In the following exercise you are asked to relate functional notation to practical explanations of what certain functions mean. The function  T(P, r, m)  gives the time required to pay off an installment loan of P dollars if the APR is r as a decimal and we make monthly payments of m dollars. Use functional notation to indicate the time required to pay off a $12,000 automobile loan at an APR of 5% if the monthly payment is $410.

Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y=6ln(x) abou...

A: Graph of the region bounded by the curves y  = 6 ln(x), x= 1 and x = e is:

Q: Assume x E R and x + E Z. Use induction to prove that for all n E N, х" + 1 E Z. Then, answer these ...

A: Given:             x∈ℝ and  x+1x ∈ℤ  

Q: A cylindrical glass jug of diameter 10cm and height 2.7mm is filled with water.Find the surface area...

A: Diameter of cylindrical glass jug is 10 cm and height up to water is filled is 2.7 mm=0.27 cm Let th...

Q: Q1: Let p and q be the propositions "Swimming at the New Jersey shore is allowed" and "Sharks have b...

A: Given propositions are, p : Swimming at the New Jersey shore is allowed q : Sharks have been spotted...

Q: Substance A decomposes at a rate proportional to the amount of A present. It is found that 12 lb of ...

A: Substance A decompose at rate proportional to initial amount A0, thus by using exponential decay mod...

Q: The total cost (in dollars) of producing a product is given by C(x) = 800x + 0.1x2 + 1200 where x ...

A: The total cost (in dollars) of producing a product is given by C(x)=800x+0.1x2+1200 where x represen...

Q: 4. DETAILS PREVIOUS ANSWERS SCALCCC4 6.1.007. MY NOTES ASK YOUR TEACHER Sketch the region enclosed b...

A: Given curves,  y=6x2  .........(1)& y2=16x ........(2) Let us sketch the graph,         

Q: The table lists the cost in millions of dollars for a 30-second commercial for selected years. Year ...

A:

Q: Recall the polar form of the Cauchy-Riemann Equations: 1 ƏV 1 ƏU r +0. r d0 av ar dr -i0 (0 + i). Le...

A: The given function is f(z)=z45. The polar form of the complex variable z is z=reiθ. Therefore, f(z)=...

Q: 1. Find the eigenvalues and eigenvectors of the following matrix 1 A = 4 -2 2. Solve the initial val...

A:

Q: Use the contour map to calculate the average rate of change from A to B and from A to C if a = -4. c...

A: The average rate of change is given by ∆altitude∆horizontal. Given that, c=-4. So, the known levels ...

Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim x→5   5 + X/X

A:

Q: Question 7 C 0/1 pt 5 2 O Details Multiply 28 x 35 using duplation. Show all work using the correct ...

A: We are to Multiply 28 and 35- Numbers which are used in adding up to 28 are-  2,4,8,16 So-   

Q: # of hours  chemistry  biology  0 70 64 1 77 72 2 82 78 3 85 82 You are taking two course...

A:

Q: Advanced Math Question

A: Given:  Point O→(0,0,0)Point A→(6,-2,3)Point B→(4,4,-4) All co-ordinates are in m(meters) (a)   rOA→...

Q: The following table gives the percent of the US population living in urban areas as a function of ye...

A: Substitute the value

Q: 5. For regular polygons inscribed in a circle of radius 1, use S6 :1 to conclude that S12 = V2 – V3,...

A: We know for regular polygons in a circle of radius 1 we have S2n=2-4-Sn2Given: S6=1

Q: Use matrix inversion to find the production vector x that meets the demand d for the consumption mat...

A: Given:C=0.10.30.20.50.10.20.20.40.3,   d=184026Consider the model (I-C)-1x=d Let A=(I-C)So,(I-C)-1x=...

Q: How would I go about deriving this with respect to the parameter mu?

A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need...

Q: area and volume

A: Given: The dimensions of a cement floor is 15 ft by 14 ft by 2 ft. 1 ft3 of cement weighs 193 lb.

Q: Find the roots of the function f(x) = (2" – 1) (a2 + 2r – 3) with r ER. %3D

A:

Q: Perform the indicated operation and simplify.       3x+3                    x^2-4x+4 _______________...

A:

Q: Find the associated exponential decay or growth model. (Round all coefficients to three significant ...

A:

Q: Below are three drcies. The circumference and diameter of each circle have been appraximately measur...

A: (a) The circumference and the diameter of Circle 1 is 39.273 units and 12.5 units respectively. Henc...

Q: On November 27, 1993, the New York Times reported that wildlife biologists have found a direct link ...

A:

Q: Verify that u(r, t) = f(e-"x) solves the initial value problem (au + z8,u = 0, u(x,0) = f(z).

A:

Q: Solve it early both subparts.

A: (a)The graph represents the function: f(t)=0        t≤0t-1   t≥0 The function is discontinuous at t=...

Q: There is a maximum of 6,000 hours of labor available per month and 300 ping-pong balls (x1) or 200 w...

A: Let x1 is the Number of  ping pong balls we can produce ping pong balls at the rate of 300 per hour ...

Q: In the figure below, the solid circle has center (2, 3) and radius 1. The dashed circle has center (...

A: The given solid circle has radius 1 and center at (2,3), whereas the dashed circle has radius 4 and ...

Q: An unknown radioactive element decays into non-radioactive substances.  In 660 days the radioactivit...

A:

Q: (a) Suppose x E Q with x # 0 and y E R – Q. Show that their product ry is irrational.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Suppose that you are thinking about buying a car and have narrowed down your choices to two options....

A: Given that the new car costs $29000 and can be financed with a five-year loan at 5.46%. So, the pres...

Q: I need help

A: From the given information, it is observed that the company charges $4.25 for the first half mile an...

Q: Find the general solution to 2y" + 18y = 0. Give your answer as y=...

A:

Q: Use the method of Lagrange multipliers to solve this exercise.Hercules Films is also deciding on the...

A: Given that at a price of p dollars, sell and costs of each copy is  q=544000-17000p, c=$4

Q: If two dice are rolled, find the probability that the sum of the die is 8. Probability that sum is 8...

A: (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,2) , ................... , (6,5) , (6,6) ...

Q: The fish population P(t) (in millions) in a large fish farm where 2 million fishes are dP = 3P – p² ...

A: An equilibrium solution is a solution to a differential equation whose derivative is zero everywhere...

Q: 1. The graph above shows the base of an object. Compute the exact value of the volume of the object,...

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve the fir...

Q: I have submitted this answer and I’m not sure why it is counting it wrong. It is through Edfinity an...

A:

Q: Let 0 < 0 < 1 be a rational number. Show that the sequence {cos(nT0)}-1 is divergent.

A:

Q: 12-

A: The given function fx=ax2-3ax at x=2.   Formula used:   Formula for finding normal to the function i...

Q: in pic

A: The given initial value problem given is y"+3y'+2y=6δ6t       with conditions y0=0, y'0=-1 Lδ6t=e-6s...

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.