Suppose sin(2x) Then sin(x) = = 5 13

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Q: Find the interest rate needed for an investment of $5,000 to grow to $7,000 in 6 years if interest…

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Q: Given f(x)=-25sin (Sx) and f₁0) = -5 and f(0) = 4 Find F(1) 2

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Q: Find the indefinite integral. (Use C for the constant of integration.) [ 14. (4 + x + 2ex) dx

A: We need to find indefinite integral ∫(4+x+2ex) dx We know from integration formulas that, 1. ∫(a)…

Q: 8. For the curve given by r(t) = (2 cos(t), 2 sin(t), 2t + π), find (a) the unit tangent vector (b)…

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Q: Convert the given i-system to an e-system using slack variables. Then construct a table of all basic…

A: Given that x1+x2≤6x1+4x2≤12x1,x2≥0 We have to convert the given i-system to an e-system using slack…

Q: Find and Let 13.5 √10 f(x) dx = 10, 12 [1² f(x) dx = 10.5 √1⁰³ 10f(x) - 5 dx = 12 10.5 Si 9 f(x) dx…

A: Given integrals ∫913.5f( x )dx = 10∫910.5f( x )dx = 5 ∫1213.5f( x )dx = 1

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Q: Find the centroid of the region bounded by the graphs of the functions y = 3x², y = x² +5 The…

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Q: Find an equation of the sphere with center (-5, 1, 7) and radius 7. (x+5)² + (y-1)²(2-7)² = 49 What…

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Q: Find the general solution of the differential equation (4)-40y (3) -40y +400y"=0

A: Given differential equation y( 4 ) - 40y( 3 ) + 400y'' = 0Let d be the differential operator

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A: Given function y = 16x2y = 6

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Q: Show that ∞ Σ n=1 3 n' +1 3 diverges using the Integral Test.

A: As you posted multiple questions I need to solve only one question.

Q: = $2000e0.06x35 35 [ e-0.06t 35 = $2000e2.1 161105 = −$33,333.33e².¹ (e−0.06×35 — e−0.06x0) ,-0.06t…

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Q: A plane P₁ in R³is perpendicular to the vector n = (6, 9, 6), and contains the point (-4, 1,6).

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Q: Write an equation of the form y=a sin bx or y= a cosbx to describe the graph below. MA 150 X

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Q: What substitution will be the most helpful for evaluating this integral? OA. x=2 sin 0 OB. x=2 tan 0…

A: Substitute x=2tanθ  dx=2sec 2θ dθ

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 00 n14 n=1…

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Q: Find a vector a with representation given by the directed line segment AB. A(2, 0, -3), B(2, 4, 3)…

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Q: A chemist, running tests on an unknown sample from an illegal waste dump, isolates 61 grams of what…

A: Given: Initial amount=61g Final amount=12g  Time=66days

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Q: Which of the following is the location of a vertical asymptote of f(x) =tan(2x + 3) − 1? O O O O O X…

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Q: Evaluate the given integral by changing to polar coordinates. dA where D is the region bounded by…

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Q: Growth of Bacteria Under a set of controlled laboratory conditions, the size of the population of a…

A: give bacteria growth function f(t)=3t2+2t+1

Q: The monthly demand function for a product sold by a monopoly is p = 1,988 - R(x) = 1988x X C = 1,000…

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Q: || 4 (x + 4) dx 0 4 2 = [= ² + 4x] 2 0² [( ½ + 4×4) − ( ½ + 4×0)] 2

A: The integral is given by ∫04x+4dx To determine: the value of the definite integral. Formula Used:…

Q: 3 8) fx(x² − 3)dx -1

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Q: (a) Evaluate the sum 20 Σ(2k2 + 3k – 5). k=1

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Q: Use the​ price-demand equation p+0.001x=50​, 0≤p≤50. Find the elasticity of demand when p=​$22. If…

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Q: 1. For all n > 2,¹ 1, e, 4. For all n > e, arctan(n) n³ In(n) n In(n) >, and the series n >, and…

A: we are not allow to solve more than 3 subpart in each question.  Thank you

Q: Please solve this answer ASAP and correctly thanks. Given the function f(x) = x3 - 6x2 + 9x + 10…

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Q: Find an equation of the plane. The plane through the point (5, 0, 6) and perpendicular to the line x…

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Q: afdæ dx Find + C

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Q: dy (a) Show that y*+x-4 = 0 is an implicit solution to dx on the interval (-∞0,4).

A: To show that y4+x-4=0 is an implicit solution  to dydx=-14y3 on the interval -∞, 4. Note: Since the…

Q: If a = (2, -1, 9) and b = (8, 2, 1), find the following.

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Q: Write the e-system obtained via slack variables for the given linear programming problem. Maximize P…

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Q: 2 2. Consider the series Σx-₁(-). Find a formula for the nth partial sum S, and k k+2 determine if…

A: we have given series ∑k=1∞ 2k-2k+2

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Q: A stone is thrown straight up from the edge of a roof, 875 feet above the ground, second. that the…

A: Acceleration  a(t)=-32dvdt=-32v=∫-32 dtv=-32t+C Initial speed: 18 feet per second…

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Q: Use the integral test to see if it converges or diverges

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Q: 49. 8 k=3 1 In k

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Q: Find the indefinite integral. Hint: values where appropriate.) 1 t+6 dt t t + 6 = 1 6 t + 6 (Use C…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: O Write an equation for an expone function with no horizontal or vertical shift that goes through…

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Q: In which limits below can we use L'Hospital's Rule? sin(2x) 2x lim I-0 sin (3x) lim 1/3 3x - T e lim…

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Q: 00 Σ n=2 In n 2 n

A: Note:- As per the guidelines we are supposed to attempt only one question so please upload the next…