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Q: ony observed that a small colony of penguins obeys the population growth law. There were 1000 pengui...

A: we know that population growth formula. A=Pertwhere P is initial population,e is irrartional conasta...

Q: 1. Let z = f(x, y) be defined by the given equation. Find the total differential of z at any point o...

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Q: 4. Determine whether the series -D"(n³+6n) n° +n³ +1 converges absolutely, converges conditionally o...

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Q: 5. Cx sin y +x²y = Ay

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Q: If initially there are 50g of a radioactive substance and after 3 days, there are only 10g remaining...

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Q: Let G be a simple connected planai 13 vertices and 19 edges. Then, the number of faces in the planar...

A: For any planar graph with v vertices, e edges, and f faces, we have v−e+f=2  

Q: Evaluate the integral S(VE + vaj*dx; ais constant

A: Explanation of the answer is as follows

Q: Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix e...

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Q: Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengt...

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Q: 2. The volume and radius of a right circular cylinder change at the rates of 1 cm^3/s and -2 cm/s, r...

A: Given : Radius = 2cm, height = 1 cm Rate of change of radius is 2 cm/s and rate of change of volume ...

Q: Find the absolute extrema of the function fex)= +14* 2/5 on the interval I-2,41. The absolute maximu...

A: To find absolute extrema of the function f(x)=(x2+14)25 on the interval [-2,4]

Q: Write the expression as a compl I) (-8 + 8i) – (2 + 4i)

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Q: For the function g (t) = – tan(2t 4 State the period and the phase shift. Give the equations of the ...

A: Given: gt=-tan2t-π4

Q: PART I. Find the general solution of the following differential equations using FOLDE or FOBDE. ( a....

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Q: Using the ratio test

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Q: Evaluate the indefinite integral using integration by parts | et cos (2z) dæ -answer choices e4z sin...

A: As we know that the expression for the integration by parts: ∫udv=u·v-∫vdu Given: I=∫ e4xcos2xdx

Q: What is the general solution of (sin 8 – 2rcos?0) dr + rcoso (2rsind + 1) de = 0 ? - O rsine p2 cos?...

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Q: Eyaluate the following limits 1. lim x->-0 x"(- 2x² +5) x° + x°

A: As per question we solve questions 1

Q: Find the absolute extrema of the function f(x)-X-32x+256on the interval -5,5). The function has an a...

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Q: +1 dx x+1 10.

A: As we know that the power rule: ∫xndx=xn+1n+1+C ; n≠-1 From the given problem: I=∫01x3+1x+1dx

Q: Find the derivative of the following functions using implicit differentiation. 1. x^3+y^3-6xy=0 2....

A: follow next step

Q: xsin 'x =- V1-x² dy Find dx If y

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Q: Solve for x X-1-3 – 10,x e-2, 4. х+2 х-4 3 Хе-2,4.

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Q: Find the dimensions of a cylinder of volume 5 m3 of minimal cost if the top and bottom are made of m...

A: In order to solve this problem, first we need to find the expression that represents the total cost....

Q: f(x)=x(^2)e^x a) determine the inflection points of f b) find the critical numbers of f

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Q: n100100" Σ n! n = 1 Identify an 100100" n! Evaluate the following limit. an + 1 lim dn

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Q: 1 xp: J 3x/x² – 81 A farene () -e °rene () + -Arcsec 9 1 Arcsec В. 27 9 1 C. Arcsin (5) Are 1 뉴Arcsi...

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Q: Find the areo and centroid bounded by y = x, y= /x, first quadrant. Graph.

A: As we know that the expression for the centroid of the bounded region: x=∬xdAA ; y=∬ydAAWhere;A=∬dA ...

Q: (-5-х-4):(-2-х-9) Let f(x) = (4:x-2)-(5.x+3) Indicate which of the following points x are in the dom...

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Q: Twenty feet of wire is to be used to form two figures. In this following cases, how much wire should...

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Q: Solve the following problems. 'ind the value of cos 15°. Further show that cos 15 < 0. Conclude that...

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Q: PROBLEM 2: Evaluate the polynomial y = x³ – 5x? + 6x+ 0.55 at x = 1.37 , use 3 significant digits. U...

A: The given polynomial is:y=x3-5x2+6x+0.55Given that x=1.37

Q: Evaluate the definite integral and show complete solution

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Q: 24. The graph of f(x) is given below. Based on this graph detemine where the furction is discontinuo...

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Q: (a) Estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = 7/2 using four approximat...

A: The solution of the given parts a,b,c are done in step2.

Q: 9) Find the perperdicular distance between X+24+32=5 -42=10. Xey+22=12 -32-25 and 2*+39 b)Find its e...

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Q: Find the general solution to the following equations: dy у-х dx y+x

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Q: Determine the solution of the differential equation dy cos? x sinx dx + (cos³ x)y = 1 a. y = tanx + ...

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Q: Find the area and the centroid bounded by y=-x^2+6, y=x^2+3x and graph.

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Q: An RL circuit of 3-ohm resistance and a 10-henry inductance is energized by a voltage source. How lo...

A: Given the data

Q: (1.056 x 109) e - 0.55t In In (f'(t)) %3D (1+ 600 e - 0.55t) 2

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Q: Question 9 of 12 > Attem Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x6 1 g(x) бх ...

A: Explanation of the answer is as follows

Q: EVALUATE THE FF. LIMITS. 1. lim (x+2)2 +3 x6+ x3 2, lim メウ- ○ x"(-2x²+5)

A: limx→1-[1x+1-1x+22+3

Q: Use the binomial formula to find the coefficient of the q^2y^21 term in the expansion of (2q -y)^23

A: We are going to solve

Q: A passbook savings account has a rate of 10%. Find the effective annual yield, rounded to the neares...

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Q: Find 2 sin(r + sin(x + sin a)) – 2 cos(cos 1) lim 2.r – T asing L'Hôpital's Rule.

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Q: Find f + g, fg, go f, and f o g where f(x) 1 and g(x) = sin 3x – Vx + 1 -

A: Given, fx=1x   and  gx=sin3x-x+1 We have to find f+g, fg, g∘f  and  f∘g.  

Q: What is the general solution of (73 + s) dr + s2 (3r + ks ) ds = 0 0 where kis a constat . O rs + 4r...

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Q: dy 6. So 1+y+1 6.56

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Q: Decide which test for convergence is appropriate and then use it to determine whether the series is ...

A: To find whether the series icls convergent and divergent