6. Find two positive numbers such that the sum of twice the first number and three times the second number is 192 and the product is a maximum.

Q: Write the general formula for following alternating series in the form > an. n=1 5 5 - ... 8 10 11…

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Q: Find the area bounded by the curves f(x)=x+8 and g(x)=x²-x.

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Q: Solve the right triangle. Round your answers to the nearest tenth. A = 0- D. 56 22 A

A: Given, Right triangle  theta=56° adjacent =a opposite =b hypotenuse = 22

Q: 5. Let f and g be the functions R →R given by 5- 3z if z<1 5-2r - if z1 f(z) = and g(z) - 6-2.…

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Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: Let 0 (in radians) be an acute angle in a right triangle and let z and y respectively, be the…

A: Question- Let 'theta'  (in radians) be an acute angle in a right triangle and let x and y…

Q: 5. у 6. уд 4+ y - 8x /y =x y- + 2| x= 3 4 3- = x i 2 3 2. 2. 4. 3. 2.

A: Note:- As per your demand we solve question 5 and 6 for you  Given problems:- use the method of…

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: As we know that; The expression for the volume of the revolution of the function y=fx from x=a to…

Q: VECTOR DIFFERENTIATION: If A = cosxyi + (3xy -2x^2)j –(3x +2y)k find dA/dx, dA/dy, d^2A/dx^2,…

A: I am attaching image so that you understand each and every step.

Q: dy +y=e' xp

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Q: Stxª_ 3x3+ D -2)x= * (8x* -30,3+5x-80) x (8x1 -30x3+5x-80) 40

A: This question can be solved solved using integration as the inverse process of differentiation.

Q: Which of the following is the correct definition of the limit? The lim f(x) = A, if and only if, for…

A: Explanation of the answer is as follows

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: Find the total area of the region between the x-axis and the graph of y = - x´ - 3x, - 4 <x54.

A: Given query is to find the attached area of the region.

Q: allsweCI -5e" dx converges 4x to

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Q: 2. Let g (x, y) = 2x² – y² . Compute 9(1, 2), g (2, 1), g (1, 1), g (–1, 1) and g (2, –1).

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Q: In a one-dimensional Kinematics experiment, an electrically charged particle is moving along a…

A: Find your answer below

Q: 38) Assume that f(x) is a solution to the differential equation y' = 2x + y with f(0) = –1. Then…

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Q: a²f If f(x, y) = xey + 8xy, then , is given by: O + 8 O 4xe4y + 8 ○ 웃+8 O 4e4y + 8 O None of these…

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Q: The radical function f(x) is represented by the equation f(x) = x-1+4· The graph shown is the graph…

A: Given function fx=x-1+4 We know x-1 is defined for x-1≥0    ⇒   x≥1Therefore fx=x-1+4  is defined…

Q: 5. 1 de 9+x2

A: Given query is to find the integral of the expression.

Q: The base of a rectangular box, open at the top, is to be three times as long as it is wide. Find the…

A: Given, Rectangular box, l,b,h be the dimensions. l= 3b According to given, Volume= lbh= 2250 cubic…

Q: If s (t) represents the position of an object (measured in meters) at time t seconds, then the units…

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Q: pleasee answer C and E

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Q: ylz)=e y(-2)=:

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Q: dA when r = 2. dt dr Let A be the area of a circle with radius r. If = 2, find dt

A: Area of the circle with radius r is given by;A=πr2differentiating w.r.t time,dAdt=2πr drdtWhen r=2…

Q: 00 The series is convergent. n2 + cos? n n=1 This statement is true by the alternating series test.…

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Q: 22. Which of the following statements about the functions y = f(x) and y f(x) is true? A. If the…

A: Here, to find the correct statement for the functions y=f(x),y=1f(x)

Q: What's the difference between average velocity and instantaneous velocity?

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Q: Given the surface x²y + y° z+ z?x = 38. Find the normal line and the tangent plane to the given…

A: A detailed solution is given below.

Q: 1-e dx +2(xe – y)dy = 0;

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Q: 7) f(t)=e"(Acos(ßt)+B sin(ßt)) -at

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Q: Solve using an appropriate method on First Order Differential Equation. Show complete and detailed…

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Q: If+y = 25 and dz/dt = 5 , find dy/dt when y is positive and %3D %3D (a) z = 0 dy/dt = 0 (b) z=1…

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Q: dy + y = y² sin x dx

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Q: Let f(x) = – 7 cos(cos æ) %3| f'(x) =

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Q: Solve the I.V.P: dy 1 = 6y°x; y (1) = dx 21 1 y = 24+3z2 1 3z2-24 1 y = 24-3z 1 24-3z? నా నా

A: To find solution of IVP

Q: |3 cos 2.r dx 3.

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Q: St' sin(2t*)dt (sin(2t*) - 2t*cos (2t*)) + C (sin(2t*)-2t cos (2r*)) +C 14 1 (sin(2t*)-2t cos (2t*))…

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Q: 3 dx a) 3- x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the following IVP: Find the general solution. 1. y"-3y'+2y = e3t ; y(0) = 0, y'(0) = 0

A: According to our guidelines, we can answer only one question. Other questions can be reposted.

Q: The series > cos" (2) is divergent. n=1 This statement is true by the test for divergence. This…

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Q: sin(x) dx Jo

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Q: Determine if is a p-series or not. If so, determine if the series converges or 7 5ni n=1 diverges,…

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Q: |*| +1, {0, x = 0 1x-1, x >0

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Q: pon homogencous Lincar ODE y'+3y = 18x² yro)=-3 y'@)=0 And exace sol'n 5.

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Q: Find an arc length parametrization of a helix of height 20 cm that makes four full rotations over a…

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Q: use the properties of the natural logarithm to: A. expand the logarithmic expression: ln (2x/x+2)…

A: A) ln2xx+2B) 5 lnx-7 lny-8 lnz

Q: U. sine= and <e< 2n -24 25 sin을 =D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4 CSC csc* x -dx 2 cot? x

A: