-Find the directional derivative of f(x, y, z) = x²yz+z³y, as you leave the point (1,1,1) heading in the direction of the point (−3, 1,4).

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A: Given query is to find rate of change of volume.

Q: During a walk-a-thon, Noah's time in hours, t, and distance in miles, d, are related by the equation…

A: The equation is given as , 13d=t where t is time in hours and d is distance in miles.

Q: Find the area enclosed by the curve x = t² - 2t y = √t and the Y axis.

A: Eliminate the parameter t and draw the graph then find the definite integration to get the area.

Q: -3 2x + 1

A: Please see the below answer.

Q: Find the acute angle (in degrees) between the planes x + 3y - 5z = - 6 and 2x + y 4z = 9. Question…

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Q: Sketch the given region of integration R and evaluate the integral over R using polar coordinates. 1…

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Q: tion about the origin. hat is the 13. Let T: R2 R2 be the linear transformation such that T(e₁) and…

A: Please see the below picture for detailed solution.

Q: Consider the function f(x) = 4x² - 4x4. (a) Find all critical numbers c of f. C = (b) f is concave…

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Q: A trough full of oil of specific weight w lb/ft3, has a length of 10 ft and ends in the form of a…

A: Specific Weight = w lbft3Length of trough = 10 ft,Width = 8ft,Height = 5 ft

Q: sinh(4ln(4x))

A: Given query is to simplify the expression.

Q: 12. X S (12t² – 8t) dt

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Q: › Consider the differentiable functions f(x) and g(x), for which f(0) = 4, g(0) = 3, f'(0) = -11,…

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Q: A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is…

A: We are to show  how to approximate the required work by a Riemannsum. Then express the work as an…

Q: The base of a solid is the region in the first quadrant bounded by the graph of y = 1- and the 2-…

A:

Q: The circumference of a sphere was measured to be 78 cm with a possible error of 0.5 cm. Use linear…

A: Solution: C = 2πr & SA = 4πr2 = C2/π. i.e. surface area as a function of the circumference is…

Q: Maximizing the Volume of a Box A box with an open top is to be constructed from a square piece of…

A: Four square pieces at the corners of a square cardboard of size 12 × 12 Inches  And it was made into…

Q: An object is moving with velocity (in ft/sec) v(t) = t² – 3t+4. At t = 0, the object has a position…

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Q: A rotating light is located 20 feet from a wall. The light completes one rotation every 4 seconds.…

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Q: Find dx dt dx dt at x = −5 if y = −4x² – 5 and dy dt = -4.

A: y=-4x2-5given  dydt=-4d dx(xn)=nxn-1d dx(constant)=0

Q: Consider the following. -5 -4 -3 -2 + range 1 y 5 4 2 1 -1 -2 -3 -4 -5 1 + X 2 3 4 5 Use the…

A: Consider the curve

Q: Find the horizontal and vertical intercepts for + s² - rs = 16, if the r-axis is the horizontal axis…

A: To solve the following problem

Q: A = (5,-2), B = (-1,-4) AB=(x, y) X= type your answer... y= type your answer...

A:

Q: For each of the following integrals, decide if it is a proper integral or improper integral. Justify…

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Q: Evaluate the integral using s integration by parts (3 (r³ +9r² + 1)e³r dr

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Q: When recording live performances, sound engineers often use a microphone with a cardioid pickup…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: f g is a differentiable function, find an expression for the derivative of each of the following…

A: Given query is to find indicated derivative.

Q: Find a fourth-degree polynomial with integer coefficients that has zeros 3i and -1, with -1 a zero…

A: To find a fourth-degree polynomial with integer coefficients that has zeros 3i and -1, with -1 a…

Q: A police car is located 30 feet to the side of a straight road. A red car is driving along the road…

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Q: Find the complex zeros of the quadratic function. Graph the function and label the intercepts.…

A: Given equation:- fx=x2-12x+52

Q: )(a) Let g(x) g'(x) = = (c) Let H(x) = H'(x) = 6 √7x² + 3 (b) Let G(x) = √√√8 + √5x. Find G′ (x).…

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Q: 8. Draw a right triangle (with labeled sides) representing the angle (cot-¹(x/2)) and find sin(cot…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Derivatives inverse thank you

A: Here we have to find the tangent line.

Q: Consider the following function: Step 4 of 4: Enter the x-values of any relative minima, maxima, and…

A: A detailed solution is given below.

Q: Evaluate cosh -1(3).

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Q: Magnitude: A = 10 A Direction: 060° A = (x, y). Round your answer to the nearest hundredth X= type…

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Q: 2. The function P(t) 2t² + 3t + 1models the population of fish in a lake, where P is the population…

A: We put t=2000 and 2008 respectively to find the value of P(2000) and P(2008).

Q: Find all the real zeros of the polynomial P(x)=x²-x³-3x²+x+2 List the real zeros below. If there is…

A: Solution: Given Polynomial, P(x)=x⁴ -x³ -3x² +x+2

Q: J sin’rVcos ad

A: Here is the solution:

Q: Suppose f(-10) = -9 and f'(-10) = 8. Find the following. d (10x² + x − 9) f(x) at x = −10 is dx d de…

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Q: Find the dimensions of a rectangle with a perimeter of 160 ft that has the largest possible area.…

A: We know formula for rectanglePerimeter of a rectangle=2l+bArea of a rectangle=length×breadthGiven:…

Q: A manager estimates the daily output of their robot model OYW931 at one of their factories to be…

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Q: Solve the initial value problem. Ꮎ +y=3 sin 0, 0>0, y dy de E|N = 1

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Q: If the vector field F = (f.g) is source-free (zero divergence), then a stream function y exists such…

A:

Q: sin 0 cos² 0-cos 0-2 2. S. de 3. fx² tan-1 (1) dx 4. f(cot ¹ x + tan-¹ x) dx

A: The given integral is;  3) x2tan-1(x/2) 4) cot-1x+tan-1x.

Q: Add as indicated. Express your answer as a single polynomial in standard form. (x² + 4x +9) + (8x-7)…

A: The given expression is: x2+4x+9+8x-7  Express as a single polynomial in standard form.

Q: A street light is at the top of a 18 ft pole. A 5 ft tall girl walks along a straight path away from…

A: As given the girl walking away from pole with a speed of 7ft/sec.Height of the pole is 18ft and girl…

Q: Use the first derivative to find all critical points and use the second derivative to find all…

A: Given:   fx=x4-18x2+4 To Find:  By using the first derivative test to find all critical points  and…

Q: A graphing calculator is recommended. Graph the function in each of the given viewing rectangles.…

A: The given function is: kx=x432-x2+2

Q: Use Newton's method to approximate the value of 45 as follows: Let 13 be the initial approximation.…

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Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

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