The ideal gas law crates that the preccure [p], temperature [T], & volume [v] of a confined gas are related by the equation P= KT where k is some constant. V With K = = = 1/2 use differentials to approximate the change in the pressure of a confined gas when its temperature increased from 80 to 80.7 and its volume decreased from 5 to 4.8.

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Q: What is the equation of the asymptotes of the hyperbola defined by x² - 4y² + 4x + 40y - 92 = 0

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Q: a) [ ] Show that the equation 4x8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

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Q: 3. x' = 3/2 +|+ X

A: Given x'=-321-14-12x ………………(1) First, we find the eigenvalues of the coefficient matrix A…

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A: To Sketch: The curves  r=cos2θ, r=2cosθ. To Evaluate: Area between the curves r=cos2θ, r=2cosθ.

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Q: 3) Convert the following triple integrals to cylindrical coordinates or spherical coordinates (do…

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Q: Technical Question: Which of the following best characterizes the statements A) f(x) = x²+xlg²² B)…

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Q: 5. Find the equation of the hyperbola with vertices at (3, 3) and (-13, -3), and passes through the…

A: Given, Vertices of hyperbola are (3, -3) and (-13, -3) And hyperbola passes through point (5, 0)…

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Q: (2x, 1) and let g(x, y) = x² + y². Find all the points on the curve g(x, y) = 1 for which Vf(x, y)…

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Q: 2) Solve the difference equation using z-transform yk+2-3 Yk+1 + 2yk = 0, with y₁ = 0, y₁ = 1.…

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

Q: 4. Determine if the following statement is true or false. Theorem 1.2.1 in your textbook (Existence…

A: Solution 1: dydt=ty, at (1,1) Let  f(t,y)=ty Now ∂f∂y=-12ty32 Now ∂f∂y=12ty32 At point (1,1) ∂f∂y≤12…

Q: Question 1 a. For each of the following partial differential equations: i. iii. iv. V. Ꭷ-u Bu Әх2 т…

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Q: Determine the form of a particular solution yp of y" + 4y = x cosx. Do not solve the equation.

A: Given DE is y"+4y=xcosx .....(1) We find the form of particular solution yp.

Q: EXERCISE 6.1. Let f: XY and g: Y Z. Prove that gof:X-Z is a bijection.

A: From the above details we have,

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A: To compute the volume of the solid region enclosed by the curves y=fx and y=gx, where a≤x≤b and…

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Q: 3. Identify the values of a in which exist integer solucions of the equation: 3827x + 1634y = a

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Q: c) Solve the differential equation ydx = (ye" - 2x)dy.

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Q: Indicate which of the following relations is an equivalence relation or is a partial order relation.…

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Q: 6. For f(x) = 2x - x, construct the second Lagrange interpolating polynomial using the nodes xo = 1,…

A: Given as, f(x)=e2x -x x0 =1,x1 =1.25,x2 =1.6.

Q: 5. Find the orthogonal complement of matrix M given below. -4 M = -3 05 1 3 2

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Q: Express the function as the sum of a power series by first using partial fractions. (Give your power…

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Q: Compute lim by following these steps lim Missing steps A lim 87 XXIN Missing steps B What do you…

A: limx→∞ex+2xex+5x

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A: The optimal choice for the Lili is shown below as,

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Q: Consider the function [cos 30 Sın 30 f(x)=x₂ +- x² x₁x₂-1 Determine the directional derivatives in…

A: Directional derivative of a two variable function f(x1,x2) at a point x1,x2 along the unit vector U…

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Q: 10. x 유 3 4 X, x, x(0) = (2 ; see Problem 2.

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Q: Find In z if z = (3+j4)³(8-j5)¹/³

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Q: The average height of water in a harbour is 5 m. At low tide, the water height is 3 m. The tide…

A: The equation of the sinusoidal function is of the form y=AcosBx+C+D. Here, x and y are variables and…

Q: Xx: the function f(x) = 2 * sincx) - e/4-1 is Zero for two values near x = -5. use bisection to find…

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Q: Which of the following limits meet (or does not meet) the requirements to apply L'hopital's rule…

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Q: Consider the vector spaceU33 a b C 0 d e la, b, c, d, e, fER. So 0 0 f a 0 C (0b0 The orthogonal…

A: Note :  " I am proving the given question as nothing is mentioned in the question . " Given vector…

Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

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Q: (b) Solve the initial value problem y" - 3y + 2y = 0, y(0) = -3, y'(0) = 5 by Laplace transforms.

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Q: What is the equation of the asymptotes of the hyperbola defined by x²- - 4y² 4y + 4x + 40y - 920

A: There are two asymptotes of a hyperbola. The hyperbola touches its asymptotes at infinity.

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Q: Get the Karnough Map of the ff. black diagram. Identify the number minterm with 1 value

A: Given: The logic diagram, as follows: To determine: The Karnaugh map of this diagram and the…

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Q: By using fixed point approach solve the Value of A=√√20 A = √√² + √2 + √2+..

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

Q: Then use the table to fill in the apparent value of the following limit. 7(5-x) lim x-5 25-x² Round…

A: limx→575-x25-x2 we have to find the limit value using approximation

Q: 3.7.5. Given a finite-dimensional normed space X, prove the following state- ments. (c) No proper…

A: We know that ,  A normed space is a pair ,  X , ·  where X is a vector space and · is a norm on X.…

Q: Consider following t= 7 pi/3 Find reference number value of t Find the terminal point (x,y) of t

A: Reference number value is π/3 Terminal point is (0.991,0.127)

Q: Renting a car costs $40 per day or $750 per month. Renting daily is cheaper for a few days, but…

A: Rentinng of car per day = $40 Monthly charge= $750 Let after x days daily price will be more than…

Q: 1. Consider the set A = {a,b,c,d,...,x,y,z} of the 26 letters os the alphabet. Determine the total…

A: Given A = {a, b, c, ..., x, y, z} As Total vowels = 5 Total consonants = 21