Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

Q: b. Determine the gradient of the following function at Po h(x, y, z) = cos xy + e + In zx, Po(1, 0,…

A: We need to find gradient.

Q: 2. find the derivative 725 - 2z² - 3z + 12 Enter your answer

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Q: A tank contains 80 gallons (gal) of pure water. A brine solution with 2lb/gal of salt enters at 2…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

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Q: a f(x) = x² sec (ax)

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Q: Solve the I.V.P using [x = zry]. y di dx + (y cos ( 1 ) - x) dy = 0, y (0) = 262

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Q: Determine dy/dx, if the curve is described by the equation 4y^3-5x^2y=4x^2

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: When the expression - log, (5) - log, (4) + log, (7), b > 1, is written in the form log, a, the…

A: We have to find value of a to the nearest hundredth.

Q: Q5: Find the inverse Laplace transform of: f(s) = 3²(²-3)

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Q: Solve the differential equation. 10. ( cos 2y – 3x^2y^2) dx + (cos 2y – 2x sin 2y – 2x^3y) dy = 0

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A: We have to check series is convergence or divergence by ratio test

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Solve the Homogeneous Equation using the given substitution. State the value of a. a= x² - y² - xy =…

A: As per the given condition I have to use the substitution y=vx such that dydx=v+xdvdx

Q: c - [² x ² (1 - √x ) ³dx 0

A: In this question we have to evaluate the Integral.

Q: Prove the identity sin(-0)- cos (+0)

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Q: Integration of Inverse Trigonometric Functions 1 1). fsinødø.; cos² Ø+9 1 2). Scotødø.- √9-In² sino

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Q: The domain of the logarithmic function y = log4 (x + 3) is Ox>0, XER Ox-3, x=R Oxz-3,TER OX>0, XER

A: Let's find domain of given logarithmic function.

Q: 1. Find the volumes of the solids generated by revolving the regions bounded by the lines and curves…

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Q: 3. Find the volume of the solid that results when the region enclosed by the curves x = = y² and x =…

A: If the region bounded by x=f(y) and x=g(y) on [ a, b], where f(y)≥g(y)is rotated about the y‐axis,…

Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: Calculus I

A: Given, h(x)=x2-f(g(x))

Q: 4. Classify the following differential equations according to whether they are linear or nonlinear.…

A: For (A), The above differential equation is linear. For (B), It is the same as dydt+1=0. So, the…

Q: sec5 (sin ¹(7x)) √1 - 49x² dx

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Q: sin () cot ()+cos ( cos (1) sec (7)

A: We use  sin(π+x)=-sin(x) cot(π-x)=-cot(x)  sec(π+x)=-sec(x)

Q: 4) y(2xy +1) dx - xdy = 0

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Q: Given the matrices A: = [1-4] 0 21. B=( )-C-1) ₁ [1 -5 5 and C= the matrix X in the equation AX + 5B…

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Q: d- d³y dx3 d²y +69² y dx² - dy 15- dx 100y = 0 equation

A: Topic = Differential equation

Q: dy = y cos(x), Where y(0) dx = : 1.

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Q: 5. find the derivative 2x (7) + 6x (7) - 2x (²) + 210 Enter your answer

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Q: rite the first five terms of the sequence: √n² +10n-n}+1 = etermine whether the sequence converges,…

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Q: ) Solve the Recurrence Relation Xk+2 +4Xk+1+3Xk = 3K where x₁ = 0, x₁ = 1

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Q: 20 18- 16 14- 12 10 8 b 4 2 1 2 Estimate the instantaneous rate of change at x = = 1

A: To find the instantaneous rate of change.

Q: (X^1/2 + 6) (X^3/2 -32)

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Q: If all the letters in the word FUNCTIONS are used, determine the number of different 9 letter…

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Q: Evaluate the given Laplace transform xe { filt L (t-T)²cos(2T)dt

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Q: Determine the equation of the line that is tangent to y = 2 tan x, where x = 4. O-4x + y - (2-) = 0…

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Q: I'm seeking help on the 2nd bullet point starting with "Now find the equation of the tangent line...

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Q: Correct the answer Find the median for the following numbers: (21, 32,29, 8, 18, 3, 25) A-8 B-7 C-9…

A: To find the median of given set of numbers.

Q: The differential equation y"(1-x)+xy'=y is linear homogeneous O non linear homogeneous linear…

A: We have to choose correct option

Q: 3. find the derivative 513.5+412.52¹.7 lt Enter your answer

A: Taking derivative of the function with respect to t and using power rule of derivative gives the…

Q: 9. 5²-2 dz 10. fdx

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Q: An engineer working for Florida Power and Light has been given the task of enclosing a 72-m²…

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Q: 6X-1 4X+1 X+7< 6 OX<-89/2 (-∞, - 89/2) O X<- 89 (00,- 89) O X<-2/89 (-∞, -2/89) O X<∞ (89/2, ∞) 8

A: x+7&lt;6x-14-4x+16x+7&lt;6(6x-1)-4(4x+1)4×6x+7&lt;36x-6-16x-424x+7&lt;20x-1024Multiply 24 on both…

Q: There are 30 students registered for a multi-sport camp. There are 4 students who will play Hockey…

A: I have appended the formula used in the solution part of the question

Q: Based on the graphs of f(x) and g(x), what must the domain of (f. g)(x) be? 10 8 7 6 5 2 g(x) 1…

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Q: d dx sin(t) dt

A: We have to find derivative

Q: Find an equation of a line that passes through a point P (-3, 5, 4) and is parallel to the given…

A: Given problem:- Find an equation of a line that passes through a point P (-3, 5, 4) and is parallel…

Q: Pre-Calculus  :  if x=2x=2 is a solution to the equation x^3-4x^2-31x+70 = 0x3−4x2−31x+70=0, find…

A: We have to find out solutions

Q: Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to…

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