1. Use deductive reasoning to show that the following procedure produces a number that is three times the original number. Procedure: Pick a number. Multiply the number by 6, add 10 to the product, divide the sum by 2, and subtract 5. Hint: Let n represent the original number.

Q: 89. y √3+ Vy 1- √5 3 √r + √2 5 95. Vx² + 1 - x 91. 91-96 Rationalize Numerator Rationalize the…

A: 94) [sqrt(x)-sqrt(x+h)]/[h sqrt(x) sqrt(x+h)].   95) sqrt(x2+1) -x 96) sqrt(x+1) - sqrt(x).

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form…

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Q: 1. Given the algebraic function x² xy + y² = 3

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Q: If 2 is a differentiable function of x and y satisfying the equation sın (x²z + y²) + 2x³=y2²+2,…

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Q: The population of a town is increasing at a rate given by P'(t) = 420.0181 where P is the population…

A: The population of a town is increasing at a rate given by P't=42e0.018t, where P is the population t…

Q: Find the following derivatives. Express your answer in terms of the independent var 3x-3z 2y +3z Ws…

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Q: 2. A balloon is released upward from the ground at a speed of 5 m/s. When the balloon was 10 m above…

A: Concept Used: Rate of change Rates of change are defined as the rate at which one quantity changes…

Q: 1. Given the algebraic function x² − xy + y² = 3

A: Here is the solution:

Q: Give the actual solution of dy -= 2xy² + 3x²y² if y = -1 when x = 1 dx

A: Given query is to find the solution of the differential equation.

Q: 2. A balloon is released upward from the ground at a speed of 5 m/s. When the balloon was 10 m above…

A: In such type of problem we generally use the pythagoras triangle rule . ie.x2+y2=z2

Q: #1 Cπ/2 ST 0 (8 + 4 cos x) dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: lim Y->+00 In (ett & +4e¯Y)

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Q: 1. Find the equation of the tangent line to the given curves at point of tangency, if given. 2. y =…

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Q: Make an ORIGINAL EXAMPLE OF "Elimination of Arbitrary Constants (Differential Equations)" A) GIVEN…

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Q: 5. Find the second derivative of f (x) (x² + 1)³.

A: Given query is to find the second derivative.

Q: 44. Suppose that f(4) = 2, g(4) = 5, f'(4) = 6, and g'(4) = -3. Find h'(4). (a) h(x) = 3f(x) + 8g(x)…

A: Simply use differential formula and we can easily solve it Please see the solution Thanks

Q: 8. Consider the following sign diagrams relating to the graph of y = f(x) Sign diagram of f(x): +…

A: Given 1.   2.

Q: Use vector notation to describe the points that lie in the given configuration. (Let t be an element…

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Q: Find an arc length parametrization of r(t)=

A: Given, r(t)= <6t2,t3> Formula : Length of parameterization: L= ∫0t|r'(t)| dt

Q: Find an arc length parametrization of r(t)=⟨e^t*sin(t),e^t*cos(t),9e^t⟩

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Q: (x + 2y ²) dy (xy²-y) dx + ( 0

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Q: The equation P=15sin(2πt)+90 models the blood pressure, P, where tt represents time in seconds.…

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Q: 11. The Australian Teal Frog is a species that has become endangered due to inability to defend…

A: As per Bartleby guidelines we only give first three questions answers. Please repost for other…

Q: Solve the DE (6x + y2) dx + y (2x - 3y) dy = 0. Hint: Exact O 3x^3 + xy^2 - y^3 = c O 3x^2 - xy^2 -…

A: Given differential equation:- 6x+y2dx+y2x-3ydy=0

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: If z is a differentiable function of x and y satisfying the equation sin(x²z+ny²) + 2x³ = yz² + 2,…

A: Let's find partial differentiation at given point.

Q: 2. Evaluate the following limit (tabulate). 4- x² lim x+2 3-√√x² + 5 O None of the choices. O 0 O It…

A: limx→ 24-x23-x2+5

Q: b) lim 818 c) lim 818 2x³-3x+1 3x4+7x³-2x-1 sin (x+3) X

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Q: 1. Find the equation of the tangent line to the given curves at point of tangency, if given. 3.…

A: =2SOLUTIONGiven data:-The equation on the given curve is y=7x-63…

Q: 13. Find the point (x, y) on the curve y = x² + 1 that minimizes the distance to the fixed poi (4,…

A: Given curve:- y=x2+1 We know distance between points x1,y1,x2,y2d=x2-x12+y2-y12

Q: y = tan-¹(7x)

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Q: 2x Eliminate the arbitrary constants of y=x²+c₁e²x+c₂e 2 3x

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Q: 1 c) [xln (25) dx =

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Q: y (8x² + 11x-4) 1¹0

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Q: The weekly demand for Math Wars - The Force Multiplies video games is given by Р 420 x - 6 +4000…

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Q: Solve the problem. Find an equation for the least squares line representing weight, in pounds, as a…

A: Solution: We can directly use here Excel for regression, Step1) Enter data in Excel.

Q: Based on the given table of data, compute each of the following derivatives (fog)'(2) (gof)(4) = X 2…

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Q: 3 dx - (3xsiny + 2ysiny-2) dy=

A: Let's solve given differential equation.

Q: w = xy + yz + xz, x = r cos 0, y = r sin 0, z = re. Findow, when r = 2,0 = π/2. dw 20

A: Concept: Partial derivative: Let's say we have a function f(x, y) that depends on the values of two…

Q: Find an integrating factor for the D.E. (2xy³ – 2x ³y ³ − 4xy² + 2x) dx + ( 3x²y² + 4y) dy = 0

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Q: Question 7 In the Four-Step Rule, which among the steps is the most important, upon which the…

A: A differential equation is an equation that involves a function and it's derivatives.

Q: Make an ORIGINAL EXAMPLE OF "Variable Separable" A) GIVEN B) SOLUTION C) ANSWER D) WITH EXPLANATION

A: Given expression, Solve 1+x2dydx=1+y2

Q: Below are the graphs of 6 functions A-F. There are also graphs of 5 derivative functions 1-5. Match…

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Q: Determine the rate of change of the function g(x, y) = y² tan(x − 2y + 4) 2) in the direction of the…

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Q: Name: opez Show work/reasoning. 1. Solve the initial valued problem: y'=e' with y(0) = 0. Give your…

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Q: y = ln(5x² + 7x + 4)

A: Given y=ln5x2+7x+4

Q: Suppose that y is a differentiable function of x and z = cos (x5,8). Express in terms of x, y, and…

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Q: Find the solution of the given DE. Linear or Bernoulli

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Q: Find the differential equations of the following primitives by eliminating the arbitrary constants.…

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Q: Which of the following are equivalent to asking "Find the derivative of f(x) = x² at x = 3"? (Select…

A: Topic- limits ,functions and derivatives we are given f(x)=x2 x=3 we know that slope of tangent line…