An open box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimensions 6 inches by 6 inches. (answer 4°x4"x1")

Q: Find dy/dæ in terms of æ and y if æ°y – x – 2y – 1 = 0. dy dx

A: We have to find dydx in terms of x and y if x3y-x-2y-1=0.

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A: Answer is given below .

Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the po...

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Q: f(x) = V3x–1 c = 1

A: As we know that; If the function fx is continuous at x=c then, limx→c-fx=limx→c+fx=finite value=fcor...

Q: Activity 1. Slope of the Tangent The rate of change at any point on a function is the slope of the t...

A: We want to find rate of change of the function at the given point. 

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A: The maximum speed of a simple harmonic motion is given by, vmax=2πTA Where, A is the maximum displac...

Q: (n!)² ". Show your work. (5) Find the interval of convergence of the power series (2n)!

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Q: The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the re...

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Q: 69 -24 A) -24 Solve lim B) 4 9+2 2-9 C) 24 D) -

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Q: A formula for a function y = f(x) is f(x) = 4x°. Find f(x) and identify the domain and range of f(x)...

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Q: Question 4 Given: f (x) = x +7 and g (x) = x² . Find the limit: lim, -3 9 (f (x)). O (E) O 18 O 12 O...

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

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Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x ddxu(x)v(x)=v(x)ddxu(x)-...

Q: Find the direction angles of the vector. (Round your answers to one decimal place. 3(4, –6, –8) u = ...

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Q: Find the angle 0 between the vectors in radians and in degrees. u = (2, 2), v = (4, –4) (a) radians ...

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Q: - y² dy 3y 50.

A: Simplify the expression and integrate it.

Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: Find the volume of the solid generated by revolving the specified region about the given line. R abo...

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Q: Next que Does the sequence (a,) converge or diverge? Find the limit if the sequence is convergent. a...

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Q: In your notes, create an interval table for f(x) = x* - 8x? by testing values around the critical va...

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Q: Consider the following planes. 3x + 6y - z = 84 x - 12y + 2z = 0 (a) Find the angle between the two ...

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Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3), P2(5,...

A: We can solve the given problem as follows:

Q: Find the unit vector in the direction of v v = -6.3i + 3.7j u %3D

A: Let the unit vector in the direction of v be u.

Q: Covider r the following diferental equation 2x+3y +22 7x +6y +50 ミ A variable chonge to turn the equ...

A: (b)   x = z-2 and y = w - 6

Q: If f(x) = 2 sin(x) + 3x", find f' (3). f' (3) =

A:

Q: Find a basis for the vector space of all 3 × 3 diagonal matrices. 100 o o o o o0 O0 0 o 0 10 00 o 0 ...

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Q: When two pure notes that are close in frequency are played together, their sounds interfere to produ...

A: Given data÷ f1t=cos17t f2t=cos19t ft=f1t+f2t

Q: Use Lagrange multipliers to solve the following exercise. Find three positive integers x, y, and z t...

A: f(x, y, z) =x+y+zg(x,y,z)=kxyz=8F(x, y, z, λ)=f(x,y,z)-λ(g(x,y,z)-k)F(x, y, z, λ)=x+y+z-λ(xyz-8)

Q: a1 五 Check Answer May leave numerator and denominator factored, 4-3 - 4. 6. 7. 6. Write the equation...

A: Graph will be of the form f(x)=p(x)/q(x). As vertical asymptotes are x=-2 and x=3 , x=-2 and x=3 wil...

Q: solve and equation using separation of variables e^y dx - x^2 dy = 0

A: First separate x variable and y variable and then integrate.

Q: 6 Convert your original pair of complex numbers to polar form. D= 1-j2 A = 2+j3

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Q: 6 Convert your original pair of complex numbers to polar form. D=1-j2 A = 2+ j3

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Q: 6 Convert your original pair of complex numbers to polar form. D = 1-j2 A = 2+ j3

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Q: Find the angle 0 between the vectors in radians and in degrees. u = (2, 2), v = (4, -4) %3D | (a) ra...

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not un...

A: let the two vectors bev=<a , b , c>w=<-a , -b , -c>Since two vectorrs are in opposite di...

Q: 3The bell tower of the cathedral in Pisa, Italy, leans 5.6 from the vertical A tourist stands 105 me...

A:

Q: Fihd thẻ čentroid of the region bounded by the graphs of the functions 1 y = 4 sin(x), y = and x = a...

A: Find the centroid of the region bounded by the graphs of the functions    y = 4 sin(x), y=x/9, and x...

Q: Find u v, u· u, ||v||2, (u · v)v, and u · (3v). = (2, 11), v = (-5, 2) %D (a) A. n (b) u u (c) ||v||...

A:

Q: Evaluate: 1 dx 2(х — 1)? 1 О а. + C 2(х-1) O b. * + C 1 2х + C 1 d. + C 2(х-1)

A: The integration of the integral is 1/[2(x-1)2].

Q: txH Find Maty min Satle ex

A:

Q: Determine the equation of a tangent to the curve: y =. (x3 - 5x + 4)(3x2 - 2x) at the point (1,-2)

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Q: Find w such that 2u + v- 3w = 0. %3D u = (0, 5, 7, 2), v = (-3, 4, -8, 1) W =

A: vector

Q: Let f(x)= x/x-2.Show that there is no value c ∈ (1, 4) such that f'(c) = f(4)−f(1)/4−1.Why is this n...

A: Given: f(x) = x/(x - 2) Show that there is no value c ∈ (1, 4) f'(c) = f(4) − f(1)/(4 - 1) If f(x) i...

Q: If we want to evaluate the integral x+18 1= +64 dx, and dx = do and therefore the integral becomes, ...

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Q: The masses m; are located at the points P;. Find the center of mass of the system. m1 = 7, m2 = 2, m...

A: Given : The masses mi are located at the point Pi.m1=7   ,m2=2   , m3=9P1=(-8,-8)   , P2=(-9,-8)  , ...

Q: sin (:) tan r 2. Find the derivative of f(r) = using logarithmic %3D differentiation.

A: To find the derivative of fx=sin31x tan x5π-x5e2x using logarithmic differentiation.

Q: 3. r3D 0, 6ө > 0 34. r = 0², –2 < 0 < 2T 35. r 3 3 соs 30 36. r = -sin 50 37. r3 2 сos 40 38. r = 2 ...

A: Given

Q: Consider the following. u = (1, -9, -7), v = (6, -2, 0) (a) Find the projection of u onto v. (b) Fin...

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Q: SHOT# BS Hエ ELEV Remarks FS BM- A 1.567 200.000 Tp-1 199.333 3.579 197. 88 Tp- 1.136 197.709 196.573...

A: