equations for the line tangent to the curve of intersection of the…

Q: f(x) = 5x² - 8x + 15 3x² + 6x 12

A: here first we have  to find domain of function  here domain is which value we can put in function so…

Q: 11. A dangerous toxic pollutant has been accidentally spilled in a lake. t The speed of water…

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Q: where y is considered to be a function of . In this exercise, you will determine whether or not y =…

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Q: 12-f(t)= -31 e-³¹ sin 2t t

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Q: Solve the following deferential equations a) (x² - 4xy - 2y²)dx + (y² - 4xy - 2x²)dy = 0. e-2√x : 1…

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Q: ¹ (²³) 4- If f(r) = cot-1 + tan-¹ prove that f'(r) = r²+4

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Q: Evaluate the limit using L'Hopital's rule. Ansu an INTEGER value, with NO decimals, no spa lim (x-7)…

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Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = − 9x² - 2xy –…

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Q: Select all statements which are TRUE. For statements with cross products, assume the vectors are in…

A: Let's find.

Q: Answer and give a complete solution. A ladder 25 ft long stands against a wall. The lower end is…

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Q: If the function u = 2e^u e^2u 1/2 Other: In (2² +2²¹²) then ro + you is 4

A: First we calculate partial derivative.

Q: 10) x² + y² - 28x - 6y + 189 = 0 12) x² + y² - 32x+22y+376 = 0 2 14) x² + y² - 4x + 24y + 144 = 0…

A: Standard form of a circle is x-h2+y-k2 =r2,    where h, k  is the center of the circle and r is the…

Q: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed…

A: fix cost $200 20 item cost $400 here per item cost = 400/20 = $20 cost function  C(x) = 200 + 20x…

Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

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Q: -3x² 2(T T + 10 25)

A: Follow the procedure given below.

Q: Which of the following statements are FALSE about the method of variation parameters? I. II. If y₁ =…

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

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Q: An aircraft sets a course with a certain bearing and at a speed of 500 mph. A horizontal wind…

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Q: Given f and g are continuous functions and f(x) dx = -3 and g(x) dx = 5. What is [3f(x) + 2g(x)] dx…

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Q: Find the value of k such that the perpendicular distance of the point (2,k) from the line x - 2y =…

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Q: The force on the triangular plate that is submerged in water as shown below waters surface 6m 4m is…

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Q: What is the equation of a circle having (10,2) and (6,-4) as endpoints of its diameter? x² + y² 16x…

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Q: A body cools from 75°C to 70°C in 2 minutes. What will additional time (in minutes) it takes to cool…

A: Topic:  Newton's Law of cooling using application of calculus

Q: Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) 4 with initial vector

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Q: Numerical Integration: 2 1 1. 2. =dx X 5 (2x² – 3x) dx 0 2

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Q: An inner city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

A: here lets assume width of rectangle is b length of rectangle is 2b width change is db/dt = 43 m /…

Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: 7. A rope that weighs 0.5lb/ft is attached to a bucket filled with cement plaster. The cement…

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Q: 15. Iv X V9 – x2 - dx

A: We want to integrate the given function.

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 ex cos (yz),…

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Q: 4 cos z at the point (5,2). The Find the equation of the tangent line to the curve y = 2 sec z…

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Q: the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², ind: dz dz and 2- (by chain rule) ди…

A: differentiation

Q: 12

A: