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 Question

Solve the first order differential equation using any acceptable method.

(6x+1)y2 dy/dx+3x2+2y3=0,    y(0)=1

Solution

Step 1

Given the differential equation is

Now separate the variables as follows

Step 2

Then,

 

Step 3

Then take partial differentiation,

Hence the differential equation is exact

Step 4

Therefore, the general solution of the given differential equation is,

Step 5

Now applying initial conditions,

Substituting the value for C

ST

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QUESTION 6 (a) The bar shown in Figure Q2(a) is subjected to tensile load of 150 Kn. If the stress in the middle portions is limited to 160 N/mm², determine the diameter of the middle portion. Find also the length of the middle portion if the total elongation of the bar is to be 0.25 mm. E E = 2.0 + 105N/mm². (12 marks) 150 KN 10 cm DIA 10 cm DIA 150 KN 45 cm Figure Q6(a) (b) A brass bar, having cross-section area of 900 mm², is subjected to axial forces as shown in Figure Q2(b), in which AB = 0.6 m, BC = 0.8 m, and CD = 1.0 m. Find the total elongation of the bar. E = 1.0 + 105N/mm2 . (8 marks) Page 4 of 5 B D 40 KN 70 KN 20 KN 10 KN Figure Q6(b) (TOTAL = 20 MARKS)

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  Introduction To find incremental revenue and cost, we subtract Current revenue and cost from Projected revenue and cost. Answer Current Situation Projected Sales and Profit Incremental Revenues and Costs Total Revenue Php1,500,000 Php1,800,000 + Php3000,000 Variable Cost 575,000 425,000 - Php 332,000 Direct Fixed Costs 625,000 700,000 + Php 75,000 Indirect Fixed Costs 100,000 100,000 No change Profit Php 200,000 Php 575,000 + Php 375,000 Profit increases by Php 375,000, thus a new camera and coffee maker must be purchased.

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