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Q: A. Find the arc length of the curve c(t) = (x(t),y(t)) = (sin(3t), cos(3t)) for 0 les or equal to t ...

A: Given the curve we need to find the arc length in the interval 0 les or equal to t and less or equal...

Q: Solve the following IVP using Laplace Transform. (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y...

A: given Initial Value Problem is, (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y=e^(-t), y(0)=0 y...

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A: We know that simple interest on a given sum is given as: INT=p·r·t , where p is the principal sum, r...

Q: I need help with 20

A: We find dydx using implicit differentiation. x2-xy+y2=32x-y+xdydx+2ydydx=02x-y-xdydx+2ydydx=0xdydx-...

Q: Solve the equation using the quadratic formula. 14x - 4 = 7x² %3D

A: The given quadratic equation is

Q: Consider f(x) = x – 5 and g(æ) = x2 – 81 • You must combine all like terms before you submit your an...

A: Given: f(x)=x-5 and g(x)=1x2-81

Q: Times for a bank teller to serve a customer are exponentially distributed with a mean of 2 minutes. ...

A: Given that Times for a bank teller to serve a customer are exponentially distributed with a mean of ...

Q: Calculus Question

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Q: A 13 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding dow...

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Q: Solve the following IVP for the 2nd order linear equations y′′−4y′+9y=0 y(0)=0 y′(0)=−8

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Q: Question 8. Consider the surface defined by x² – - = 1. Draw the traces of this surface correspondin...

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Q: The rate of change of the value of goods exported from a country between 1990 and 2001 can be modele...

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Q: Our goal is to use function notation to represent the total fuel cost, in terms of the distance (in ...

A: Given that we need to represent volume using function notation in terms of the distance d of a trip...

Q: Find the value a>0 such that the tangent line to the graph of f(x) = x^2(e^-7x) at x = a passes t...

A: The given function is fx=x2e-7x. At x=a , fa=a2 e-7a. The derivative of fx=x2e-7x is f'x=2x e-7x-7x2...

Q: Trigonometric integrals Evaluate the following integrals. ∫cot5 3x dx

A: Evaluate: ∫cot53xdx

Q: The greatest integer function is defined by [x] = n, where n is the unique integer such that n< x < ...

A: given: the greatest integer function [x]=n where n≤x<n+1 the given expression are: limx→-5.8+xlim...

Q: Evaluate the following: fx sin 3xdx

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Q: 1. lim x-> -7 f(x)= 2. lim x-> -3 f(x) = 3. lim x->-2- f(x)= 4. lim x-> 1 f(x) = 5 ...

A: Note : As per the authoring guidelines,when multiple subparts are in one question,then only first th...

Q: What is the property of the function and its inverse? Graph the two functions show that f[f-1(x)] =x...

A: Given: f(x)=1/2(x-1)

Q: Consider the function g(w) = 3ln(w) - w for w > 0

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Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

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Q: Determine the following limit or state that it does not exist. 4x-64 lim X-4 X-4 Simplify the expres...

A: Given, the limit is We have to evaluate the limit or state that it does not...

Q: Fill in the blank/s:

A: given that limx→af(x)=L.

Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in ...

A: Given length of a rectangle, l =25 cm Width of a rectangle, w=36 cm We know that, Area of...

Q: EXAMPLE 6 Slopes of tangent lines Find for the following curves. Interpret the dx result and determi...

A: a). x=ft=t, y=gt=2t Differentiating with respect to t, we get dxdt=1 & dydt=2·12tdxdt=1 & dy...

Q: We are standing on the top of a 1520 feet tall building and launch a small object upward. The object...

A: Given the vertical position of the object , measured in feet after t seconds is, ht=-16t2+224t+1520

Q: A force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length. How much wor...

A: force = 8 lb spring stretched (x)= 8 in. According to Hooks law,F=-k×xk=-Fxk=-88k=-1 lb/in.

Q: Explain the best way to evaluate 900!/899! without a calculator

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Q: Calculus Question

A: 1

Q: Explain Properties of the Solutions of y''+y=0 ?

A: Given differential equation, y''+y=0 is represented by linear differential equation with constant co...

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. xe269x dx U...

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Q: Use intercepts to graph equation. 6x - 9y - 18 = 0

A: 6x-9y-18=0. To find x-intercept, put y = 0 in the given equation, we get 6x-90-18=0⇒6x=18⇒x=3 Theref...