+3J -7x -21 0 ENGINEERING MATHS TECHNICIAN PROGRAMMES ASSIGNMENT TWO TERM 2 AND 3 2024 QUESTION Express In (x)+ In 4- ½ ln x as a Smale log 6) Solve the Simultaneous equation x+2y+2=3 2x+y+32=-1 3x+2y+ 2 = 7 QUESTION 2 from A Cylindrical Can (with lid) of radius rcm is made from 300cm of Thin Sheet metal a) Find and hs a) Show that the height, hem is given by h = 150-xr b) Fmd and h So that the Can will Contain Ar the maximum possible volume and Find This Volume. QUESTION 3 From the point P(1,3), a perpendicular PQ Is drawn to the line Joining A(-4, -8) B(4,4) find a) £quations of AB and the perpendicular 6) Coordinates of the point where they Intersect c) Distance of P from the line AB P(-1,3) A(-4,-8) B(4,4) →x о

Q: Condense 1 log5 (y) +-log5 (y - 3)- 6 log5 (y + 7) = 3 The answer format in lowercase characters is:…

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Q: = If log, (x+ 1) = then x اختواحد الخيارات 20 3 2.

A: Given log9x+1=12 Apply log rules logbx=yThe anti logarithm is calculated by raising the base b to…

Q: 1 2 log125 (5x - 5) = 1 + 6 1 3 1 log25(x - 1) + log5 (x − 3) 3

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Q: Solve equation 3* e4x-1 = 5 for x giving your answer in the form of a, b, c and d are integer…

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Q: 1. Solve the following equations: - a) b) c) log₂ (5x - 1) - log₂ (16-3x) = 5 253x+2x625 1258x = 1…

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Q: solve: loga (4x+4)= log₂ (-7x+19) = X= AS lenter DNE if no rolution)

A: topic - logarithmic equations

Q: A) √9-x2 (7) According to the method of partial fractions, C) -1 DY (x-1)(x-2)(x-3) D)3 = (x-1) + B…

A: If the expression of the partial faction after simplification is of the form:px+q= A(x-a)(x-b)…

Q: 1 14) log, 3 + 2 log, 25-log, r 15) log x + log 5 = 2

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Q: 4) 19-17-log₂ (2x+4)

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Q: 15 loyy o4=x 16 og 2 243: 2x+l 64=7

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Q: 7) log-2(-8) = x 8) logix = 5 2 9) 2* + 2* = : 10)3*+2 = 92x-3 2

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Q: Solve each equatio

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Q: A) 4 2 (9) The derivative of 2sin-¹x (2sin-1x) In 2 A) √1-x2 B) is: 2sin 1x √1-x² (2sin 1x) In 2 C)…

A: The given problem is to find the derivative of the given function.Given function,2 sin^(-1)x

Q: Make the substitution v = ln x of Problem 51 to solutions (for x > 0) of the Euler equations in Prol…

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Q: 1 1B= (1 – i)10 + 40eš", and 1+ 1+i If A = 1+ C = log [2 + In(3 + 4i)] Solve for A + B + C. Reduce…

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Q: Solve for x log₂ (x) + log₂ (x + 12) = 6 a) 4 b) -16 O c) 4,-16 d) -4, 16 e) None of the above E

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Q: 7. Simplify the following expressions: a) Ine-7x² = b) log4 17 = c) In(-2) =

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Q: 4. log5 x > 3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Example 2: Solve the following equations for x. a) log, 30x-log₂ 5 = log₂ 12 b) log (2x+1)+log(x-1)…

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Q: = SCADX (40x e**²-5) dx 1. S[(GN=51) 10 Jax = log2 (OXP²41) 6X 7- ² 105_ [ [10CC (1014 4X²-5 8. 5 e…

A: Note:  As per our guidelines we are restricted to solve more than 3 subparts of a problem.…

Q: Combine the two equation and make Eeq the subject , no value need just one equation

A: The combined equation for (Eeq​) is:…

Q: a) Solve the following equations: i) 3* . 42r+1 = 6*+2. ii) 2 log,(VT) – log,(6x – 1) = 0.

A: '' Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Method 2: 51-3 = 10 => log, (5-) = log, 10 t-3 = log, 1C by(2) a) 4·73t-1 = 7 35t b) 7 – 4 = 6 c)…

A: The following properties are used, logaxy=ylogaxlogaa=1logab=logblogalogax=y⇒x=ay

Q: xquis 1+4 3 & Wä

A: The given expansion is:                                                         ∑n=1∞-1n+1sin nxn

Q: Ive 24 = 6 3 BO x = log₂24 Cox = log₂ Dor=! I= log₂6 log₂3 2

A: Given equation:- 24x=6