Question Solved1 Answer Evaluate the indefiniteintegral given below using the indicated substitution.∫(4x3+x2)(3x4+x3)8dxu=3x4+x3Please help I have submitted twice and all been wrong. Evaluate the indefinite integral given below using the indicated substitution. | (4x2 + x>) (3x* +x2) * d u = 3x4 + x3 Provide your answer below: S(4x3 + x2) ( 3x4 + x3) dx = F

A box with a rectangular base, square ends and no lid is to be made out of two types of wood. The wood for the ends and the front costs \( \$ 15 / \mathrm{m}^{2} \) and the wood for the base and the back cost \( \$ 8 / \mathrm{m}^{2} \). If the total volume of the box must be \( 7 \mathrm{~m}^{3} \) find the dimensions that will minimize the cost of the wood.

Derivatives using Product and Chain Rules 12 of 14 An engineer is considering possible trajectories to use for emergency descent of a lunar module from low moon orbit to the lunar surface and decides to investigate one for which the vertical component of velocity as a function of time is described by ,(0) mu? where evo 0.49 km/s.to 390 s, and a 658. Part F For this trajectory, what would the vertical component of acceleration for the module be at time to -325s? Recall that acceleration is the derivative of velocity with respect to time View Available Hint(s) HÅ 9? dey (325 s) = de Value Units Submit Request Answer scent of a lunar module from low moon orbit to the lunar surface and decides to inv (t-to)2 -(t) = voe where vo = 0.49 km/s, to = 390 s, and o = 65s. 202

If A=xyz-2y2z+xz?, find del. (del A) at the point (2, 4, 1) g. 4 o b.-6 O c. -4 Od. 6 e. O

(17%) Problem 6: Two stones are separated by a vertical distance y (in meters) from each other. One stone is thrown down with an initial velocity vol=-32 m/s and the other is thrown up from the ground with an initial vo2-32 m/s at the same time the other is thrown. Status - for iew atus mpleted mpleted tial tial 33% Part (a) How far, in meters, must they be (17%) Problem 6: Two stones are separated by a vertical distance y (in meters) from each other. One stone is thrown down with an initial velocity vol=-32 m/s and the other is thrown up from the ground with an initial vo2-32 m/s at the same time the other is thrown. Status - for iew atus mpleted mpleted tial tial 33% Part (a) How far, in meters, must they be separated so they hit the ground at the same mpleted time? Grade Summary y Deductions Potential Submissions sin() tan() cos() asin() acos() Attempts remaining E 4 S 6 cotan() atan() acotan() sinh() (per attempt) detailed view 123 cosh() tanh() cotanh() ● Degrees Radians Submit Hint I give up! Hints: deduction per hint. Hints remaining Feedback: deduction per feedback. & 33% Part (b) What is the impact velocity, in meters per second, of the first stone? & 33% Part (c) What is the impact velocity, in meters per second, of the second stone? 0% 100%

cal 3 question. Thanks for your help and wish you the best 😊 6. Find the curl of the vector field. F(x,y,z) = 2xyi + (x2 + z2)j + 2yzk

3. (Taken from Rossiti chap-ex 1.3) Customers arrive to a gas station with two pumps. Each pump can reasonably accommodate a total of two cars. If all the space for the cars is full, potential customers will balk (leave without getting gas). What measures of performance will be useful in evaluating the effectiveness of the gas station? Describe how you would collect the inter-arrival and service times of the customers necessary to simulate this system. 4. (Taken from Rossiti chap-ex 2.3) Consider the multiplicative congruential generator with (a = 13, m = 64, and seeds X0 = 1,2,3,4) a) Does this generator achieve its maximum period for these parameters? Use Theorem 2.1 to justify your answer. b) Generate a period's worth of uniform random variables from each of the supplied seeds. 5. (Taken from Rossiti chap-ex 2.4) Consider the multiplicative congruential generator with (a = 11, m = 64, and seeds X0 = 1,2,3,4) 0.409 a) Does this generator achieve its maximum period for these parameters? Use Theorem 2.1 to justify your answer. b) Generate a period's worth of uniform random variables from each of the supplied seeds. 6. (Taken from Rossiti chap-ex 2.5) Analyze the following LCG: Xi =(11Xil +5)(mod(16)), X0 = 1 using Theorem 2.1. a) What is the maximum possible period length for this generator? Does this generator achieve the maximum possible period length? Justify your answer. b) Generate 2 pseudo-random uniform numbers for this generator. 7. (Taken from Rossiti chap-ex 2.10) Consider the following sequence of (0,1) random numbers: 0.943 0.398 0.372 0.943 0.204 0.794 0.498 0.528 0.272 0.899 0.294 0.156 0.102 0.057 0.398 0.400 0.997 Test if the sequence is distributed U (0, 1) using both a K-S test and a Chi-Squared test. 8. (Taken from Rossiti chap-ex 2.15) Suppose that customers arrive at an ATM via a Poisson process with mean 7 per hour. Determine the arrival time of the first 6 customers using the data given in Exercise 2.10 (starting with the first row). Use the inverse transformation method. 9. (Taken from Rossiti chap-ex 2.17) The service times for an automated storage and retrieval system has a shifted exponential distribution. It is known that it takes a minimum of 15 seconds for any retrieval. The parameter of the exponential distribution is = 45. Using the sequence of (0,1) random numbers in Exercise 2.10 (starting with the first row) generate 2 service times for this situation. 10. (Taken from Rossiti chap-ex 2.20) The interest rate for a capital project is unknown. An accountant has estimated that the minimum interest rate will between 2% and 5% within the next year. The accountant believes that any interest rate in this range is equally likely. You are tasked with generating interest rates for a cash flow analysis of the project. Using the sequence of (0,1) random numbers in Exercise 2.10 (starting with the first row) generate 2 independent interest rate values for this situation. 11. (Taken from Rossiti chap-ex 2.21) Customers arrive at a service location according to a Poisson distribution with mean 10 per hour. The installation has two servers. Experience shows that 60% of the arriving customers prefer the first server. By using the first row of (0,1) random numbers given in Exercise 2.10, determine the arrival times of the first three customers at each server. 12. (Taken from Rossiti chap-ex 2.25) Consider the following probability density function: 05:55 f(x) = 25 otherwise a) Derive an inverse transform algorithm for this distribution. b) Using the first row of random numbers from chap-ex 2.10 generate 2 random numbers using your algorithm. 0