Let f and g be functions that are differentiab

Q: Find the solution to the differential equation (dy/dx) = y2(x+7) such that y=6 when x=1 y=?

A: Please see the below picture for detailed solution.

Q: Given the vectors u, v and w in R³, which of the following calculations could result in the answer…

A: Given: Vectors u, v and w in R3. Final answer of Operation should be 3. Cross product of two…

Q: State whether the following is true or false by differentiation. 1 [cos²(x) dx = x + ¹/ sin(2x) + C…

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Q: Consider the curve defined by x² + xy + y² = 8. Find the slopes of the lines tangent to the curve at…

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Q: Find the velocity and position vectors of a particle with acceleration a(t) v(t) = ( (0, 0, 10), and…

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Q: A. Find all the partial derivatives of f(x,y) = 12x²y + 2xy + 5y²

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Q: Write the trigonometric expression as an algebraic expression in u and v. Assume that the variables…

A: This is question of trigonometry Here trigonometric  expression is given  We have to solve for it…

Q: The expression e^x/e^(7+x) can be written in the form e^f(x), where the exponent f(x) is a function…

A: To find the exponent as a function of x.

Q: Problem 3. A farmer has a rectangular field with dimensions 200m (north) by 150m (east). A sheep is…

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Q: Suppose that cot a = 1 2 and 0° < a < 90°.

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Q: dy dx = y-x y+x

A: To solve the following differential equation.dydx=y-xy+x

Q: Find the equation of the sphere if one of its diameters has endpoints (6, 4, -7) and (8, 8, -1)…

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Q: Given that the function f(x)=x²-2x+1 İS continuous on [0,2] and differentiable on (0,2), which of…

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Q: Solve the differential equation given below. 77-2 141H

A: The given differential equation is: dydx=7y-24x-1

Q: 3. The rate of change of the number of people who knows a certain rumor is proportional to the…

A: The rate of change dNdtof the number of persons who have heard a certain dt rumor over time is…

Q: 3. The figure on the right side shows the circumscribed (big circle) and inscribed (small circle)…

A: Given Data : In the figure we have given thecircumscribe  ( big circle ) and inscribed ( small…

Q: Kindly resolve this problem/solutions. Do mot copy the solutions above.

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Q: Find the an equation of the plane passing through points (−5,3,8), (10,9,8), and (-6,-3,8)

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Q: k X L n X L n Y d X + dy=o 2 (x²-xy + y²) dx-xydy =o

A: Disclaimer:  Since you have asked multiple questions, we will solve the first question for you. If…

Q: The position function of a particle is given by r(t) = (-51², 5t, t² + 4t). At what time is the…

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Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) 1 x + 3 ✔…

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Q: 06 * 1. Fish enter a lake at a rate modeled by the function E given by E(t) = 20+ 15 sin (Z). a rate…

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Q: When an object is dropped on a certain earth-like planet, the distance it falls in t seconds,…

A: The function is  s(t)=17t2 a) At t= 3 second S(2)=17×(2)2 S(2)=68 ft so , the the hammer will fall…

Q: If PCO) is a point in the unit circle and use the reference angle ۱۱۲ 6 = 6 to find the exact values…

A: Given P( θ ) is the point on the unit circle θ = 11π6

Q: Find the values of a and b that make f continuous everywhere. a = b = f(x) = X x² 2 4 X - 2 ax² - bx…

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Q: A particle's acceleration is given by the expression a(t) = 2t3 m/s². The particle was measured to…

A: we need to find the velocity and position of the particle.

Q: Question 3 Evaluate lim,-1+ f(x) if f(x) = = x +4 -x+1 x -1

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Q: Given the equation f(x) = a(x-p) + q what does the represent?

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Q: Consider the curve defined by the equation y — sin y = x − 1 for 0 ≤ y ≤ 2π Find d²y/dx² in terms of…

A: Solution: To find the second derivative of y with respect to x, we need to first find an expression…

Q: Solve using the quadratic equation. 2x^2 + 4x - 1  Mark all the solutions for x. 2.346…

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Q: For the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t.…

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Q: Let the graph below represent f(x) on the interval [−2, 2]. For which values of x is ƒ'(x) = 0? 3

A: We know that the function has derivative 0 at the bumps. So, from the given graph, f'(x)=0 will be…

Q: Find the sum of the given infinite geometric series. a₁ = -8, r=-0.17 O-9.64 O-13.88 O -6.3 O-6.84

A: The geometric series has a1=-8, r=-0.17. We have to find the sum of the infinite series.

Q: 03* Which of the following is the direction vector from the point A(4, -3, 2, 1) point B(-7,2, -4,…

A: Direction vector from point A to point B is AB→

Q: 1. (a) By reading values from the given graph of f, use five rectangles to find a lower estimate and…

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Q: [ (ln(7x))²dæ

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Q: 1) Find the domain: A) f(x) = √TXT 2) Find the range: A) y 1-2x-x² √2X (x-1) C) lim 241+ x-1 X--XX…

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Q: At a certain factory, the marginal cost is 2(2q - 3)² dollars per unit when the level of production…

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Q: Use the information given below to find cos (a −ß). 8 17' 3 tan B with B in quadrant III 4 sin a =…

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Q: Rewrite sin (2 sin ¹4v) as an algebraic expression in v.

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Q: Find the exact value of cos(-165degrees) by using a sum or difference formula.

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Q: For the following functions find the partial derivatives toe te te + ехе ће хе Fel t tel дгох даду…

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Question 2 Solve the following simultaneous equations xy = 256, 3log (v) = 1

A: Explanation of the answer is as follows

Q: can you write it and take a picture becasue I am very confused with how it is written

A: The given function is; y=(6x^2-4x)/(5x^2-6)

Q: Where does the line with parametric equations −1+3t y = 2 - 2t 2 = 3+ t intersect the plane 3x + y -…

A: Given parametric equation of line x = -1 + 3t y = 2 - 2t z = 3 + t Given plane 3x + y - 4z = -4

Q: Find the total area bounded by the x-axis and the curve y(x) on the indicated interval. Enter your…

A: To find the total area bounded by the x‐axis and the curve y=fx on the indicated interval.fx=27x-9;…

Q: a) α (²)+(!)-(3) Suppose the above equation is expressed as Ax = b with x = matrix form as (Ab)= = α…

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Q: Find the derivative of the following -→7 Fcx) = sin-¹ (In x)

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Q: what is -16 IT 3 52" ST 5² p²rin & dp dp de 0

A: Recall the formula:

Q: QUESTION 16 What is the area under the curve between x=0 and x=П y=xcos 2 A=2-2 A=27-4 A=2.83…

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