I. Find the natural logarithm of the following when z equals: 1. –10 2. –3 - j4 3. 0.6 + j0.8 II. Evaluate the following. 1. z = ji 2. z = (1+j)¯j³ 3. z = -j3(0.6-j0.8) III. Solve the hyperbolic function of the following. 1. Find x in coshx = sinhx + 2sechx. %3D 2. Express sinh*x in terms of hyperbolic cosines and multiples of x, and hence solve 2cosh4x – 8cosh2x + 5 = 0. (x+y 3. Prove that coshx – coshy = 2sinh (2) sinh (). 4.Show that sinhz = sinhx cosy + jcoshx siny

Q: X² test for goodness of fit for Ho based on Po(x)

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 10. fill in the missing valuesto make thė true equations . joa. Toga 7- 1o9g8= 109 a [ - 10g

A:

Q: Solve for x. log,(x² – 4) – log4(x+2) =2

A: Solve for x -> log4(x2-4)-log4(x+2)=2

Q: 9. (log3 x)? – log3 x² = 3 10. 2 In x- In 5 = In (x + 10)

A: 9. log3x2-log3x2=310. 2 lnx-ln 5=lnx+10

Q: Find dy/dx. Do not simplify the answer. 4* +4 csc a.) y = log4 x-csc(4) b.) x3 y + cosh¬1 3 = e –…

A:

Q: f(z) = a log,(Vdecz

A: Given, z = 8 + 9i  when  a=50 , b = 7, c = 10,  d = 12 and n = 6 .

Q: Solve the following log functions to find the value of y:

A:

Q: 4. Find all the values of z for which each equation holds. (a) Log(z – 1) = -i. (b) exp(z+1) =…

A:

Q: 2. Transform the following exponential forms to logarithmic forms or vice versa. f. log2 8 = 3 g. 9x…

A: Since there is multiple questions, we will solve the first 3. Repost the question again to get the…

Q: Logz dz = 0. z-21=1 :Select one True False Clear my choice

A:

Q: 2) If x=0 and y=5 Check if the following statement is true. Explain and show your work. log, (5x –…

A: log of negative number does not exist

Q: ] Evaluate the following (Express all answer in Rectangular Form) a. cot log(1 – 4i) i b. (2ea C. z²…

A:

Q: 1. log(2+ j7) 2. log3(0.223 - 10.332)

A:

Q: Write the following expression as a logarithm of a single quantity. 6lnx – 10ln(x² +3) a. In(6x –…

A: Use log property

Q: 9. (log; x)² – log3 x = 3 %3D

A:

Q: 4. Find all the values of z for which each equation holds. (a) Log(z - 1) = -i.

A:

Q: Drag the tiles to the correct boxes to complete the pairs. Match each equation with its solution.…

A: We know log a + log b = log(ab) log a = log b ⇒ a=b ea=eb ⇒ a=b log a = b ⇒ a=10b

Q: Q.3. Use the Laws of Logarithms to expand the exp

A: given expression is :-logax2yz4then   by using  laws of logrithms  to expand the expression

Q: 5. (i) Evaluate logs 15 + logs 20 – logs 12 (show sufficient working). (ii) Given that y = 3 × 10²",…

A: Use properties of log:  log5ab=log5a+log5b

Q: Q3. Find y, b, or z as indicated (1) Find y: y = logg 27 (2) Find : log, z = -1 (3) Find b: log,…

A: To find y, b, or x as indicated.1 To find y: y=log9272 To find x: log3x=-13 To find b: logb1000=3

Q: h = log(x² + y² + z²), Find hx when x = 1; y = xsinx ; z = xcosx a. 0.89 b. 0.86 C. 0.88 d. 0.87

A:

Q: 60. y = (x² + 1)" (24+7)(2z+1)7 8

A: Formula used log( x )y = ylogx log( xy ) = log( x ) + log( y ) log( xy ) = logx - logy

Q: 1. (x³-2x²+2)dx x-1 sec² xtanxdx 2. S 4+tan² x

A:

Q: Which of the following equations is equivalent to the equation below? 6 8 a) O log, (-8) = 6 1 b) O…

A: Solution

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.