6. Consider the mass spring system whose motion y(t) is governed by y" + 4y' + 3y = 30 cos 3t, y(0) = 1, y'(0) = 7. 1. Is this system underdamped, critically damped, or overdamped? 2. Determine the solution y(t) of the initial value problem. Notice that the solution is a sum of terms, one of which has exponential decay to 0 and the other of which is periodic, with values that repeat without decay. Identify the terms: which decays to 0 ("transient solution") and which is periodic ("steady-state solution").
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- 6 A valve manufacturer produces a butterfly valve composed of two semicircular plates on acommon spindle that is used to permit flow in one direction only (seen here:http://en.wikipedia.org/wiki/Butterfly_valve). The semicircular plates are supplied by a vendorwith specifications that the plates be 2.37 millimeters thick and have a tensile strength of fivepounds per millimeter. A random sample of 20 such plates is taken. Electronic calipers are usedto measure the thickness of each plate. A universal testing machine was used to test the tensilestrength. The sample data are found in homework 5.xlsx.a. Find point estimates of the thickness and tensile strength data. Compare with thespecifications.b. Construct a 95% confidence interval for mean thickness. Draw conclusions regarding thespecification relative to the confidence interval.c. Construct a 95% confidence interval for mean tensile strength. Draw conclusionsregarding the specification relative to the confidence interval.d. Construct…An investigation was conducted into the dust content in the flue gases of two types of solid-fuel boilers. Thirteen boilers of type A and nine boilers of type B were used under identical fueling and extraction conditions. Over a similar period, the quantities of dust were deposited in similar traps inserted in each of the twenty-two flues. Presented below are the collected dust content (in grams) given the source broiler type. Type A 73.1 56.4 82.1 67.2 78.7 75.1 48.0 53.3 55.5 61.5 60.6 55.2 63.1 Type B 53.0 39.3 55.8 58.8 41.2 66.6 46.0 56.4 58.9 questions are in inserted imageLow Carbohydrate Low Fat Mediterranean TOTAL n % n % n % N % Gender 26 26 26 78 Female 15 57.7 15 57.7 14 53.8 44 56.44 Male 11 42.3 11 42.3 12 46.2 34 43.6 Age Group 18-34 years 7 27.9 7 26.9 6 23.1 20 25.6 35-40 years 13 50 14 15.4 15 57.7 42 53.8 50+ years 6 23.1 5 19.2 5 19.2 16 20.5 BMI Category Normal weight 9 34.6 6 23.1 7 26.9 22 28.2 Overweight 11 42.3 13 50 12 46.2 36 46.2 Obese 6 23.1 7 26.9 7 26.9 20 25.6 Write a narrative summary of these findings. Be sure to include a description of the total sample as well as a description of each intervention group.
- Low Carbohydrate Low Fat Mediterranean TOTAL n % n % n % N % Gender 26 26 26 78 Female 15 57.7 15 57.7 14 53.8 44 56.44 Male 11 42.3 11 42.3 12 46.2 34 43.6 Age Group 18-34 years 7 27.9 7 26.9 6 23.1 20 25.6 35-40 years 13 50 14 15.4 15 57.7 42 53.8 50+ years 6 23.1 5 19.2 5 19.2 16 20.5 BMI Category Normal weight 9 34.6 6 23.1 7 26.9 22 28.2 Overweight 11 42.3 13 50 12 46.2 36 46.2 Obese 6 23.1 7 26.9 7 26.9 20 25.6 Low Carbohydrate Low Fat Mediterranean TOTAL Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Age 39.58 (10.257) (35.54, 43.29) 39.27 (9.594) (35.58, 42.54) 39.69 (10.403) (35.88, 43.65) 39.51 (9.961) (37.17,…Low Carbohydrate Low Fat Mediterranean TOTAL n % n % n % N % Gender 26 26 26 78 Female 15 57.7 15 57.7 14 53.8 44 56.44 Male 11 42.3 11 42.3 12 46.2 34 43.6 Age Group 18-34 years 7 27.9 7 26.9 6 23.1 20 25.6 35-40 years 13 50 14 15.4 15 57.7 42 53.8 50+ years 6 23.1 5 19.2 5 19.2 16 20.5 BMI Category Normal weight 9 34.6 6 23.1 7 26.9 22 28.2 Overweight 11 42.3 13 50 12 46.2 36 46.2 Obese 6 23.1 7 26.9 7 26.9 20 25.6 Low Carbohydrate Low Fat Mediterranean TOTAL Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Age 39.58 (10.257) (35.54,43.27) 39.27 (9.594) (35.58,42.54) 39.69 (10.403)…Low Carbohydrate Low Fat Mediterranean TOTAL n % n % n % N % Gender 26 26 26 78 Female 15 57.7 15 57.7 14 53.8 44 56.44 Male 11 42.3 11 42.3 12 46.2 34 43.6 Age Group 18-34 years 7 27.9 7 26.9 6 23.1 20 25.6 35-40 years 13 50 14 15.4 15 57.7 42 53.8 50+ years 6 23.1 5 19.2 5 19.2 16 20.5 BMI Category Normal weight 9 34.6 6 23.1 7 26.9 22 28.2 Overweight 11 42.3 13 50 12 46.2 36 46.2 Obese 6 23.1 7 26.9 7 26.9 20 25.6 Low Carbohydrate Low Fat Mediterranean TOTAL Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Mean (sd) 95% CI (LL,UL) Age 39.58 (10.257) (35.54, 43.29) 39.27 (9.594) (35.58, 42.54) 39.69 (10.403) (35.88, 43.65) 39.51 (9.961) (37.17,…
- Construct the joint probability mass table of (X,Y)2. A valve manufacturer produces a butterfly valve composed of twosemicircular plates on a common spindle that is used to permit flow inone direction only. The semicircular plates are supplied by a vendor withspecifications that the plates be 2.37 millimeters thick and have a tensilestrength of five pounds per millimeter. A random sample of 20 suchplates is taken. Electronic calipers are used to measure the thickness ofeach plate. A universal testing machine was used to test the tensilestrength. The sample data are found Below. a. Determine, with 95% confidence, if mean tensile strength is less than five pounds permillimeter. Use the critical value approach.b. Are more than half of plates thicker than 2.37? Use the p-value approach with 95%confidence. Thickness Strength 2.4066 4.9175 2.1328 4.8067 2.5937 5.1246 2.1933 4.7555 2.4579 4.7233 2.0665 4.3934 2.1994 4.4609 2.4575 4.7377 2.6724 4.3407 2.2738 4.9487 2.5392 4.4265 2.7956 4.3583 2.1228 4.5608…No. Emp. No. Prod. Wkrs. Value Added by Mfg. Cost of Materials Value of Indus. Shipmnts New Cap. Exp. End Yr. Inven. Indus. Grp. 433 370 23518 78713 4 1833 3630 1 131 83 15724 42774 4 1056 3157 1 204 169 24506 27222 4 1405 8732 1 100 70 21667 37040 4 1912 3407 1 220 137 20712 12030 4 1006 1155 1 89 69 12640 13674 3 873 3613 1 26 18 4258 19130 3 487 1946 1 143 72 35210 33521 4 2011 7199 1 171 126 20548 19612 4 1135 3135 1 21 15 23442 5557 3 605 5506 2 3 2 287 163 1 2 42 2 2 2 1508 314 1 15 155 2 6 4 624 2622 1 27 554 2 52 47 2471 4219 2 292 929 3 74 63 4307 5357 2 454 1427 3 13 12 673 1061 1 20 325 3 17 13 817 707 1 84 267 3 169 147 8986 10421 3 534 2083 3 51 41 3145 4140 2 220 697 3 55 44 4076 7125 2 176 1446 3 84 76 3806 8994 2 423 1014 3 61 47 4276 5504 2 464 1291 3 27 22 1239 716 1 22 356 4 200 178 9423 8926 3 200 2314 4 294 250 11045 11121 3 189 2727 4 38 32 1916 2283 1 29 682 4 17 14 599 364 1 21 197 4 34 28 2063 1813 1 20…
- lineer sistemin varsa çözümünü bulunuz. (Gauss Metodunu uygulayınız.)Observation Brand Price ($) Megapixels Weight (oz.) Score 1 Canon 330 10 7 66 2 Canon 200 12 5 66 3 Canon 300 12 7 65 4 Canon 200 10 6 62 5 Canon 180 12 5 62 6 Canon 200 12 7 61 7 Canon 200 14 5 60 8 Canon 130 10 7 60 9 Canon 130 12 5 59 10 Canon 110 16 5 55 11 Canon 90 14 5 52 12 Canon 100 10 6 51 13 Canon 90 12 7 46 14 Nikon 270 16 5 65 15 Nikon 300 16 7 63 16 Nikon 200 14 6 61 17 Nikon 400 14 7 59 18 Nikon 120 14 5 57 19 Nikon 170 16 6 56 20 Nikon 150 12 5 56 21 Nikon 230 14 6 55 22 Nikon 180 12 6 53 23 Nikon 130 12 6 53 24 Nikon 80 12 7 52 25 Nikon 80 14 7 50 26 Nikon 100 12 4 46 27 Nikon 110 12 5 45 28 Nikon 130 14 4 42 Consumer Reports tested 166 different point-and-shoot digital cameras. Based upon factors such as the number of megapixels, weight (oz), image quality, and ease of use, they developed an overall score for each camera tested. The overall score ranges from 0 to 100, with higher scores indicating better…A municipal solid-waste site for a city must be located at Site A or Site B. After sorting, some of the solid refuse will be transported to an electric powerplant where it will be used as fuel. Data for the hauling of refuse from each site to the power plant are shown in Table P2-4. If the power plant will pay $8.00 per cubic yard of sorted solid waste delivered to the plant, where should the solid-waste site be located? Use the city’s viewpoint and assume that 200,000 cubic yards of refuse will be hauled to the plant for one year only. One site must be selected.