Suppose that a continuous income stream has an annual rate of flow given by f(t) = 5000e20.01t, and suppose that money is worth 7% compounded continuously. Create the integral used to find (a) the total income for the next 5 years. (b) the present value for the next 5 years. (c) the future value 5 years from now.

Q: A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20 cosh (x/20) ...

A: Given: A telephone line hangs between two poles 14 m apart in the shape of the catenary y=20coshx20-...

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Q: Plot the point (-4, 4π/3) in polar coordinates and find its rectangular coordinates.

A: Given -4,4π3

Q: Verify by differentiation that  ∫ ln x dx = x ln x - x + C.

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A: A function f(x)=sin4x2x. We have to graph this function in an appropriate viewing rectangle.

Q: Differentiate the function using one or more of the differentiation rules. y= (2x+ 5)10 y' =D %3D

A:

Q: The radius of a circular manhole cover is estimated to be 16 in. with a maximum error in measurement...

A: Due to our guidelines I am solving only first problem  The radius of circular manhole r = 16 in

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Q: Find f(-x) - f(x) for the given function f. Then simplify the expression: f(x) = x3 + x - 5.

A: Given function,  f(x) = x3 + x - 5 To find f(-x) - f(x) 

Q: Solve the polynomial inequality 2x2 + x < 15 and graph the solution set on a real number line. Ex...

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A:

Q: If one of the zeroes of the quadratic polynomial (k-1)x2+kx+1 is - 3 then find the value of k

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Q: Describe the domain of the function ƒ(x, y) = √(y - x2).

A: Function: f(x,y)=y-x2The domain of the function f(x,y)=y-x2 isy-x2≥0

Q: 1 -dx. J x2 + 2x +2

A:

Q: This is a plan of a bedroom drawn to a scale of 1 to 50 5.5 cm 1.2 cm 2. 3 ст 0.8 cm 2 cm a) What do...

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Q: hello i need help wolving this example

A:

Q: The graph of a logarithmic function is given. Select the function for the graph from the following o...

A: From the given figure, it is observed that the graph of function is 0 at x=2.  

Q: Sketch a graph of a function ƒ that is continuous on (- ∞, ∞) and has the following properties. ƒ'(x...

A: To sketch the graph if a function f which is continuous on (-∞, ∞)  and first and second derivatives...

Q: Absolute maxima and minima Determine the location and value of the absolute extreme value of ƒ on th...

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Q: Let lim, 1 h(x) = 5, lim, 1 p(x) = 1, and lim, 1 r(x) = 2. Name the rules in Theorem 1 that are used...

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Q: Comparing growth rates Determine which of the two functions grows faster, or state that they have co...

A: Definition: Let the functions fx  and  gx takes the positive value for sufficiently large values of ...

Q: the radius of a circular manhole cover is estimated to be 16 inch with a maximum error in measuremen...

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Q: Identities Use the given identity to prove the related identity. Use the identity cosh (x + y) = cos...

A:

Q: Solve the given linear inequality. Write the solution set using interval notation. < 4

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A: Given,  P(1, 2),  v = -i - 2j

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

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Q: Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is a posit...

A: Consider the integrals, ∫xax+bdx                                                                    ...

Q: If the common difference of an AP is 5 then what is a18 - a13

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Q: Let f(x) = 6x² – 4x + 7. - When f(x) is divided by x + 2 the remainder is: When f(x) is divided by x...

A:

Q: A CAT scan produces equally spaced cross-sectional viewsof a human organ that provide information ab...

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Q: Determine the following indefinite integral. Check your work by differentiation.

A: ∫3u-2-4u2+1 du=3·u-2+1-2+1-4·u2+12+1+u+C   ∵∫xn dx=xn+1n+1+C=-3u-4u33+u+C

Q: Find the product and write the result in standard form: (7 - 5i)(-2 - 3i)

A: Given: z=7-5i-2-3i given product can be find as below z=7-5i-2-3i=7-2-3i-5i-2-3i=-14-21i+10i+15i2   ...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.