Use the Chain Rule to find dz dt = " where z = 2x cos y, x = t4, dz dt (Type an expression using t as the variable.) and y = 3t².

Q: Find d2y/dx2 by implicit differentiation. y + sin y = x

A: To Find d2y/dx2 by implicit differentiation.y + sin y = x

Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

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Q: Graphs of the position functions of two particles are shown, where t is measured in seconds. (Enter…

A: Given graph of position function

Q: X X+1 11

A: To evaluate the following integral.

Q: The slope of the tangent line to the curve y = 4x³ at the point (-1,-4) is: The equation of this…

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Q: Find dx (In √æ²+1).

A: Given that expression we have to find evaluate the value

Q: d. Find the derivative of the function. y = (5x-1)4(8x² - 1)-3 ||

A: Since you have asked multiple questions to solve which are not interlinked, we will solve the first…

Q: Evaluate 1³e¹² dt.

A: Using integration by parts we can find the integral.

Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock (see the…

A: We have to find the rate at which the boat approaches the dock when 125 ft of rope is out.

Q: Calculate the derivative using implicit differentiation: x4w + w8 + wz2 + 9yz = 0 dw/dz =

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Q: -1 The function ƒ(x) = 6x + 2x¯ has one local minimum and one local maximum. This function has a…

A: Take derivative.Take the second derivative.

Q: The base of a three-dimensional figure is bound by the line y = 4 - x on the interval [-1, 2].…

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Q: 1. An ordinary differential equation (ODE) is an equation that relates x, y (function of x) and the…

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Q: The half-life of a radioactive substance is 4000 years. How long will it take for the substance to…

A: Half-life of a radioactive substance  years. i.e.  Let original size of substance is , Then

Q: Suppose f(z), f'(z) have the values shown: T f(x) f'(x) -2 2 -4 Find the following. d dr d da…

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Q: Compute the area of the region enclosed by the polar coordinate equation r = 2 - sin(0).

A: Area of the region enclosed by the polar coordinate equationr=2−sin⁡(θ)

Q: Let f(x) = -4 + 5x - x³. (a) Find the interval(s) where f(x) is increasing. (Enter your answer using…

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Q: Differentiate the function. f(x) = 260 f'(x)

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Q: f(x) = = -6 x + 3 3 3-x+6 if x < -5 if -5 < x < 5 if x ≥ 5

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Q: The graph below is of f'(x) for some function f(x) with domain (-00, 0o) (i.e., the graph of the…

A: Given graph of derivative of function

Q: 12/1 (6) Evaluate_lim (1-2)(72) = (A) - (B) -e¹4 818 (C) e-14 (D) 100⁰ DNE

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Q: Solve the following differential equations: y ln ydx + (1+x²)dy = 0

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Q: Suppose that z = x³ x³y², where both x and y are changing with time. At a certain instant when x = 2…

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Q: 2-3 Given A = -3 -3 2, B= 0 1 -3 01 -2, find 2A 4B. 0-3]

A: A=[2−3−32−30],B=[10−3−20−3]

Q: 26. Draw a scatter plot for the data provided in Table 3. Then determine whether the data appears to…

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Q: exi solve the Disserentail equatione using homogenous method (x₁² + y) dx-xdy -o

A: given differential equation

Q: The rocket, rising vertically, is tracked by a radar station that is on the ground 6 miles. from the…

A: The rocket is rising vertically, is tracked by a radar station that is on the ground 6 miles from…

Q: A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude…

A: A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude…

Q: Evaluate the integral using partial fraction method J (3x²+2) dx (x + 2) (x² + 4)

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Q: Calculate the derivative using implicit differentiation: x4w + w8 + wz2 + 9yz = 0 dw/dz =

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Q: 45. A 250(1.045) 4t

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Q: Write the composite function in the form f(g(x)). y = e³√z u = g(x) = y = f(u) = Then find the…

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Q: 5. Evaluate Σ n=3 O Cannot be determined O √73 O3+√√√31 O √√10+ √13+9+ √19+ √22 3n+ 1

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Q: A price p (in dollars) and demand x (in items) for a product are related by 2x² - 5xp + 70p² =…

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Q: A model for the population P(t) in a suburb of a large city is given by the initial-value problem dP…

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Q: . If a cup of coffee is left on a counter top, it cools off slowly. The temperature in degrees…

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Q: Write a polynomial function of minimum degree in standard form with real coefficients whose zeros…

A: Given zeros, 11i and -11i

Q: Consider the function f(x) = 12x - 80x³ +6. f(x) has inflection points at (reading from left to…

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Q: 0 A1 y=f(x) 3 A2 5 A3 7 A4 10

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Q: 1) Determine whether the sequence converges or diverges. If it converges, find the limit 1 a) an =…

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Q: Find a vector which is orthogonal to both v = (1,2,3) and u = (4,5,6). What is the area of the…

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Q: Consider the arithmetic sequence presented in the table below. What is the first term, a₁, and the…

A: The objective of the question is to evaluate the 1st  and 22th   terms of the given arithmetic…

Q: Consider the following. 8x² - y² = 7 (a) Find y' by implicit differentiation. y' = 16x 514 (b) Solve…

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Q: 2) Check the convergence/divergence of the following series a) Σ=1th, k >1 b) Σ1 - (-3)"} -)”) 5…

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Q: Find the limit. lim 0 0 cos(0) 1 sin(0) -

A: Explaination of the answer is as follows

Q: Find the inverse of the matrix B = B-1 = ab sin (a) Use B x = 1 di sin (a) f to solve BT 8 f ?х = 8…

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Q: Let f(t) = 6t2/3 + 5/3 (a) Find all partition numbers of f'(t). (Enter your answers as a…

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Q: Write the function as a product of linear and irreducible quadratic factors, all with real…

A: Consider the function

Q: dy Given that x²y + 7xy³ − x = 1, find dx dy dx || by implicit differentiation.

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Q: 6. Show that the minimum distance from the point (ro, yo) to the line ax+by+ c = 0 is given by…

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