I Have a question regarding cross products, if you know one of the vectors to be crossed and the result of the cross product how do you find the other vector. For example Vector A is unknown and Vector B=-2 Z and the result is a vector that 5X+8.66Y
A) Check that z(t) = 1 + sqrt(1 + 2t) is a solution of the autonomous differential equation dz/dt = 1/(z-1) with initial condition z(0) =2 b) Estimate z(4) if z obeys the differential equation dz/dt = 1/(z-1) with initial condition z(0) = 2.
Dy/dx= 4x+ 9x^2/(3x^3+1)^3/2 given point: (0,2) (that's 4x plus 9x squared over (3x cubed + 1) to the 3/2 power) Use the differential equation and the given point to find an equation of the function.
The rate at which a bacteria population multiplies is proportional to the instantaneous amount of bacteria present at any time. The mathematical model for this dynamics can be formulated as follows: db/dt = kb where b is a function in terms of the time t, b(t) is the number of bacteria at the time t, and k is a constant.
1) The marginal cost (dollars) of printing a poster when x posters have been printed is dc/dx = 1/5√x^4 Find the cost of printing posters 18 through 130 The cost of printing posters 18 through 130 is $ _ (Round to the nearest cent)
Problem: Find the area of the region in the first quadrant bounded by the line y=6x, the line x=4, the curve y=2/x(squared), and the x-axis. (1) Part A: Solve the above problem using any methods, concepts.
I really need assistance on these three calculus problems.... Evaluate the sum: 7 ∑ k (6k+5) (Simplify your answer) K=1 Evaluate the sum: 6 ∑ (-13k) K=1 (Simplify your answer) Find the function y(x) satisfying dy/dx=6x-5 and y(5)=0 is y(x) = ? (Simplify your answer)
Find the critical point(s) of f(x,y)= [-4x^2 e^y + 2x^4 + e^4y] and classify each using the Second Partials Test. Does anything seem unusual about your results?
Please show your work: 1. Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c. a. f(x) = x + 5 b. f(x) = 3 if x>2 otherwise f(x) = -2 c. f(x)
Please help with these problems, I am stuck so if you could please post your steps, id appreciate it. 1.Use Newton's method to estimate the one real solution of x(exponent 3)+5x+1=0. Start with x0=0 2. If sinh x= 16/63, find cosh x, tanh x, cothx, sech x and csch x. 3. A right triangle whose hypotenus is square root of
Suppose that each dollar introduced into the economy recirculates as follows: 85% of the original dollar is spent then 85% of that $.85 is spent, and so on. Find: The economic impact (the total amount spent) if $1,000,000 is spent.
A body falling in a relatively dense fluid, oil for example, is acted on by three forces: the weight W due to gravity (acting downwards), a resistence force R and a bouyant force B (both actin upwards). The wieght W of the object of mass m is mg. The bouyant force B is equal to the weight of the fluid displaced by the object.
See the attached file. 1. Find the particular solution of the differential equation that satisfies the boundary condition. , y(1) = 2 A) B) C) D) E) 2. Find the particular solution of the differential equation that satisfies the boundary condition.
I have an exam coming up and I am having problems with these two questions. Please show work and final answer. That way I can rewrite what you do so I understand it. 1. d/dt (x sin x + x^2)/ (x^2 + 1) 2. Find the second derivative if f(x)= sec(4x)
(2) For the function g whose graph is given (see attached), state the following: (a) lim x->∞ g(x) (b) lim x->-∞ g(x) (c) lim x->3 g(x) (d) lim x->0 g(x) (e) lim x->-2+ g(x) (f) The equations of the asymptotes.
4. Solve: a Solve for x if 2logx = 2 + log25 b Simplify log3 81 - log3 27 + 4log3 v3 c Find the inverse of the function f(x) = e^x + 1 5. This is completing a piecewise function which consists of 2 straight lines and a parabola. Coordinates given are (-6,0) (-3,6)-straight line, (-3,6) (.5, -6) (2,-4) -parabola, and last
1.Find the values of a and b for the polynomial f(x) = 2x^3 + ax^2 - 4x + b, given that f(x) is divisible by x+1 and x-3. Write f(x) in a factorised form. Hint: consider f(-1) and f(3) 2. The population of a country is found to be growing continuously at an annual rate of 1.98% t years after 1 January 1960. The total populat
1. A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30° angles with the vertical. Knowing that the z component of the force exerted by wire BD on the plate is 232.14 N, determine ( a) the tension in wire BD, ( b) the angles ux, uy, and uz that the force exerted at
1. Find an equation for the line tangent to y= -5-5x^2 at (5,-130) 2. Find the slope of the function's graph at the given point. Then find an equation for the line tangent to graph: f(x) = x^2 + 2, (-2,6) What is the slope of the function's graph at the given point? 3. Using the defenition, calculate the derivative
Calculus applications Exercise 6.1 23. Manufacturing A company manufacturing two types of leaf blowers, an electric Turbo model and gas-powered Tornado model. The company's production plan calls for the production of at least 780 blowers per month. a. Write the inequality that describes the production plan, if x represents
1. What is missing in this surface of revolution as a function of x revolved around the y-axis: ? A) Nothing, the formula is fine as is. B) Nothing, but the limits of integration should be on the interval [c, d]. C) The variable x should be x2. D) The constant 2π is missing. 2. Find the solid of revolu
I need help on these two problems please 1. Does the existence and value of the limit of a function f(x) as x approaches x_o ever depend on what happens at x = x_o? Explain and give examples. 2. What does it mean for a function to be continuous? Give examples to illustrate the fact that a function that is not continuous on
Find the volume of the unbounded solid generated by rotating the unbounded region around the x axis. This is the region between the graph of y= e^-x and the x axis for x> or= 1. [Method: Compute the volume from x=1 to x=b, where b> 1. Then find the limit of this volume as b -->+infinity] What about if y=1/SQRTx.
Find the interval on which the function f is increasing and or is decreasing and label the local maxima and minima if there is a global extrema is should be so identified. 1, F(x)= x^3 + 3x 2. F(x) = (x-2)^2(2x+3)^2 3. F(x)= 1/x 4 F(x)=6-5x-6x^2 5. F(x)=x^3 +4x
Please help simplify the following: write dy in terms of x and dx y=2SQRTx -3/cubed root x write dy in terms of x and dx y=1/x-SQRTx write dy in terms of x and dx y=x/x^2-4 write dy in terms of x and dx y=1/(x^2-1)^4/3 write dy in terms of x and dx y=x^2 sin x write dy in terms of x and dx y=cos^3 3x.
Consider a market with the following supply and demand functions: QD = a0 - a1PD a0, a1 > 0 QS = b0 + b1PS b0, b1 > 0 (a) Find the equilibrium quantity and price as a function of the parameters (use any method you like). Are there any additional restrictions that you must impose on the parameters for thi
Problem 3. POLLUTION CONTROL Commissioners of a certain city determine that when x millions dollars are spent on controlling pollution, the percentage of pollution removed is given by P(x) = (100 Sqrt(x))/0.04x^2 + 12 a. What expenditure results in the largest percentage of pollution removal? Problem 4. Compute the
A point is rotating about the circle of radius 1 in the counterclockwise direction. It takes 8.4 minutes to make one revolution. Assuming it starts on the positive x-axis, what are the coordinates of the point in 7.4 minutes?
The positions of two particles on the s-axis are s1=sin t and s2=sin(t+ π /3), with s1 and s2 in meters and t in seconds. a) At what time(s) in the interval 0 ≤t ≤ 2π do the particles meet? b) What is the farthest apart that the particles ever get? c) When in the interval 0 ≤t ≤ 2π is the distance between the parti
1. Compute the derivative of the given function and find the slope of the line that is tangent to its graph for the specified value of the independent variable. (Compute the derivative of the function from the definition only, using limits. More advanced methods are not allowed here. Show your work.) (i) f(x) = x^2 - 1 x = -