Prove that for any positive integer n, 4 evenly divides 32 -1.

Q: The average cost per item to produce q items is given by a(g) 0.01g²-0.6q+17, for q>0. What is the…

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Q: Solve by separation of variables: dy dx y²-4 x²-1

A: According to our guideline we are supposed to do the only first question if you want any particular…

Q: Differentiate the function. g'(x) = g(x) 에너 1 VX +x

A: Given:g(x)=1x+x5

Q: Obtain the general solution of the D.E. y - 4y + 4y=e²x O 1 + y=c₂e²+ = x²e² O 1 2x y=₁₁²³² +₂²² + =…

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Q: Determine the exact value of the following expression. tan 137) 8

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Q: Write Sk 1.13+2 14+3•15+...+ Write SK+1- (Type your answer in factored form.) 1.13+2+14+3•15++=…

A: To evaluate:  ------------------------------------------------------------------------------- Basic…

Q: Which of the graphs below could be the graph of a power function with an even power? (a) ☐ (b) ☐ (c)…

A: Even power function With even-powered power functions, as the input increases or decreases without…

Q: A ladder 15 feet long is leaning against the wall of a house (see the figure below). The base of the…

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Q: Find the slope of the function's graph at the given point. Then find an equation for the line…

A: Given query is to find the slope and the equation of the tangent.

Q: Consider the following functions. f(x) = x², g(x)=√x-7 Find (fog)(x).

A: Given,            fx=x2 , gx=x-7

Q: (n^ + n)(n^ − n) = (n)H = H'(u) = Differentiate.

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Q: 1 x 69. g(x) = ₁ ₁³ + 14 dt 3

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Q: 14) y = Tan¹ (3); dy =?

A: 14) y = tan-1( x2 ) dydx = ?

Q: 8. The following table shows the number of Facebook members f(t) in millions over time t, where t =…

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Q: find either lim 5x3 x→∞ ex one that takes less time!) Find lim (1 +5)* X→∞ 5x3 x→0 ex-1 or lim using…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

Q: Find the angle co-terminal with O Ο Σπ 3 - 1/30 17π 2

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Q: O A. No, since we have only shown that Sk+ 1 satisfies the statement. OB. No, since we must show…

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Q: Find the area of the surface generated when y = 2√x from 1 ≤ x ≤ 4 is rotated around the x-axis.

A: We are required to find the area of the surface generated when y=2x is rotated around the x axis…

Q: Find angle A to the nearest degree. 37° 30° 39° 42° 32 37 25 B

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Q: 11. a =(3, 1); b =(− 6, − 2). Evaluate 2 12. a =(3, 1); b =(-6, -2). 3(a - b) Evaluate 3 a-b

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Q: Find the derivative of the function. y' = an−¹(x - √√₁+x²) 2 1 y = 5 tan

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Q: 6) Show that (2xy, 2yz + is conservative.

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Q: Determine the solution of the following differential equations. c) (D¹ + 2D6 + 7D5 + 14D4 + 8D³ +…

A: To determine the solution of the following differential equation.D7+2D6+7D5+14D4+8D3+16D3-16D-32y=0…

Q: List the first five terms of the sequence. an = cos(npi)

A: Given query is to find first 5 terms.

Q: Find the open interval(s) on which f(x) = -5x² + 50x+8 is increasing or decreasing. O increasing on…

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Q: Find the point on the graph of the function f(x) = √x that is closest to the point (30, 0). 59 (2)…

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Q: a) which of the following is the graph. of y = X² ex # B) 2 of 44 c)

A: Shown below...

Q: Differentiate the function. 1 g'(x) ॥ g(x) 1 2x 2 = = VX + X 1 5.( ) *

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Q: Is the function T(s) = (6s-4) (es-5) a power function? If so, identify k and p such that T(s) = ks².…

A: The given function is:T(s)=6s-4es-5

Q: Find the length and width of a rectangle that has an area of 392 square feet and whose perimeter is…

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Q: The cost function for a particular product is given by Cx) - 0.0001x³ +0.018x² +26.7x + 190 dollars,…

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Q: EXAMPLE 5 Evaluate 9x² 8x + 8 x(x² + 4) SOLUTION Since x³ + 4x = x(x² + 4) can't be factored…

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Q: (b) Given the graph of f (x) below (blue), select the correct graph of the transformation y = 2f (x)…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3,    0 ≤ x…

A: I have appended the formula used in the solution part

Q: Find the derivative of the function. y = sin ¹(cos-¹(t))

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Q: Use Stokes' Theorem to find the circulation of F = 4y? +7zj + 7xk around the boundary of the surface…

A: According to question,Given vector,F→ = 4yi→ + 7zj→ + 7xk→z = 64-x2 + y2for z≥0.

Q: The indefinite integral ſ(4x – 4)e¹ª dx can be evaluated using integration by parts. Even though you…

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Q: 20. The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as…

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Q: Consider the ellipse defined as 9x² + 25y² +90x-50y +25=0 • write the standard form equation of the…

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Q: Find all relative extrema of the function f(x) = 3x4-36x³+ 5. Use the Second Derivative Test where…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Differentiate. g'(0) = g(0) = eº (tan(0) — 0)

A: dexdx=ex  d(tanx)dx=sec2xd dx(a.b)=adbdx+bdadxgiven  g(θ)=eθ(tanθ-θ)

Q: Two oil tankers crash in the Pacific Ocean. The spreading oil slick has a circular shape, and the…

A: We need to find radius and area.

Q: 1 1 1 은 관 + dt

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Q: f(x) = x4−32x−12  Determine where the function is concave up and concave down. Enter your answers…

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Q: Sketch the graph of the following function and determine whether the function has any absolute…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 6x + 6 between x =…

A: The function is given as f(x) = 6x+6

Q: 11. -log/2x+3

A: To graph the given function. To state the domain and range. To identify the parent function and to…

Q: Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the…

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Q: Given the homogeneous differential equation, (4D³-3D+1)y=0. The roots of the auxiliary are Om = -1,2…

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Q: 3 7. Given that sec x = =, 270 < x < 360° find 2 (a) sin(2x) Answer: - 4√5 9

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