Q: Solve y" - by'tlly - Slt-1), ylo)= 1, y'lo)=0 ylo) = |
A: The given function is y''-6y'+11y=δ(t-1) The initial conditions are, y(0)=1, y'(0)=0 We find the…
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A: The given differential equation is x dy-y dx=xy2 dx Dividing y2 on both sides, we get x dy-y…
Q: 3. Solve, using the method of variation of parameters: y" + 4y' = sec 2x
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Q: 5olve The simultaneaus.equation 22 tiw - 2 2+ (1ti)w =3;
A: Given : 2z + i ω = 2 .................(1)2 + (1+i)ω = 3i ..............(2)then we…
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Q: 3. In trapezoid ABCD, AB || CD, LA 3x+18, ZC 3x+1,2D= 6x . Setup an equation that could be used to…
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A: The given equation is lny-30=5t.
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Q: The position of a particle is given by s(t) 2t3- 12t2 +18t, %3D is in seconds.
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Q: Solve, using the method of variation of parameters: et y" – 2y' + y =: 1+x²
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Q: Find a (real) general solution. y" + 2y' + 2y = 4e¯* sec³x
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Q: Solve: y= 10cos(2pi/3 (17.2-0.3))+50 show your work
A: Solution: The objective is to solve the given equation
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Q: solve given IVP showing details of your work, y^iv +3y'' -4y=0; y(0)=3,…
A: solve given IVP showing details of your work, y^iv +3y'' -4y=0; y(0)=3,…
Q: Jo x² +6x+10 n of the trapezoidal ru idal Lru Owit
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Q: Solve y”+9y = 2cos(3x)+3sin(3x) using the method of undetermined coefficients. Show all support…
A: The given differential equation is…
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A: Given, 4sin2θ-3=0
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A: Given : Let X : Number of people received flu vaccine p = 0.45 (Proportion of people received flu…
Q: Solve using the method of variation of parameters: y" + 9y = 12 sec 3x. %3D
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Q: (a) y' = = ing 3t²y y+1' are probler y(2) = 1 biems
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Q: 3.Find [, L (3x² + y)dydx
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Q: 5.) y = x3 + 1, y = 0, x = 1 around the a axis.
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Q: Determine whether the statement is true or false. True False The equation y' = 4y - 2x + 8xy - 1 is…
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Q: uestion hat is y' (x) when y(x) = (4x³ + 6x)*?
A: * Logarithmic function property : ln ( an ) = n ln ( a ) * Product rule of derivative : ( f • g )…
Q: 5) 6dh = 2y %3D
A: Given , 6dh = 2y. we have to solve for d .
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Q: Define properties of Solutions of y' = y?
A: Solution: Consider the given equation is y' = y First, find the solution to this equation. dydx =…
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A: Given, y3-y=2x
Q: Solve, using the method of variation of parameters: 2?y" – 2xy + 2y = x*e*
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Q: Solve. Vy-15 +y 15 %3D
A: Given that √(y-15) + √y = 15 We have to solve for y.
Q: 3. Solve, showing details: y₁ = 4y2 + 5et y2 -V1-20e-t yı(0) = 1, y2(0) = 0
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Q: lim (2,y)→(1,1) 2a2 – ry – y? 2² – y?
A: Evaluate the limit
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Q: /| +* dA; Ris y² + 2² < 2.
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Q: Q7 Integrate by completing the square: dx 16x2 + 8x + 2 08 Integrate by porto:
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Q: linear congruence has 2 incongruent solutions
A: b is correct. We have to find out the total number of solutions of the given linear congruence.
Q: 2y"+18y=6tan(3t)
A: Given differential equation is 2y"+18y=6tan3t
Q: 3.) y = Vr, y = 3, x = 0 around the x axis.
A: To find: The volume of the solid that is generated by the revolving the given function y=x around…
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- A bird is hunting for fish in a pond. She swoops down from a height and picks up a fish from the water surface and flies back up, all along a path y=4x2−(2k+2)x+1, where k≥0, y is its height from the water surface, and x is the horizontal distance from a fixed origin which is in the plane of the path. Then, the value of k can be:Find a point with z = 2 on the intersection line of the planes x + y + 3z = 6 and x - y + z= 4 . Find the point with z= 0. Find a third point halfway between.R is the region bounded by y= sqrt x , and y= 6-x and the vertical y-axis. Q is the region bounded by y= sqrt x, and y=6-x, and the horizontal x- axis. (They Intersect at (4,2) ) Label both regions on the graph.
- Steepest ascent on a plane Suppose a long sloping hillside is described by the plane z = ax + by + c, where a, b, and c are constants. Find the path in the xy-plane, beginning at (x0, y0), that corresponds to the path of steepest ascent on the hillside.You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle x^2 + y^2 ≤ 900 on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.Parabolic dome H(x, y, z) = x2√5- 4z, over the parabolicdome z = 1 - x2 - y2, z ≥ 0
- Using Lagrange Multipliers, find the highest/lowest points on the surface: x^2+y^2+z^2-xz-yz=5, given that f(x,y,z)=z and g(x,y,z)=x^2+y^2+z^2-xz-yz.Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces. Cone: x2 + y2 − z2 = 0 Plane : x + 2z = 4The plane x=3 cuts the sphere x2 + y2 + z2 =25 What shape does their intersection make? Find a formula for the intersection curve, and the area enclosed by the intersection curve in the plane x=3.
- The long run. A chair manufacturer hires its assembly-line labour for $18 an hour and calculates that the rental cost of its machinery is $6 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. The firm is currently using 1 hour of labour for every 3 hours of machine time. (Assume that labour is on the horizontal axis and capital is on the vertical axis). 3. Graphically illustrate your answer by drawing an isoquant, an isocost line for the current combination of labour and capital and an isocost line for the optimal combination of labour and capital. An isocost corresponding to the optimal combination of labour and capital is [a vertical line, a horizontal line, an upward sloping straight line, an upward sloping curve which is not a straight line, a downward sloping straight line, a downward sloping curve which is not a straight line, L-shaped] has slope [ ] at the optimal combination of inputs An isoquant…Find equations for all the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and are tangent to the sphere (x-2)^2 + y^2 + z^2 = 4. Do not use calculus7 please The final answer is (7A vertical plane that intersects the xy-plane in the line y = 2 - x, z = 0)