Question

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

257

likes
1284 views

Answer to a math question two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

Expert avatar
Rasheed
4.7
57 Answers
Find the equations for the velocities of both particles. v_1=x_1^{\prime}=\frac{\differentialD}{\differentialD t}\left(\cos\left(t\right)\right), v_1=-\sin\left(t\right) v_2=x_2^{\prime}=\frac{\differentialD}{\differentialD t}\left(\exponentialE^{-3t}+1\right)=-3\left(\exponentialE^{-3t}\right)+0, v_2=-3\exponentialE^{-3t} Now, let v1 = v2. v_1=v_2, -\sin\left(t\right)=-3\exponentialE^{-3t}, \sin\left(t\right)=3\exponentialE^{-3t}, \sin\left(t\right)-3\exponentialE^{-3t}=0 Then, find the values of t, from 0 to 10, as separated by commas. t=0.5712,3.1414,6.2832,9.4248

Frequently asked questions (FAQs)
Question: Given two vectors A = (3, 8) and B = (-2, 5), find the sum of A and the difference of A minus B.
+
What is the amplitude and period of the sine function f(x) = sin x?
+
What is the minimum value of the function f(x) = x^2 - 4x + 5 for x in the interval [0, 5]?
+
New questions in Mathematics
A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?
11(4x-9)= -319
All the liquid contained in a barrel is distributed into 96 equal glasses up to its maximum capacity. We want to pour the same amount of liquid from another barrel identical to the previous one into glasses identical to those used, but only up to 3/4 of its capacity. How many more glasses will be needed for this?
prove that if n odd integer then n^2+5 is even
Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.
Solve : 15/16 divide 12/8 =x/y
I want you to solve this problem as a grade sixth pupil in primary school: 8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?
It is known that the content of milk that is actually in a bag distributes normally with an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by 𝐶(𝑥) = { 3800 𝑠𝑖 𝑥 ≤ 890 4500 𝑠𝑖 𝑥 > 890 Find the expected cost.
You are the newly appointed transport manager for Super Trucking (Pty) Ltd, which operates as a logistics service provider for various industries throughout southern Africa. One of these vehicles is a 4x2 Rigid Truck and drawbar trailer that covers 48,000 km per year. Use the assumptions below to answer the following questions (show all calculations): Overheads R 176,200 Cost of capital (% of purchase price per annum) 11.25% Annual License Fees—Truck R 16,100 Driver Monthly cost R 18,700 Assistant Monthly cost R 10,500 Purchase price: - Truck R 1,130,000 Depreciation: straight line method Truck residual value 25% Truck economic life (years) 5 Purchase price: Trailer R 370,000 Tyre usage and cost (c/km) 127 Trailer residual value 0% Trailer economic life (years) 10 Annual License Fees—Trailer R 7,700 Fuel consumption (liters/100km) 22 Fuel price (c/liter) 2053 Insurance (% of cost price) 7.5% Maintenance cost (c/km) 105 Distance travelled per year (km) 48000 Truck (tyres) 6 Trailer (tyres) 8 New tyre price (each) R 13,400 Lubricants (% of fuel cost) 2.5% Working weeks 50 Working days 5 days / week Profit margin 25% VAT 15% Q1. Calculate the annual total vehicle costs (TVC)
Engineers want to design seats in commercial aircraft so that they are wide enough to fit ​95% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.2 in. Find P95. That​ is, find the hip breadth for men that separates the smallest ​95% from the largest 5​%.
Find the center coordinates and radius of a circle for an equation written as: 3x2 + 3y2 - 6y = —12× + 24
(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B
Calculate the change in internal energy of a gas that receives 16000 J of heat at constant pressure (1.3 atm) expanding from 0.100 m3 to 0.200 m3. Question 1Answer to. 7050J b. 2125J c. None of the above d. 2828J and. 10295 J
Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?
Given the word WEIRD, determine a four-letter offspring that can be formed with the letters of the word written above
A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be Normally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and Standard deviation is measured in millimeters. What is the probability that an arbitrary route has a thickness less than 4.00 mm?
A 20-year old hopes to retire by age 65. To help with future expenses, they invest $6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?
Define excel and why we use it?
The length of a rectangle is five more than its width. if the perimeter is 120, find both the length and the width.
13/25+7/16