PART 1: State the characteristics (order, degree, type) of the given DE. 1. (1-x)y" - 4xy' + 5y = cos x 2. 3. 4. 5. 6. 7. 8. a²w dt² (x² + y²) dx + 2xydy = 0 y - 3y + 2y = 0 J²u a²ua²u + əx² Əy² əz² ₂0²w ?х2 + d'y dx² X d³ y dx³ w(x) (dy (14)*=0 dx. d²u du +- dr² dr +U= cos(r + u) 9. y sino-y'cos0 = 2 10. (x+y)dx + (3x²-1)dy=0

Q: Determine if 4x² + y = -5 is an ellipse. O Not an Ellipse O Ellipse, we can write the equation of…

A: Here given that 4x2 +y =-5  now  4x2 = -(y+5) x2 = -(y+5)/4

Q: Evaluate the line integral curve C′ : x = 4 cost, y = 8 sint (0 ≤t≤7) NOTE: Enter the exact answer.…

A:

Q: Which of the following represents the graph of (x + 2)² = 4y - 6)? O -83 4 ry 14 11 10 9 8 " 5 4 3 2…

A: The given function is x+22=-4y-6

Q: Find the limit lim x →∞ √1+ 2x + 9x² -2x + 5

A: This question is related to limits, we will solve it using given information.

Q: Find the minimum value of the function f(x) = 2x² +18.3x + 45 to the nearest hundredth. Answer:…

A:

Q: ******* +70+ -10 -8 -6 -4 -2 ✔ +10+ y H 6 8 10 Q Write the standard equation for the hyperbola…

A: Given,

Q: Fill in the blank. (Enter your answer in terms of t.) 1 * ¹{2 ² - S 2

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Q: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: 4. Which of the following is the vector projection of (1,0, 1) onto (-2, 4, 0)? 2 B. (-1,2,0) c.…

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Q: Which are the foci of the ellipse represented by 25x² + 16y² = 400?

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Q: = √x³ + 2x³-3x d (x²+1)³ dx

A: Topic:- application of integration

Q: A solid right circular cone is made of brass. The mass of the cone is 5080 grams, to the nearest 10…

A: Formula to calculate :-Density=MassVolumeVolume of the cone=13πr2hwhere r=radius of the base of the…

Q: Consider the function f(x) = 1 - 2x², -4≤ x ≤ 2. The absolute maximum value is and this occurs at x…

A: Given: fx=1-2x2, -4≤x≤2   As we know the Power law: ddxxn=nxn-1 For maximum and minimum values,…

Q: 1. By eliminating the parameter t from the following parametric equations, find an equa- tion in…

A: As per the instruction, we will be answering the first one. For (a), Given: Now,…

Q: Your answer is correct. Find a differential equation whose general solution is = = C₁e⁹t + c₂e-³t.

A:

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

Q: II. Consider the function f(x, y) defined for all (x, y) by ƒ(x, y) = 232/32 + 2xy + 4x²y (a) Find…

A: Here we have to find the critical points.

Q: Let C be the curve represented by Ŕ(t) = (cos 2t, 2√3t, 5 — sin 2t). - ㅠ Determine the curvature of…

A: To find out the curvature of C.

Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

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Q: f(t) = (t + 1)³

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Q: Find the solution of the given initial value problem in explicit form. y' = (1 - 11x)y², y(0) y(x) =…

A: Given initial value problem is : y'=(1-11x)y2,   y(0)=-14

Q: 3. Determine the point(s) where the function y=₁, has a maximimum and/or a minimum. Find BOTH…

A: The given function is y=x2x-1

Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

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Q: Determine whether the equation is exact. If it is exact, find the solution. (e'siny + 3y)dx -…

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Q: The function f(x) = = The smaller one is x = 2x³36x² + 192x - 1 has two critical numbers. and the…

A: The given function fx=2x3-36x2+192x-1

Q: A triangle ABC has sides that is equal to 11m, 13m, 15m. find the length of median of the 11m-side.…

A: formula: ma = (1/2)2c2 + 2b2 - a2

Q: Find the curvature and the radius of curvature at the stated point ㅠ r(t) = 11 cos(t)i + 10 sin(t)j…

A: The expression for the curvature is: κ=r't×r''tr't3 And The expression for the radius of the…

Q: Find the exact value of each of the remaining trigonometric functions of 0. 2 5 sin - and tan 00 cos…

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Q: Which of the following is true when a plane intersects a cone to form a parabola? The plane slices…

A: The objective of the question is choose the correct option to make a parabola

Q: Problem #1: Which of the following functions is continuous at (0,0)? to yo (i) f(x,y)= = (ii) g(x,…

A: The objective of the question is checking the continuity of the given functions.

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: Question 7 of 8 View Policies Show Attempt History Your Answer Correct Answer (Used) Your answer is…

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Q: Evaluate the limit ALGEBRAICALLY (by simplifying), NOT just by graphing: lim h→0 (6 + h)² - 36 h

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Q: Which are the foci for the hyperbola modeled by the equation (Y-32 (x-1)² _ -1? 36 13

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Q: Evaluate the surface integral s G(r) dA, G(r) = x+y+z, S: z=2x-y, 0 ≤ y ≤ 1, 0 ≤ x ≤ y

A: Given:    Gr=x+y+z,    S: z=2x-y       0≤y≤1, 0≤x≤y Substitute z=2x-y in Gr     Gr=x+y+2x-y…

Q: Solve: x"-x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: 31 Given: f(t) = -213/2+4e² Evaluate: F(2) Use 2 decimal places.

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Q: y = x -1 and y2 = x + 1 Set up the limits of both iterated integrals (No evaluation!): ∫ ∫ f(x,y)…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Here, the diameter of the hemisphere is 30 m. So, the radius of the hemisphere is: r=302=15m=1500 cm…

Q: Give the Particular Solution of the following Differential Equation d² y dy +2 -8y = 0 dx² dx IBC:…

A: To find the particular solution of given differential equation.

Q: Given [*₂h(t)dt = -5 h(t)dt = 22 and evaluate the following integral. ["h(t)dt = | [h(t)}dt h(t)dt =…

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Q: A trader buy's 80 mangoes. she finds that 8 are bad and a further 22 are unripe ,show on a pie chart…

A: Given data:- Total number of mangoes = 80 Bad mangoes = 8 Unripe mangoes = 22

Q: KS Profiles Tab Window Help 6 Integrals Involving Exponer X +…

A: The given integral is xe-x^2.

Q: The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. Use linear…

A:

Q: The weekly marginal cost of producing x pairs of tennis shoes is given by the following function,…

A: The weekly marginal cost of producing x pairs of tennis shoes is given by the following​ function,…

Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Show that the differential equation x³y² + x(1+yº)y' = 0 is not exact, but becomes exact when…

A: To show that the differential equation x6y7+x1+y6 y'=0 is not exact, but becomes exact when…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}…

A: Given function f(t)=(et-e-t)2  f(t)=e2t+e-2t-2×et×e-tf(t)=e2t+e-2t-2   Formula L(eat)=1s-aL(c)=cs

Q: 3. A theatre has determined that its profit function is given by P(x)=x² +9x-11, where x is the…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…