Use the principles of mathematical induction to the statement is true for all natural numbers 4+9+ 14+...+(5n – 1) = (5n + 3)|

Q: Annie's cafe borrows $6,200 at 5% for 280 days. Find the total amount that must be repaid after 280 ...

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Q: The function f has continuous second derivatives, and a critical point at (-4, -4). Suppose frz (-4,...

A: We want to find type of critical point at (-4, -4).

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A: System of linear equations, by solving using Matrix echelon form and back substitution method.

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Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy + 2 at Po(5,2). Then find an upper bo...

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Q: 1 Prove by induction that for any n > 1, ) 1 ji + 1) 1 n + 1 j=1 Your answer must include (1) Proof ...

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Q: Exercise 3 Use Lagrange multipliers to find the maximum and minimum of f (x, y,z)= e»= subject to th...

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Q: Music Preferences Students at a high school were polled to determine the type of music they preferre...

A: Total number of students who completed the poll = 1950 Number of students who preferred alternative ...

Q: The terms of the Maclaurin series of the function f (x) = are 1-x OA. 4-2x +-x 2 4 3 OB. O B. 1+-x+ ...

A: Given f(x) = 41-x

Q: (4) Consider the statement "There exists an even integer n, such that for all rational number q, we ...

A: Statement "There exists an even integer n, such that for all rational number q, we have n²>q" 

Q: Express the given decimal as a percent. 0.3878 %

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Q: Fluid flows into a tank with velocity y. There is a hole in the tank that causes the fluid to flow o...

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Q: ntx" For what value of x the inf inite series al n converges? Ax=Ve. B. xe. E. x=e.

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Q: Give the reason(s) for each step needed to show that the following argument is valid. [p^(p→q)^ (s v...

A: We have to write the reason for the steps.

Q: Detrmine the form of a particular solution of 1. y"-8y'+25y=5x^3e^-x-7e^-x 2.y"+4y=xcosx

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Q: Find the area of the largest rectangle with one corner at the origin, the opposite corner in the fir...

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Q: Solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has...

A: we can solve as

Q: Please write if the set that is given is a semigroup or a monoid or a group of none of all with cons...

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Q: Consider the following system of equations. 2x  +  3y  =  10 3x  +  5y  =  16   (a) Write a matrix ...

A: The system of linear equation can be written by the matrix equation. Matrix equation is an equation ...

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent: (-1)"...

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Q: Find the volume between the cone y = Vx2 + z² and the sphere x2 + y? + z2 = 4. Hint: Use spherical c...

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Q: Write the sentence in symbolic form. Use v, p, and t as defined below. v: "I will take a vacation." ...

A: v: "I will take a vacation." p: "I get the promotion." t: "I will be transferred."

Q: O Reverse the order of integration and do not evaluate. xp hp Show the region.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: 4x^3+48x^2+130x+50 = 0 please solve for X values and show all steps. thank you

A: To find roots of the polynomial, 4x3+48x2+130x+50.

Q: The power series representation of f (x) =- will be given by 3+x OA (-1)"x" - 4<x<4. n=0 4+1 OB. (-1...

A: Introduction: When a function is infinitely continuous and differentiable, it has a power series rep...

Q: 4. Perform each of the following; i. Find all unit normal vectors to the line 3.x + 2y + 10 = 0. 11....

A: Given, Line : 3x + 2y+ 10=0 To find : i) All unit vectors along the given line ii) All unit directio...

Q: Use the circle graph to answer the question. A library classifies its DVDS into one of the categorie...

A: Total number of DVDs = 1717 Percentage of Foreign DVDs = 6%

Q: 2. Express as a single power series form: Σ У(п - 2)аn+1(2х — 3)n+1+ > ап-1(2х — 3)п-1 n=0 n=2

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Q: Let f(x) = (x - 3)-2. Find all values of c in (2, 5) such that f(5) – f(2) = f'(c)(5 – 2). (Enter yo...

A: Introduction: The mean value property is a very important and advanced property shown by a different...

Q: Match each of the following with the correct statement. A. The series is absolutely convergent. C. T...

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Q: Let f and g be continuous functions on [a, b], and suppose that f(a) g(b). Prove that f(c) = alc) f...

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Q: (-1)*+3 Consider the series Which one of the following is TRUE? O A. None of the choices in the list...

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Q: Question 1. Consider the second order partial differential equation = c2 (1) for an unknown real-val...

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Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression...

Q: Change the percent to a decimal number. 7.75% 7.75% =

A: To convert percentage into a decimal numberwe divide the number whose percentage is to be calculated...

Q: 00 (-1)" Given the series 2 n=0 Which one of the following is TRUE? n2+1 A. The series is divergent....

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Q: find the volume under the surface z = f(x, y) over the rectangle R. 1. f(x,y)=4xy, R = [0,1] × [0,1]

A: We can solve this using double integral  

Q: Two vertical poles, 8 ft and 16 ft high, stand 18 ft apart on a flat field. A worker wants to suppor...

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Q: Please help me with this one question (has multiple parts): Which of the following sets form a linea...

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Q: Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answe...

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Q: Evaluate, in spherical coordinates, the triple integral of f(p,0, ¢) = sin ø, over the region 0 < 0 ...

A: Volume by using special coordinates.

Q: 4 The terms of the Maclaurin series of the function f (x) = are given by OA 4 – 2x+ 2-+. 3 2 4 O B. ...

A: We have to find the maclaurin's series to the given function.

Q: -900 4. 6 1 3 1 Let V = span Which of the following set is a basis for V? 2 2 3. -1 -1 1 -1 -1 -1 (2...

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Q: Prove that: ā x (B xẽ) = (ã č)b – (ā-B )ë |

A: We have to prove that a→×b→×c→=a→⋅c→b→−a→⋅b→c→. Let a→=a1i^+a2j^+a3k^ b→=b1i^+b2j^+b3k^ And c→=c1i^+...

Q: 2. Find the coordinate vector of i = (2,3) relative to the basis B = {(1,0), (1, 1)} in vector space...

A: 2. v = (2,3) = -1(1,0) + 3(1,1) 

Q: 1 0V 1- x 0 -1 0 1 A = 2 2x 1 0 0 1 Find the values of x € C such that the matrix M is invertible. W...

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Q: Question 3 What is the equation of a parabola with a vertex at (4,8) and directrix at y 4 Ox+4)^2-16...

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Q: Find the simple interest. Assume the rate is an annual rate. Assume 360 days in a year. Principal Ra...

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Q: Find the interest earned after 3 years if Php12,000 is deposited in a savings account which earns 5%...

A: given  t=3 years principle deposit P=Php12,000 rate of interest, r=5% claim- find the interest earne...

Q: The population of a country has been increasing for several decades. In 1990, the population was abo...

A: The percentage change in a quantity is given by the equation; % change=changeinitial value ·100