Determine by direct integration the centroid of the area shown in the figures. Express the answer in terms of a and h. y=mx h y=kx² X

Q: A small store sells spearmint tea at $2.79 an ounce and peppermint tea at $4.77 per ounce. The store…

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Q: 21. Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a…

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

Q: Find the volume of the following solids by double integration: 10. The solid in the first octant…

A: We have to find the volume of the given solid by double integration.

Q: L[(2t – e^5t)^3]

A: Please see the next step

Q: What is the limit of limx→0 sin_x? 0 1/2 1 -1

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Q: (a) Find all solutions of the equation x³ + x² −2x=0 in Z₁. (b) Let R be a ring. Define what it…

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Q: 12. Curtis bought a condominium for $319 000 and made a down payment of $64 000. The annual interest…

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Q: Determine whether each of the following statements is true or false. If a statement is true,…

A: This is the problem of Laplace Transformation.

Q: For each pair of functions f and g below, find f(g(x)) and g (f(x)). Then, determine whether fand g…

A: (a) Given f(x) = 6x and g(x)=x6   To Find: f(g(x)) and  g(f(x))   Also, find whether f and g are…

Q: 1 0 21 21 4. If M = -1 3 4 and B: = 3 4 078 L5 61 Find the matrix C such that MC = B.

A: To find- If M = 102-134078 and B = 123456 Find the matrix C such that MC = B

Q: 3. Find the full disjunctive normal forms of wffs: (1). p→((p→q)/^\-(-pV¬r)); (2). (p/q) V…

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Q: For the equation y 00 + by0 + 3y = f(t), where y 0 = dy/dt. (a) Find the range of values of b for…

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Q: A ball at 1200K is allowed to cool down in air at an ambient temperature of 300K Assuming heat is…

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Q: Which of the following represents the derivative of f at x? f'(x) f(x₁-x)+f(x₁) Ax f'(x)…

A: Which of the following is the derivative of the function :-

Q: 2 f(x) = √4-x² [-1,1] n = 4 a = -1 right left & middle hand rule b=

A: The given function is fx=4-x2 over the interval -1, 1. The number of subintervals is n=4.

Q: 변 X I sintLy, y Ha จา

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Q: What is math?

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Q: ۵ ۲ ۸۴ ۶ ۲ ۱ می داند؟ مر لا كه - -√ sino 5

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Q: Q1: Find the Fourier coefficients and Fourier series of the triangle function f(x) defined by +x, if…

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Q: What is the indefinite integral of f (x) = x² + 12? S(x² +12)dx= - 1 3x³ + 12x + C S(x² + 12)dx =…

A: We have to find the indefinite integral of f(x)=x2+12 i.e. ∫x2+12dx .

Q: 8. Given the function f(x) = -x³ + x² a) Determine the intervals in which the function is increasing…

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Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

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Q: Let ƒ be a Riemann integrable function on [0, 1]. n (i). Let g be in (0, 1). Find lim La n→∞…

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Q: (1).p^(p→q)^(-qVr) →r

A: We shall solve first question only as you have asked more than one distinct questions. For others…

Q: Find the Parallel Realization for : z² H(Z) = (2-1) (Z-0.5) N

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Q: التاريخ 27 أمر موح let I = (a,b) be an open interval show that - for every positive sM(IDS.

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Q: Let A be the area enclosed between p(x)=- 1 √2-sin x x=³7 ; let B be the area enclosed between…

A: Use the following formulae, to obtain the solution. sinx=2tanx21+tan2x2ddxtanx=sec2x∫dx1+x2=tan-1x+C

Q: What makes a function f(x) continuous at x = c? I. f(c) is defined II. lim f(x) exists X-C III. lim…

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Q: xe -Х

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Q: Determine the following, if possible: (a) intercepts, (b) symmetry, (c) asymptotes, (d) behavior,…

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Q: 9. Convert ₁(4-4x² - y²)dydx into a triple integral with dV = dydzdx.

A: Given, I=∫-11∫-4-4x24-4x24-4x2-y2dydxor I =∫-11∫-4-4x24-4x2∫z=0z=4-4x2-y2dzdydx

Q: B. The dimensions of a rectangular solid at a given instant (t.) are (a = 13 cm). (b=9 cm) and (c =…

A: Given  Dimensions of rectangular solid  a=13cm, b=9cm, c=5cm .Rate of change of a and c increase…

Q: INSTRUCTIONS: ● Please write clearly and understandable way. ● ● Write all the corresponding Given…

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Q: Solve in digital format please and step by step 6. Consider the family of lines (k+1)x+ (k-1)y=k2 -…

A: In given family of lines k is any real number, it means for various values of k we get different…

Q: To Find The outer and inner measure of the following sets: (a) Qn[0,1] (b) [0,1]\Q

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Q: 1. Use Stokes' Theorem to find the portion of the sphere x² + y² +2²=5 inside the cylinder z² + y² =…

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Q: 8. Show that the volume of a cone with height h and radius a equals iterated integrals in…

A: 8 We have to show that the volume of a cone with height h and radius a is equals 13πa2h by using…

Q: Below is a table of data that have been collected Price,p,($) Weekly Demand,s,(1,000s) 150 210 170…

A: Given Data: Price Weekly Demand 150 210 170 203 190 199 210 183 230 185 250 176…

Q: لا sino 5 - امر ir dz ar do

A: Solution :- ∫02π∫02∫04-rsinθ1· rdzdrdθ =∫02π∫021· rz04-rsinθdrdθ=∫02π∫02r-rsinθ+4drdθ

Q: 4. A witness to a hit and run accident told the police that the license number contained  the…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: What is the instantaneous rate of change of the secant function at ? O 2√3 02 0²/0 113 O 03/13 28

A: Solution

Q: Let u, v and w be three vectors in R³. Which of the following is not defined for all u, v and w?…

A: Here u , v and w are three vectors in R3.  We find which of the given is not defined for all u , v…

Q: d. L[eln (te³t)]

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Q: Using Ralston's Method, calculate y(0.4) for the following: y = -5x¹y², y (0) = 1, h = 0.2 y = The…

A: Ralston's method is a 2nd order Runge-Kutta method that uses the formulas below to perform the…

Q: · Let A = {(x₁4) & TR² | xy ≤ 1₂ x+4 >1}. al Graph A. Is A bounded? Is A path connected? O b) Using…

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

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Q: Prove that provided f(z) is analytic at Res (z = ∞0) = lim [-zf (2)] ZIX

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Q: 2.26 let a be a translation of R Then (i) Da is a continuous bijection from onto R an open set under…

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Q: Show That Zero is measurable any function on aset of Measure

A: We have to show that any function on a set of measure zero is measurable. Let E be a set with m*E=0…

Q: 1. Let ƒ : N × N → N be defined as f(m, n) = 2m−¹(2n — 1). (a) Show that f is a bijection. (b) Using…

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