Q:01:Why we study Cylinder and what is its importance in daily life routine.

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under condi...

Q: L{t? e¬at } =

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Q: Theorem 3.7. Let {fn} be a sequence of real-valued (or complex-valued) function on a X. Then, fn 3ƒ ...

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Q: а) b: G' → G such that o o = idg', where idG' is the identity map on G'. Show that o is injective. S...

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Q: (d) Find o51 Suppose G is a group with order pq, where p and q are distinct prime numbers. If G has ...

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Q: How far is the centroid of the area bounded by the curves y = e^x, y = e^-x, and x = 1 measured from...

A: Centroid

Q: 2. Use projections or transposes to determine the least squares quadratic that best fits the points ...

A: Curve fitting quadratic equations

Q: (xy + x²)dy + ydx = 0

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Q: Consider the equation below. f(x) = 6 sin(x) + 6 cos(x), 0 sxs 2n Exercise (a) Find the interval on ...

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Q: Determine the area of the region enclosed by the curves y=1/x, y=1/x2, and x=9.

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Q: Let f = x? + y² + z² be a zero-form on R. Suppose that P and P2 are two distinct points on a sphere ...

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Q: 1. Use the Monotone Convergence Theorem to show that the sequence (a,} converges, where a, = n! for ...

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Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of  1.25% per ...

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Q: (2v2 + 4u?v)du + (4uv + 3u³)dv = 0

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Q: y + yi = 1, - yi = 1, 6. when x = 0,y = 4 dx

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Q: A tank contains 100 kg of salt and 2000 L of water. Pure water enters a tank at the rate 6 L/min. Th...

A: Given : Amount of salt initially=100 kg Amount of water initially=2000 L Pure water enters at the ra...

Q: Rewrite the ODE y" = y" + y +t² as a system of first-order ODES. Solve the system y' = 3x, x' =x+ 2y...

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Q: Use the formula to compute In(1.11) correct to five decimal places. In(1 - x) = - n= 1 In(1.11) =

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Q: Suppose a 10-foot ladder is leaning against a building. The bottom of the ladder slides away from th...

A: Solution:-

Q: Which of the following integrals give the volume obtained from revolving the region bounded by y = z...

A: Using ring method volume of revolution of the region bounded by y=fx and y=gx, a≤x≤b about the line ...

Q: (7) Given the following pieces information, describe the set of solutions x such that Ax = b: (a) b ...

A: We shall solve first question only as you have asked more than one unrelated questions • for others ...

Q: Answer the following True or False. (h) (0,1/2) is an element of Q x Z (i) (0, 1/2) is an element of...

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Q: Find the inverse Laplace Transform of: s- 1 (s – 2)(s – 3)(s – 4)

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Q: . a) For spring-mass model a" + 4x' + x = part and the steady periodic part of the solution, and fin...

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Q: Lush Gardens Co. bought a new truck for $50,000. It paid $5,500 of this amount as a down payment and...

A: Solution 

Q: For a given vector a E R" and scalar A > 0, show that the following problem 1 minx, ||x – all +A ||x...

A: Given: A vector a∈ℝn and a scalar λ>0   To show: The problem minx12x-a22+λx2 has the optimal solu...

Q: 1 if n is odd Prove that the alternating series £=1(-1)" diverges. 2 if n is even' 2. Let an = an n%...

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Q: Determine the dimensions (radius and height) of the largest right circular cylinder. volume that can...

A: Solution:-

Q: k and Ĉ = к апd rs along the a ICorteeion

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Q: -10 -2- -34 -5

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Q: Answer the following questions about the function whose derivative is given below. a. What are the c...

A: Given: f'(x)=3sinx-32cosx+1, 0≤x≤2π To find: a) Critical points of f. b) The intervals in which f is...

Q: On the decibel scale, the loudness of a sound, D, in decibels, is given by D= 10 log (1/1,), where l...

A: D=10(logI-logI0)=10logII0 Where I= intensity of the sound in watts per square meters I0=intensity of...

Q: If you have been hired at an annual salary of $23,000 and expect to receive annual increases of 5%, ...

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Q: This question concerns the vector field F= -ry'i – ryj+ z(1² + y°) k. (a) Calculate the divergence o...

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Q: Evaluate the integral of the two-form w = (a* + 4y) dx A dy over the region D bounded by the curves ...

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Q: Leslie matrix the Leslie matrix, which is used to model population growth. Consider the following ex...

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Q: (w² – z² – 4z – 1))dw + 2w(z + w + 2) dz = 0

A: By Bartleby policy I have to solve only first one as these are all unrelated & lengthy problems....

Q: Find the Vertical and Horizontal Asymptote for the function 3x - 1 f(x) = x + 1

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Q: „3 Determine the volume of the solid created by rotating the region bounded by y = x°, y= 125, the x...

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Q: Gt) = e2-t U lt-2) L{ Gt} = }00 G4) e st dt %3D e2-t Ult-2) est dt ° e2-t est dt de-t -st) dt 2-t-st...

A: Laplace transferom

Q: e of mwl

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Q: Evaluate the following integral by appropriate method: L 12+ |x] dx dx Jyz xVx2-1 L, 12x – 1| dx

A: We are entitled to solve only one question at a time. As the question number is not specified, so we...

Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli eq...

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Q: A loan of $26,300.00 at 5.00% compounded semi-annually is to be repaid with payments at the end of e...

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Q: Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3 usin...

A: We use Newton's Divided Difference Interpolation Formula.  x             x0            x1           ...

Q: 1. Where does the graph of y = x“ + 4x – 1 have horizontal tangent? %3D - 2. Use the chain ule findd...

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next ...

Q: 1. (w? – z? – 4z – 1))dw + 2w(z + w + 2) dz = 0 2. (s-s? – t²)ds + (t + s² +t?)dt = 0

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Q: (s-s²-t²)ds + (t + s? +t ?)dt = 0 %3D

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Q: 1.) Find v(t) 4+ 37 2-

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Q: 2p a) n! = 2 (mod p), where for 0 <k < n. %3D k!(n - k)!

A: To prove the given part (a) 2pp≡2mod p where nk=n!k!n-k! for 0≤k≤n  

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.