Use the Chain Rule to find dw/dt. dw dt || w = xeylz, xey/z, x=t5, y = 9-t, z = 2 + 9t X

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A: We need to find derivative and dot and cross products.

Q: Given that sin(20)? sin0 = = 1 0<0<= /₁ 3 and 2, what is the value of

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A: According to Poiseuille's laws The velocity V of the blood is given by V = k( R2 - r2 )  where R is…

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Q: the integral using integration by parts: [p³ In

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Q: Find the partial derivative of f(x, y) = 2x³ - 3xy + y² with respect to x at the point (1, 6, 20).

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: -) Solve the linear system, KER x+x₂+(2k-1)x=8 kx₁ + x₂ + x₂ = 1 kx +(K-2)x₂ +2(4-3k) x₂ = 3k-26 2x…

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Q: Consider the parametric curve: x = 7+4 cost, y=9+4sint, 9+4 y = sint, The cartesian equation of the…

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Q: Consider the function f(x) = 3 – 7x² on the interval [-6, 6]. (A) Find the average or mean slope of…

A: Consider the function fx=3-7x2 on the interval -6, 6. (a) To find the average or mean slope of the…

Q: The base of a solid is the region in the first quadrant bounded by the - and y-axes and the graph of…

A: The region in the first quadrant bounded by th x and y axis and the graph y=3-xx+1 Graph

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be…

A: The given differential equation is;  y'(t) + 2 y(t)/t = 2 -5t, y(3)=0.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). r(t) = 2t²1 - 4tj + ²t³k (a) r(t) (b) r"(t) (c)…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: 70. a(t) = t² − 4t+6, s(0)=0, s(1) = 20

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F=…

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Q: Find the absolute maximum and absolute minimum values off on the given interval. f(x) = 14 + 2x -…

A: For a given function f( x )  First find critical points by f'( x ) = 0 Given function  f( x ) = 14 +…

Q: (d) Intervals where the graph of f is increasing, decreasing, concave up and concave down. Use a…

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Q: * The legs of a right triangle are measured as 50 centimeters and 70 centimeters, with the maximum…

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Q: [x² 18-9x . if -1 ≤ x ≤0 if 0 < x≤ 1

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Q: Consider the function f(x) = 2 - 2x²/³ on the interval [1,1]. Which of the three hypotheses of…

A: We check the hypothesis of Rolle's Theorem .

Q: Identify the inflection points and local maxima and minima of the graphed function.

A: The given function is:y=-2x+sin(4x) ;            -5π12≤x≤5π12

Q: 2

A: Here the given function y=9/x and x belongs to 1to4

Q: Find an equation of a plane containing the three points (2, -1, -5), (0, -6, -4), (0, -5, -2) in…

A: Given three points and the coefficient of x (-11) in the equation of plane.

Q: Assume x and y are functions of t. Evaluate dy dt (Type an exact answer in simplified form.) for 3xe…

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Q: (a) Solve for x (find the exact value, do not approximate): €²x = 2 et + 24.

A: We have to solve for the value of x.

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 2x3/2…

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Q: X 2x X log2*

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Q: 3. Find the absolute minimum and absolute maximum value of the function f(x, y) = eªy subject to the…

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Q: Let C₁ (t) esti + 7 sin(t)j + tªk and c₂ (t) = e¯5¹i + 5 cos(t)j – 7tªk. (Enter your solution as a…

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Q: 2. Find the derivative of y in each case. (a) y = sin³x + cos³x

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i + 4 sin(t)j; t = -4 T() = (₁7⁰7) V17) ,0, 3…

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Q: x3 If f(x) = ª -3 f'(x) = t²dt then

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Q: 89. Let f be a continuous function for all real numbers. Let g be the function defined by g(x) = f*f…

A: The solution is shown in step-2

Q: If a sequence C1, C₂, C3, ... has limit K then the sequence e¹,e,e,... has limit e*. Use this fact…

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Q: solve the differential equation (full procedure) dy/dx= 2sec2x-cos(x), y=0 when x=1

A: solve the differential equation (full procedure) dy/dx= 2sec2x-cos(x), y=0 when x=1   integration of…

Q: QUESTION 16 Change the order of integration and evaluate the integral. 7/2 7/2 6 cos q Į Į Į 9772…

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Q: Compute the given integral. - [ s 1 9x² + 1 dx +C

A: Explanation with required formula:-

Q: A used car is purchased in 2019 and its value decreases according to V(t) = 5400(0.96) where t is…

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Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x³ - 3x on…

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Q: Evaluate the integral and interpret it as the area of the region. Be sure to include a graph of the…

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Q: · ƒ' (5) = 0, ƒ' (x) 0 when x > 5, ƒ" (2) = 0, ƒ” (8) = 0, f″ (x) 8, ƒ" (x) > 0 for 2 < x < 8, lim…

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Q: A colony of bacteria in a culture grows at a rate given by N(t) = 2^t/5, where N is the number of…

A: Nt=2t5Kt=et3

Q: · (-²)* +7 has the ---Select-- asymptote y = The exponential function f(x) = · ( ² )* + · This means…

A: NOTE: Refresh your page if you can't see any equations. . the given function is an exponential…

Q: It was shown in class that the closed cylindrical can of maximal volume that may be constructed to…

A: Given that , Surface area = SA units2

Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of…

A: Given Data: The volume of the storage shed is: V=729 ft3 The cost of base concrete is: Bc=$5 per…