Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter. Area: 25 square feet ft (smaller value) ft (larger value)

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A: Description about graph is given.

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Q: I need all the integrals of the trigonometric ratios

A: ∫sin x=-cos x+C∫cos x=sin x+C∫tan x =-ln|cosx|+C

Q: = ||r' (t) x r' (t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7 sin(9t)j + tk Use the formula…

A: find curvature

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Q: (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C…

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: Given problem:- Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to…

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Q: = Write the Taylor series for f(x) Find the first five coefficients. Co= C1= C2= C3= C4 e about x =…

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Q: What is the domain of the following function: f(x) - ○ (2,00) Or 2 O[-1,00) O [− 1, 2) U (2, o) O…

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Q: Find the area of the part of the circle r = 5 sin 0 + cos in the fourth quadrant. Answer:

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Q: 2 QX = X² x + 2

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Q: 27 SECOND DERIVATIVES Find TUTORIAL 22 if y-In (x + 1). Answer 2-2x² 22-2

A: Note:-As per your mentioned request i am solving question 1 from the given figure.

Q: Solve the following differential equations of y" + 6y' + 5y = 10 sin (2x)

A: The given differential equation is  y''+6y'+5y=10sin(2x).

Q: Question 7 Given the function f(x) = 8 +5x², calculate the following values: f(a)= f(a+h)- =…

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Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: Solve for the solution of: (D3 + D)2y = 0

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Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

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Q: Let ƒ(x) = √x(2 − x)². Use the local linear approximation of f(x) at x 1 to estimate the value of…

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Q: fand sketch it, for f(x, y) = x²

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Sketch a graph of the function. Given the piecewise definition f(x) = Draw the graph of f. 4. 3 2-…

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Q: Convert the polar equation to rectangular form. r = 5/1+sin(theta)

A: Note that, the rectangular(cartesian) to polar conversion is given by: x=r cos θ, y=r sin θ And, the…

Q: integral x²y dx - xy²dy where C: is the circle x² + y

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Q: For the function f(x) = x² + 7, find the equation of the tangent line at x = -1. Answer: Submit…

A: Let's find.

Q: 1. Find f(x) if f'(x)=12x¹+3√x+7-2e -4 and f(1) = 4

A: Given f'x=12x3+3x+7x-2ex-4  and f1=4 To find f(x):

Q: 7. Using differential, approximate (8.01 ) correct to 4 decimal places. 8. Use differential to…

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Q: Which of the following is the derivative of x³ + 4x + 1? x² + 4x 3x² + 4 x²+4 3x²+4+1 3x² O

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Q: Express the integral as a limit of right endpoint Riemann sums. Do not evaluate the limit. 4 Sª √5 +…

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Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

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Q: 17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Find in terms of x. dx 18. Given y = 5t (3 - t), t =…

A: Let's find.

Q: Write the Taylor series for f(x) = sin(x) at x = Find the first five coefficients. Co C₁= C2= C3=…

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Q: 5. S COS X 2+3sinx dx

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Q: (-3,0) (0, -1) (-1,-2) y = h'(x) (0, -2) (3,0) c

A: Given problem:- Suppose that h(x) is continuous everywhere, with the graph of h'(x) given on the…

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Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

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Q: e3x-6-2, [2x - 5], √x²-9, if x ≤ 2 if 2 3

A: answer is in next step

Q: An ellipse of equation 4x²+2y²=k the distance between its foci 3√2 Find the value of k

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

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Q: Find the work done by the force field F(x, y, z) = (x - y², y - z², z - x²) on a particle that moves…

A: Work done on particles: W = F.dr

Q: A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the…

A: Solved below

Q: f(x)= x² + 5x + 6 g(x)=x+2 Find (+)(*) (-) (2²) The domain of = (4) (2) is x + [ a

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Q: Write the Taylor series for f(x) = x³ about x = −2 asen(x+2)". n=0 Find the first five coefficients.…

A: Given that      f(x) = x3

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A: Explanation of the answer is as follows

Q: The equation of a curve is given by f(x) = √2x-1. a) Use the definition of derivative to find f'(x).…

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Q: an+1 Assume that converges to 'p = 3. What can you say about the convergence of the given series? an…

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Q: Differentiate using delta method y=6x2-24

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Q: Determine whether F(x, y) = 4x²y i+ 9xy²j is a conservative vector field. If so, find a potential…

A: Determine whether F(x,y) is a conservative vector??