6. f(x) = x² – 4x, g(x) = 2-3E %3D a) (f - g)(-5)

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: You wish to minimize f(x)=10X(1^2 )-X_(2^2 ). If you use steepest descent starting at (1,1)will you…

A: Consider the given function, fx,y=10x2+y2 we have given the starting point 1,1. Now, ∇fx,y=20x,…

Q: Find the marginal revenue function R(X) = x(19 - 0.02x) R'(x)= [

A: To differentiate a function, we use the following differentiation rule. Sum rule Difference rule…

Q: 20. In "x" years from now, one investment plan will be generating profit at the rate of R₁ (x) = 50+…

A: Given: R1x=50+x2R2x=200+5x

Q: The volume of fluid in an IV (intravenous) drop decreases according to the mathematical model…

A: The  given model of the volume of fluid in IV drop versus time is:   V=-0.110t+1   Where, V is the…

Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: 3. The Critical Point of y=xe*

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Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

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Q: Minimize S = xy + xz + yz subject to xyz = 3 v

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Q: 4 solve the D.E " -X² Joly =0 3x2 ydx + LY

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Q: If a quantity grows/decays at a rate proportional to its size, its growth can be expressed as dQ/dt…

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Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

Q: 11. f(x) = x² + 7x + 10 Opens up/down: Vertex: Axis of symmetry: Solution(s): y-int:

A:

Q: If the utility depends only on the consumption of x and u (x) = ( 2a¯i + 3) (-4xi +2), is Marginal…

A: Given u(x) = 2x-12 + 3-4x14 + 2

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

A:

Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

A:

Q: Pind the critical point of y=1+hx

A: Given: y=1+lnxx We know that for any given functiony=fx in it's domain, at critical point derivative…

Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

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Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

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Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A:

Q: In a hypothetical city, there is a population of 200,000 people.  During the year 2000, there were…

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Q: 5. Consider the problem: A water bucket is being filled with water from a water faucet at a constant…

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Q: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

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Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

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Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: Given that  C = 0.001x3 + 3x + 432  To Find the number of units x that produces the minimum average…

Q: 2y – x = 3t y+ x' = 3et 3e-t x (0) = y (0) = 0 3s2 L (x) = (s+1)(s–2)(s²+1) 3(2s3 –s–1) s2…

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Q: How do I solve dx/dt+2x=3 with a particular solution of xp=3/2?

A: To find the general solution of the equation, given the particular solution

Q: 3. x - y=t + 3 4. x = VT-T; y =t- 3t 5. x = vE + 2; y = t² - 3

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Q: 2) A tank, which has a capacity of 100 L, is initially half full of a solution that contains 50g of…

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Q: A manufacturing company has been experimenting with a new additive that is used to reduce polluting…

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Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

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Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: 7) 4 sec-1 Vx is equal 1 1 1 1 a) 2xvx- 1 b) 2VxVx- 1 2xv1-x d) /xVx-1 8) The derivative of y = In…

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Q: 9. The total cost and total avenue, in dollars, from producing x couches are given by C(x) = 1000(x²…

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Q: 4. Obtain the general solution of x² y2 = dx

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Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

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Q: Find the solution to the initial value problem as an explicit function of the independent variable.…

A: Given : (t2+1)y'+y2+1=0,   y(3)=2

Q: 2. For a substance D, the time rate of conversion is proportional to the square root of the amount x…

A: Given For a substance D, time rate of conversion is proportional to the square root of the amount x…

Q: 2) Show that X₁ = Xo {1+¹*exp(-)} -DC₁ = v(C₁-Cs). satisfies the steady state growth concentration…

A: Given  -DCL'=vCL-CS

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: It is minimum average cost per unit problem.

Q: Find the marginal revenue function. R(x) = 3x-0.05x2 R'(x)=

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Q: 16. If x x y and y x z, then how is x proportionally related to z?

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Q: s(x,y)=ex^2+y^2 How do I find the critical point of this function.

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Q: A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

Q: If X has hazard rate function Ax(t), compute the hazard rate function of aX where a is a positive…

A: 8) We know that if F(x) is the cumulative distribution function of random variable X  Than…

Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: 3. The Critical Point of y = xe-*

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.