The chain rule for two independent variables :looks like C) non of the other options O dw dx dw dy dw dz + ox or dy dr dz dr dw dx dx dt * variables and three intermediate ow dr dw dt = + + dw dy dy dt + A) O w dz dz dt B) O

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Q: Banach space and T E B(X) an operator TI

A: To prove, id+T=1+T Take X be the Banach space and also B(X) be the Banach space with T=supTv

Q: Find the standard matrices A and A' for T = T₂ ° T₁ and T' = T₁ ° T₂. T₁: R² - R², T₁(x, y) = (x -…

A: Given T1:ℝ2→ℝ2 by T1(x, y)=(x-2y, 2x+3y), T2:ℝ2→ℝ2, T2(x, y)=(0, x)   To Find: The standard matrices…

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A: Note: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question…

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Q: Find f if f(x, y) = 2y y+cos x 2ysinx y+cosx 8 ysinx (2y + cosx)² B ysinx y+cosx 4 2 !

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Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

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Q: H.W (5) Solve the following differential equations of (3x² − 6xy) dx + (−3x² − 2y)dy = 0 - S

A: We solve this by using exact differential equation.

Q: Solve the following linear system by using Gauss elimination method 5x₁ + x₂ + x3 = 5 x₂ + 4x₂ + x3…

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Q: * Use the chain rule to find the derivative of

A: Given,        w = xy Here,         x=tan(t),   y=csc(t)

Q: solution of the differential 4dy e²x + 4y = ² dx Find the particular d²y equation dx²

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Q: :use convergence test on the function n+1 with nth term n A diverge to infinity O C diverge to 1 O B…

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Q: 9. Simplify. State any restrictions on variables. log (x²-x-6) - log (2x-6) [K-3]

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Q: K(-2, 4) is a point on the terminal side of 8 in standard form. Find the exact value of cose.

A: If θ is in terminal side of the point a, b. It follows: a=cos θ and b=sin θ

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Q: Match the given differential equation with one or more of the solutions. (Select all that apply.) y'…

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Q: Let n = p¹, be a factorization of n into distinct primes p₁,..., Pk. Then, i=1 p(n) = n(1 - 1) (1 -…

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Q: 1-(x+3x³ sin y) dx + (x* cos y)dy = 0 2-(2x² + y)dx + (x²y-x)dy=0 3-xy'dx + (x³y² +1) dy=0 4-(3x²y +…

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Q: Part 2. Find the Standard Equation 3. hyperbola with vertices at (-2, -4), (-2, 6), foci at (-2,-5),…

A: To Find- Find the Standard Equation  hyperbola with vertices at -2, -4, -2, -6, foci at -2, -5, -2,…

Q: In a box containing 8 red balls, 8 green balls and 8 blue balls where 3 balls will be drawn in…

A: We have to find the probability.

Q: Solve y(6) — 5y(4) + 16y" +36y" - 16y' - 32y = 0. Include a plot of the solution curves.

A: There is no conditions, so i plot the six independent functions separately.

Q: Are the triangles similar? If similar, state the theorem that proves they are similar. If not…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: Use the matrix capabilities of a graphing utility to write the augmented matrix corresponding to the…

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Q: Approximate the integral using: (a) trapezoidal rule. 0.8 1.⁰0 e-² dx

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 3. The data table below shows the instantaneous velocity of a car every 5 minutes. Use Simpson's…

A: Note: We are entitled to solve the question with one method only. As the specified method is not…

Q: 1 2 01 0 0 33 1 0 0 0 5 -3 d. 0 1 0 0 0 1 2 3 4 5 1 0 7 1 3 0 0 0 0 1 LO 0 0 0 0 2. a. f. 10 10 01…

A: To Determine: which of the given matrices are in Row-Echelon or Row-reduced Echelon forms.

Q: Construct the Truth Table and determine if Tautology, Contradiction, or Contingency.

A: Contingency- A sentence is called a contingency if its truth table contains at least one 'T' and at…

Q: The partial derivative of f(x, y) with respect to y at the point (x,y) is f(x+h,y)-f(x,y) h B f(x…

A: We have to Write the Partial derivative of f(x, y) with respect to y at the point (x0,y0).

Q: 5. The set P = {a + bi|0 ≤ a < 1,0 ≤ b ≤ 1}

A: (6) Closure P¯  of P is the smallest closed set containing P. Given, P=a+bi | 0≤a&lt;1 , 0≤b≤1

Q: Q5/ Change the polar equation 2r = 2 + cos 0.(2r-1) to Cartesian equation Ans./y²-3x² - 4x-1=0

A: To find- Change the polar equation 2r = 2 + cosθ·2r - 1 to Cartesian equation.

Q: Express ow/ds in terms of r and s if w = x² + y², x=r-S, y=r+s A) 4s B) 4r C) 4sr O O

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Q: Solve the following system equations using "Solver" function : 3A+4B-5C-11 -2A+6B+2C=7 A-9B-4C=0

A: The solver function in Excel is used to solve a system of equations (linear or nonlinear).

Q: Find the accumulated future value of the continuous income stream at rate R(t), for the given time…

A: Sol For Cash Flow at period 0=C0, rate of return = r and number of periods = n, the Future Value…

Q: Part 2. Find the Standard Equation 2. circle with center at (4,-5), diameter is 6 2

A: Solution: Given center (h,k) = (4,-5) and d=6

Q: Find the area enclosed by the given parametric curve and the y-axis. x-t²- 2t, y = √t y X -1.0 -0.5…

A: The given parametric curve is                                          x=t2-2ty=t To find: the…

Q: A new, larger bottle of shampoo contains 15.6 ounces.  The bottle says you get 30% more than the…

A: Given, a new larger bottle of shampoo contains 15.6 ounces and this new bottle gives you 30% extra…

Q: Evaluate the following integrals dx (1) S 2√x (1+√x)²

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Q: Let (x, eA) be a measurable space, £: X (-∞, w) and 9:* (-∞0, ∞o) are measurable. Prove that the…

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Q: b. Describe an algorithm that runs in O(n + m) time that given a task T, outputs the minimum…

A: Given: The objective is to describe an algorithm that runs in O(+) time that given a task T ,…

Q: 30. Which of the following operations satisfy the commutative and associative property? Division O…

A: Which of the following operations satisfy the commutative and associative property?   Division…

Q: -2+z) ds over t e point (0, 0, 0)

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Q: 22. Find expressions for f(g(x)) and g(f(x)), and state their domains a) f(x)=√√√x;g(x)=x²-4 f(g(x))…

A: Solution :- The domain of a function is the set of input or argument values for which the function…

Q: Find the particular d²y equation dx² solution of the differential 4dy + 4y e2x = dx x²

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Q: Giren (1-2²) y" - 2my' + 2 c²+1 i) solve the equation at ii) (1) using Po (n) -2 (2+1)y= ห=0) other…

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Q: Which number replaces the question mark? 1 3 5 3 4 5 16 6 3 2 8 ? 7 3 9 2

A: Sum of the numbers of a portion is equal to the sum of the opposite portion for all the portions in…

Q: Part 2. Find the Standard Equation 3. hyperbola with vertices at (-2, -4), (-2, 6), foci at (-2,-5),…

A: To Find: The Equation of hyperbola with vertices (-2,-4), (-2,6), and Foci (-2,-5), (-2,7).

Q: Find the root of x² - 1000 = 0 using Newton's law of approximation

A: We have to approximate the root of x7-1000=0 now we have f(x)=x7-1000,  f'(x)=7x6 Newton's law of…