Problem: A radio transmitter is located 3 km away from a straight highway. A truck is traveling away from the transmitter along the highway at a speed of 80 km per hour. How fast is the distance between the truck and the transmitter increasing when they are 5 km apart?
1. Write down the equation of a sinusoidal function f with the mean value 2, amplitude 4, the period 3 and f(6) = 2 2. Write down the equation of a sinusoidal function f with the mean value: -1, amplitude 5, the period 4 pi and f(0) = -1 Please show all working and explanations.
Please solve the following differential equation: c(dT/dt) + v(T-Teq) = a0sin(wt) In this equation, c is effective heat capacity, T temperature, t time, Teq is equilibrium temperature, v, a0 and w are constants. Please derive an expression for T(t) in terms of the constants and show all the steps in the derivation.
The parabola C has the equation y^2 = 16x a. Verify that the point P(4t^2, 8t) is a general point on C. b. Write down the coordinates of the focus S of C. c. Show that the normal to C at P has equation y + tx = 8t + 4t^3. The normal to C at P meets the x-axis at the point N. d. Find the area of triangle PSN in terms of t, gi
Suppose consumers' demand function a commodity D(q)=50-3q-q2 dollars per unit. A. Find the number of units that will be bought if the market price is $32 per unit. B. Compute the consumers' willingness to spend to get the number of units in part (a).
The Manager of a company that produces graphing calculators determines that when x thousand calculators are produced, they will all be sold when the price is p(x)=1,000/0.3x^2+8 dollars per calculator. A. At what rate is demand p(x) changing with respect to the level of production x when 3,000(x=3) calculators are produced?
A Florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. Express the grower's total yield as a function of the number of additional trees planted, draw the grap
Please see attachment Determine whether....converge or diverge ...derive a necessary condition for the equation...to have a rational root. Then use this condition to prove... Using binomial coefficients, derive a formula for the nth derivative of the product of two functions. Suppose that f(x) has a continuous first
Please see attachment ONLY Q1,2,4 Determine whether....converge or diverge ...derive a necessary condition for the equation...to have a rational root. Then use this condition to prove... Suppose that f(x) has a continuous first derivative for all x in R. Prove that f(x) is concave if and only if....
Please see attachment Determine whether....converge or diverge ...derive a necessary condition for the equation...to have a rational root. Then use this condition to prove... Using binomial coefficients, derive a formula for the nth derivative of the product of two functions. Suppose that f(x) has a continuous first
Find the indicated probability. 1) Two fair dice are rolled. What is the probability that a sum of 6 or 11 is obtained? 1) _______ A) 7/6 B) 17/36 C) 1/66 D) 7/36 Find the simple interest. Assume a 360-day year. Round results to the nearest cent. 2) $ 49,417 at 7.7% for 17 months 2) _______ A) $
Question 5: Find the volume of the solid generated by revolving the region bounded by the graphs of the equations Please show all work. Please see the attached file for the fully formatted problems.
Please see the attached file for the fully formatted problems. Question 7: For the function find: a) its average value, (Average f), on the interval [0,9] b) the value of c in the interval [0,9] guaranteed by the Mean Value Theorem for Integrals. Question9: Evaluate the following limits: a. b.
** Please see the attached PDF for the complete problem description ** Show all work and a step-by-step solution so that I can clearly see how you arrived at your answer. No calculators or computer programs can be used to solve this problem. Thanks
Please see the attached PDF for the problem. Please show all work and step-by-step solution so that I can easily follow your reasoning. Do not use calculators or computer programs to find the solutions. Explain your reasoning and state any theorems used in the calculations.
We examine the above function and consider its limit as (x,y)-> (0,0).We take two different paths in the x-y plane for approaching the point (0,0),and find that f(x,y) approaches two different values .This enables us to conclude that the given limit does not exist.For a detailed discussion see the solution given.
Problem: From your position, an airplane is moving away from you horizontally at 60 km/hr and vertically at 1km/hr. If the position of the airplane is 200km horizontally and 30km vertically away from you, what is the rate of change of distance of the airplane relative to your position?
Details of question attached including diagram of graph. The parametric equation of a curve are: x = 2 theta + sine 2 theta y = 4 sine theta Find the value of theta at A and the value of theta at B
The function given below is a company's price function, where x is the quantity (in thouands) that will be sold at price p dollars and p = 5 - 1n x Find the revenue function R(x). Find the quantity and price that will maximize revenue. Applied Calculus 9th edition by Laurence D Hoffman and Gerald L. Bradley
2) (3 pts) Suzy Sorority agr to give Joe Student a ride lionic for spring break. They agree to meet at the corner of 12 th St. and Willow. Joe is late and Suzy gets tired of waiting, so she starts to drive off down Willow st without him. Joe was already walking down 12th St., and he starts to shout and run towards the corner whe
See attached (1) Write the general solution for: x2 y" - 2xy+2y=x3 (2) Solve: (3) Solve: x2 y" + xy' - y=0 (4) Calculate L[x sinax] (5) In the vibration of a mass-spring-damper system, the displacement is governed by If f(t) is given by Find the solution if C=0 and x(t=0)=0 and dx
Show that the following limits do not exist: use def. of convergence or cauchy or epsilon delta a. lim as x goes to 0 of (1/(x^2)) x>0 b. lim as x goes to 0 of (1/(x^1/2)) same as (1/sqrtx) c. lim as x goes to 0 of (x + sgn(x)) d. lim as x goes to 0 of sin(1/(x^2)) let f: R---> R be defined by setting f(x)= x if x is
See the attached file. Question 1 Given the first derivative of the continuous function y = f(x). Find y" and sketch the graph of f. y' = tan x, -pi/2<x<pi/2 I know y"= sec2x - I need the graph and critical, inflection, and max/min points along with a picture of the graph or what need to be entered into m
If a loan of (A) dollars is amortized over n years at an annual interest rate r ( as a decimal) compounded monthly, the montly payments (M) are given by the formula: M = Ai / 1 - (1 + i) to the -12n power a)If a home loan is made for $165,000 at 6% annual interest, compounded monthly, for 30 years, What is the montly pay
Solve each using Q = Q0 e to the rt power A radioactive substance decays exponentially, If 500 grams of the substance were present intially and 400 grams are present 50 years later, how many grams will be present after 200 years? It is estimated that the population of a certain country grows exponentially. If the populatio
** Please see the attached file for the complete problem description ** Solve the differential equation...using the undetermined coefficients method. Solve the differential equation...using variation of parameters method. Solve the initial value problem... Solve by systematic elimination....
Please see the attached file for the fully formatted problems. 1. find a formula for the function f(x,y) such that its gradient is (sin y, x*cos y) 2 Use teh answer to part 1 to compute the integral of the gradient over the path from (1,1) to (1,2)
By using partial fractions show that a. the sumation from 0 to infinity of 1/(n+1)(n+2)=1 b. the sumation from 0 to infinity of 1/(alpha+n)(alpha+n+1)=1/alpha >0 if alpha>0 c. the sumation from 0 to infinity of 1/n(n+1)(n+2) =1/4 apply the theorem: let (Xsubn) be a sequence of positive real numbers such that L := lim(Xsubn
Please see file attached. Find Limit f'(x) as x--->0 Dear TA, I don' understand the answer where limit as xïƒ 0- and lim as xïƒ 0+ don't equal each other since one equals -∞ and the other +∞. At f'(0) the function is undefined. Do I need to use the def of limit and find the limit from the right side and left side.
A)The region bounded by y = e^2x, y = e^x, x = 0, and x = 2 is rotated around the x-axis. Find the volume. b)Consider the region bounded by y = x^2, y = 3, and the y-axis. Find the volume of the solid obtained by rotating the region around the y-axis.