Solve the following equations: (You may leave your answer in exponential form or logarithmic form). a) Solve the logarithmic equation log, (r + 25) – log3 (x – 1) = 3 b) Solve the exponential equation e2 – e* = 12

Q: Problem 9. Use the following propositions to draw the corresponding Venn diagram. а. (Gray area is t...

A: The following is the Venn diagram.  

Q: [3] Write the expression below as an algebraic expression in x for x > 0. cos(2 tan x) = -1

A: This question is based on trigonometric ratios.

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Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations t...

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Q: 4.- The population of zebra in an area varies around an equilibrium level X.. The population of lion...

A: We will answer to the question 4a only as it is mentioned and demanded. 

Q: Evaluate the integral. 3. (In(x))² x3 dx 1

A: I am attaching image so that you understand each and every step.

Q: (a). Write the distance from point P(, y) on the line y = 2x to the point (3, 3) as a function of c....

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Q: Use the following propositions to draw the corresponding Venn diagram. Remember to denote the univer...

A: The universal set is the set of all undergraduate students in the University.   The Venn diagram is ...

Q: Using the diagram below, write AG using at least 2 other vectors. Use only AB, AD, and AE in your an...

A: From the given diagram we can see that- AD || BC and AE || CG    

Q: Write down the first derivative of each function in the space provided. Do NOT simplify your answers...

A: Solving questions 

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Q: Find the equation of the normal line to the graph of ey tan(xy) − ln(x2 − 4y) = sin2(πx) at the po...

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Q: Let F(x) = | f(t) dt and G(x) = | g(t) dt, where the graphs of f(x) and g(x) on [0, 6] are below. 4 ...

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Q: (x² - x') 6. Reciprocal Substitution -dx 3

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Q: Let f be a function defined by z = f(x,y) = 3xy² – 4y. Find the approximate change in z when x chang...

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Q: Given the differential equation In(2x – 2)dy + ydx x-1 = 0 then what is = ? 8x y y Зху? + х х-1 O A ...

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Q: Find if-10x – 6y = -6. dx2 Provide your answer below: %3D dx

A: We Have to find second order derivative 

Q: 28) S idx=f /2dx, 28) B)5/2.C D)글지/2.c 29) J 3.²dx=. 29) A) x3 B 3x2 + C C) 6x + C D) x3 + C 30)5sin...

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Q: 2 A = -4 1 6. has an eigenvalue A of multiplicity 2 with corresponding eigenvector v. Find A and X =...

A: Given     Matrix is given

Q: 3. Solve for x of the equation 2 In(x+1) – In(5x+1) + In(x-1) = In(2).

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

Q: The velocity and initial position are given. Find the position function. r(0) = (1, 2, 3) v(t) = (e3...

A: Given that, initial position function r(0) =1, 2,3  and  v(t) =e3t, sint, 6t where v(t) is the veloc...

Q: Differentiating Exponential Functions Find the derivative of the function ex + 2 f(x) ex - 2 f'(x) =...

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Q: dy 1 Let u = tan-y sin y – cos y -

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Q: Solve 2log (x+ 1) =log (x) + log (x+3). Don't forget to check for extraneous solutions.

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Q: 2. Find the maximum and minimum of the function f(x,y) 1 subject to the x² +2y² constraint x* + 2x²y...

A: Solution is given below:

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A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: d²y Find dx2 if –10x – 6y = -6.

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Q: 2-x'y'y'+ xy' =1

A: Let's find. 

Q: Ise the Limit Comparison Test to determine the convergence or divergence of the series V7n 7n3 + 6n ...

A: Given query is to find series converges or diverges.

Q: 1 Does the series > converge or diverge? n· [1+ (In n)²] n=1 Write a detailed solution, and mention ...

A: Use integral test for checking the convergence 

Q: dx 5. Half-Angle Substitution J 3+5cosx

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Q: 8

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Q: A potato is launched vertically upward with an initial velocity of 110 ft/s from 85-foot-tall buildi...

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Q: sin2x 4. Find f'(x) and the equation of the tangent line to y = at x = 1 1-cosx

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Q: Sole (y-+y Jde - xdy -0 When x0, y=

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Q: Find the vector component of v = (4, —1, 7) along b = (4, 4, —7) and the vector component of v ortho...

A: Given,           The two vectors are v=4,-1,7 and b=4, 4,-7.To find : 1 The vector component of v al...

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: uppose ſ, f (x)dx = 8, f(x)dx = 10 , §' g(x)dx = 4 , fó g(x)dx = %3D %3D %D ind : f (x)dx 4 [f (x) +...

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Q: equation 6 = 2*.

A: