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Q1:Engineering mathematics - Principles 5. A private plane travels from the city of Sheffield, UK, to the city of Nijmegen, The Netherlands. a) In total, the plane travels 171.32km south and 495.20km east. What is the direct distance between Sheffield and Nijmegen? a) Immediately after leaving the airport in Sheffield, the plane due north for 5km. It then made a turning of 48° towards the east and travelled for a further 5km. At this point, how far was the plane from the airport in Sheffield? Page 7 Version 1.1 Copyright © 2020 leamdirectSee Answer
Q2:4. Comet Halley is an irregularly-shaped comet which is visible from Earth every 75-76 years. For the purposes of this question, we will assume that the comet is spherical. a) Taking the diameter of the comet to be 10.6km, find the approximate volume of the comet in cubic centimetres. You may use the fact that the volume of a sphere is where r is the radius. V=R² Page 5 Version 1.1 Copyright © 2020 learndirect Engineering mathematics - Principles b) The density of (water) ice is one gram per cubic centimetre. It is estimated that the density of the comet is approximately the same as that of water ice. Given that mass = volume x density find the mass of the comet in kilograms. Hint: Find the mass in grams first and then convert.See Answer
Q3:2. A cart travels continuously around a circular track with a constant acceleration. The track has a length of 10km. At a specific time, t - 0, its position is measured. It takes half an hour for the cart to complete one full lap of the track It takes two hours (from time t-0) for the cart to complete ten full laps of the track The following formula describes this situation s=u₂t+ at² where .s is the displacement, measured in km . u, is the velocity of the cart when t-0, measured in kmh-¹ • t is the time taken, measured in hours . a is the acceleration of the cart, measured in kmh.² a) Use the information about the position of the cart after half an hour to write a formula linking u, and a. b) Use the information about the position of the cart after two hours to write another formula linking u, and a. Page 2 Version 1.1 Copyright © 2020 leadirect Engineering mathematics - Principles c) Use your equations to find the initial velocity of the cart and its acceleration.See Answer
Q4:1. A cup of tea is placed on a table. At a time of t minutes after being placed on the table, its temperature in degrees Celsius is given by T= 20+Aekt Where A and k are positive constants. The initial temperature of the tea was 70°C. a) Find the value of A b) The tea takes 4 minutes to decrease in temperature from 70°C to 50°C. Show that k = In (3)See Answer
Q5:Quiz 5 1) Let z = f(x, y). Calculate NAME 20 points 1page DIRECTIONS: Show all the work in the space provided. Box the final answers, and follow the indicated directions. where ce + zey = x+y. (20 points)See Answer
Q6:MODEL I 8. Thus. Given ARST with a point U inside such that <RST = LRTS-42°. and ZRSU - LSRU-18°. Find LUTS R PROBLEM I But Hence. Let Af be the midpoint of BC. AM intersects CP at Q. By the symmetry properties. we may have QBC (QCB = (PCB 3. LPBQ = LPBCQBC 35"- 30" - 5". and S M hence namely, BP bisects ADQ. Morover, since T 4PBQLABP. C (ADP ABC-PBC (180-(BAC)- <PBC 25. <AQP <<MQC = <MQB = 90° - 4QCM = 90 -<PCB Gr. <PQD = 2<BCQ = 2(DCP = 60°. <AQP = LPQB. namely, QP bisects <AQB. To sum up. Pis the incenter of AABQ. Thus. Ar bisects BAQ. It follows that <BAP: <BAM =<BAC 25".See Answer
Q7:- Linear Functions System of equatio K Question 18, *4.1.71 Part 1 of 3 The cost y for a company to produce x T-shirts is given by the equation y = 10x + 2000, and the revenue y from the sale of these T-shirts is y=20x. Find the break-even point, the point where the line that represents the cost intersects the revenue line. Interpret the x-coordinate and the y-coordinate of the break-even point. Use the graphing tool to graph the equations. Click to enlarge graph HW Score: 0%, 0 of 20 points O Points: 0 of 1 Amount (in Dollars) 5000- 4000- 3000+ 2000- 1000- -O 50 Save 100 150 200 Number of T-Shirts Sold 250See Answer
Q8:- Linear Functions System of equatio K Question 18, *4.1.71 Part 1 of 3 The cost y for a company to produce x T-shirts is given by the equation y = 10x + 2000, and the revenue y from the sale of these T-shirts is y=20x. Find the break-even point, the point where the line that represents the cost intersects the revenue line. Interpret the x-coordinate and the y-coordinate of the break-even point. Use the graphing tool to graph the equations. Click to enlarge graph HW Score: 0%, 0 of 20 points O Points: 0 of 1 Amount (in Dollars) 5000- 4000- 3000+ 2000- 1000- -O 50 Save 100 150 200 Number of T-Shirts Sold 250See Answer
Q9:ctions uatio Question 15, *4.4.A.1 Part 1 of 2 HW Score: 0%, 0 of 20 points O Points: 0 of 1 Save Set up an equation that describes the relationship between the two variables in the following situation. Graph that relationship. A manufacturer makes two types of products. Profit on Product A is $50 per unit, while profit on Product B is $20 per unit. Budgeted monthly profit is $4000. Let x be the number of units of Product A sold, and let y be the number of units of Product B sold. Set up an equation that describes the relationship between the two variables. (Do not simplify. Do not factor. Do not include the $ symbol in your answer.)See Answer
Q10:Functions f equatio Question 14, ARC.3.59 > Solve the following system of equations. x+8y+z= 8 -x+9y+z= 9 (2) 2x- y = -1 (3) HW Score: 0%, 0 of 20 points O Points: 0 of 1 What is the solution? Select the correct choice below and fill in any answer boxes within your choice. OA. There is one solution,... (Type exact answers in simplified form.) B. The system is dependent. OC. There is no solution. {0} SaveSee Answer
Q11:nctions quatio Solve. Question 13, ARC.3.52 > x + y + z = 0 (1) 2x+4y+2z = -4 (2) -x+9y-3z = -20 (3) HW Score: 0%, 0 of 20 points O Points: 0 of 1 B. OC. There is no solution. Save Write the solution as an ordered triple. Select the correct choice below and fill in any answer boxes within your choice. O A. There is one solution, (... (Type exact answers in simplified form.) The system is dependent.See Answer
Q12:unctions equatio Solve. Question 11, ARC.3.45 x + y + z = -2 2x + 5y + 2z = 11 -x+6y-3z = 47 >See Answer
Q13:inctions equatio < Question 9, *4.2.C.1 Solve the following system of equations. 4x-y=4 and 3y - 12x = -3 > OA. The solution is Select the correct choice below and, if necessary, fill in the answer box to complete you HW Score: 0%, 0 of O Points: 0 of 1 (Type an ordered pair.) B. There is an infinite number of solutions for this system. OC. There is no solution for this system.See Answer
Q14:unctions equatio Question 8, *4.3.B.6 > Solve the following system of equations. 3x = 2y - 3 6x + 5y = -33 X= and y=[ (Simplify your answers.) HW Score: 0%, 0 c O Points: 0 of 1See Answer
Q15:ear Functions m of equatio K Question 7, ARC.3.40 Solve by the elimination method. 4x = -6y 3x-6y = - 42 HW Score: 0%, 0 of 20 points O Points: 0 of 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set of the system is. (Simplify your answer. Type an ordered pair.) OB. There are infinitely many solutions. OC. The solution set is the empty set. SaveSee Answer
Q16:K Solve the system by graphing. 2x+y=4 8x + 4y = 16 Use the graphing tool to graph the system. Click to enlarge graph 10. 10+ 8- 6- +2 4 6 48See Answer
Q17:K Solve the system of equations by graphing. X 4x 9 = 0 9y = 36 Use the graphing tool to graph the system. Click to enlarge graph 10 -2 10- 8 6- 4- 2 d 4 -6 8 40See Answer
Q18:8. (5 points) (a) Determine the number of nonnegative integer solutions for ₁+2₂ +23+24+25 < 21? (b) How many solutions in part (a) satisfy z₁+z2+z3=3? (c) How many solutions in part (b) have #₁, #₂ > 0?See Answer
Q19:6. (1 point) In how many ways can 12 (identical) cookies be distributed among four friends so that the tallest friend gets either none or just three of them? 7. (2 points)See Answer
Q20:4. (2 points) With n a positive integer, evaluate the sum (6)-³(7) + 3² (2) + | + ... + (−1)"3" ( 74 11See Answer

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