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Q: 8) Write a system of equations that models the following problem. Then solve your system to solve th...

A: Let the speed of the child is= x m/sec and the speed of the walkway is = y m/sec So the speed while ...

Q: Find the particular solution. y' = ex − 6;    y(0) = 3

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Q: Calculus Question

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: Using calculus, find the absolute maximum and absolute minimum of the function f (x) = 6x² – 36x + 5...

A: Given,           fx = 6x2 - 36x + 5  and the interval is -3, 4

Q: Consider the following. 2xy  dy dx  = y2 + 8 Rewrite the differential equation with separa...

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Q: If $P is invested for n years at 13% compounded continuously, the rate at which the future value is ...

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Q: Find the derivative of the function. h(t)= (t+1)^2/3 (2t^2-1)^3

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Q: 300,000 The cost C (in dollars) for ordering and storing x units is C = 8x + What order size will pr...

A: Approach: take the first derivative of the given function and find the point where derivative is ze...

Q: Compute limx→∞ 4x^3+6x−2 / 3x^3−2x^2+x+1 .

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Q: I have two functions. Function f models total world population x years after 2000 and function g mod...

A: I have two functions. Function f models total world population x years after 2000 and function g mod...

Q: Graph the equation y = 2x - 2 .Let x = -3, -2, -1, 0, 1,2, and 3.

A: Given equation is y=2x-2. We will put value of x and we will get respective value of y, x -3 -2 -...

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

A: fx,y=xy+8x+8yfx=y-8x2fy=x-8y2fx=0 and fy=0y-8x2=0       x-8y2=0x2y=8              xy2=8Now we have t...

Q: How do I find the derivative at the 4 places where x=1

A: Given function is x2+y22=254xy2 We have, some rule of differentiation, ddxxn=nxn-1 ddxuv=vddxu+uddxv...

Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight tow...

A: Let AB represents the distance from the spot light to the bottom of the wall which is 12 m. Let heig...

Q: Find the second derivative of each of the following functions. s=1/2t-1 y=x2tan2(3x)

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Q: Find the area of the parallelogram that has the given vectors u = j,   v = j + k as adjacent sides. ...

A: Known facts: The area of the parallelogram that has the given vectors u  and v as adjacent sides is ...

Q: For the equation given below, evaluate y at the point (1,0). 2xy – 2x + 2 = 0.

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Q: Consider the following. y = x? - 4x + 3 Find the relative maxima, relative minima, and points of inf...

A: The given function is y=x2-4x+3. Compute the critical points as follows. dydx=0ddxx2-4x+3=02x-4=02x=...

Q: Is this the correct way to solve if not how do you solve ? Differential

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Q: The boundary of a lamina consists of the semicircles y = V4 - x2 and y = V36 - x2 together with the ...

A: Given Semicircles are y=4-x2 and y=36-x2 Here Green curve represent y=4-x2 semicircle is of radius ...

Q: A potato is launched vertically upward with an initial velocity of 116 feet per second from a potato...

A: Your question has 6 subpart we will solve first three subpart. Please resubmit question with subpart...

Q: Suppose that 6(g(x))2+13x=5x3g(x)−12, and that g(−1)=−1. Find g′(−1).

A: Given Data: Equation: 6gx2+13x=5x3gx-12 Conditional Value: g-1=-1   The derivative of the given equa...

Q: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. Fin...

A: Given data:   The degree of the polynomial is n=3. The first real root of a polynomial is x1=4. The ...

Q: Simplify:

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Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as follo...

Q: Find an equation of the tangent to the curve at the given point. x = 6 + t2 − t,    y = t2 + 7,    ...

A: x=6+t2-tdxdt=2t-1 y=t2+7dydt=2t dydx=dydtdxdt=2t2t-1

Q: Demand for an electric fan is related to its selling price p (in dollars) by the equation n=5060−110...

A: Demand for an electric fan is related to its selling price p (in dollars) by the equation, n=5060-11...

Q: Find the exact length of the curve.

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Q: 1) Find the derivative of the function. Simplify if possible.? = sin ? cot ?   2) Evaluate the limit...

A: 1) We have to find derivative of y=sinxcotx It can simplify it as: y=sinx·cosxsinxy=cosx Differentia...

Q: Describe the additional properties of the inverse trigonometric functions?

A: Inverse trigonometric functions are also known as “Arc Functions” on account that, for a given cost ...

Q: Is the set of functions f1(x) = ex+2, f2(x) = ex-3 linearly dependent or linearly independent on (−∞...

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Q: The answer of the problems are included. please show me the work to get to the answer

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re...

Q: 2. Given *(t) = (V2 – t, (e* – 1)/t, In(t + 1)) a. Find the domain of * b. Find dř(t) dt c. Find lim...

A: we have been given the vector r→(t)=(2-t,(et-1)t,ln(t+1))  

Q: Use the upper and lower sums to approximate the area of the region using the given number of subinte...

A: Given Data : Graph of Function f(x)=1-x2 To Find : Upper Sum & Lower Sum to approximate the are...

Q: The graph of g consists of two straight lines and a semi- circle. Use it to evaluate each integral. ...

A: Given, The small box of the graph is 1 x 1. To find: a  ∫02gx dxb  ∫26gx dxc  ∫07gx dx

Q: Let f(x) = cos (x). %3D If it is true that f" (x) = x(f'(x))ª for some constant a, find the value of...

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Q: Maximizing Profits  A division of a certain company manufactures a pager. The weekly fixed cost for ...

A: Given:V(x)=0.000001x3-0.03x2+70xR(x)=-0.04x2+180x      0≤x≤7500weekly fixed cost ofr the division$20...

Q: Use Newton's method to approximate a root of the equation 3x" + 2a* + 2 = 0 as follows. Let ¤1 = 2 b...

A: Given 3x7+2x4+2=0 To find root using Newton's method for approximation with initial approximation x1...

Q: The graph of f is shown. Evaluate each integral by inter- preting it in terms of areas. (a) ff f(x) ...

A: Given, The graph of function f(x) is shown as: use integration property: ∫abfxdx=∫acfxdx+∫cbfxdx us...

Q: . A trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough i...

A: Given that a though has ends shaped like isosceles triangle with width 3 m and height 4m and trough ...

Q: Without showing the details, explain how to condense ln x - 2 ln(x + 1).

A: Given: lnx-2lnx+1

Q: Calculate T, and M6 for dx. (Use decimal notation. Give your answers to five decimal places.) T - M6...

A: Let, I=∫695x dx To calculate trapezoidal T6 Δx=9-66=36=0.5x0=6,  x1=6.5,  x2=7,   x3=7.5,   x4=8,   ...

Q: Find the tangent to the curve a"-ly = x"

A: we have to calculate tangent ( dy/dx) where a is any constant an-1ddxy=ddxxn

Q: a) What is the particle's position at time 2? b) What is the particle’s displacement from t= 1 to t=...

A: (a) The function representing the position is  X(t)=t3-15t2+48t. To find the position of the particl...

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.