In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 45 + 14 sin (1) Find the average temperature Tave during the period from 9 AM to 9 PM.

Q: A circle with a radius 3 cm long is centered at an angle's vertex, and the angle's rays subtend an…

A: A circle with a radius 3 cm long and an arc length of 14 cm along the cricle.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: r(t)=cos(πt) i -ln(t) j+t-12 kDomain of:cos(πt): no restrictions.(-∞, ∞)-ln(t): defiend for…

Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: The function f(x) = − 6x³ – 29.07x² + 433.242x – 5. is increasing on the open interval ( It is…

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Q: Use the given derivative to find all critical points off, and at each critical point determine…

A: Follow the procedure given below.

Q: Let f(x) = x² - 1 on [-2, 3], Part A: What is the slope of the secant line connecting the function…

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Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

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Q: In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the…

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Q: Current Attempt in Progress Find the arc length of the graph of r(r). r(t) = ²³i+j+₂√6²² k, 25157 Li

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Q: dx/(cos(x)-1) what is the answer to this integral? Use C for constant.

A: Use simple integration formula.

Q: 3. Use Green's Theorem to find the area of the region enclosed by one arch of the cycloid x = t -…

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Q: 11. If we are told that the tangent line to the graph of y = f(x) at the point x = 3 is y = -2x + 1…

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Q: Find the arc length L of the graph of r(t). L r(t) = 12 cos(t)i + 12 sin(t)j + tk, 0≤t≤ 2m

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Q: valuate the integral of the following using Miscellaneous Substitution

A: Given function f(x)=xx2+1we want to find the intengral of given functio

Q: Q-2- A Particle moves in a straight line so that after t sec. it is Sm. from a fixed Point O on the…

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Q: [₁ 2x - x² dx

A: To integrate.

Q: Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent,…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + 1²j|| dt = |

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Q: Verify Green's Theorem by evaluating both integrals ƏN [ 1² dx + 2² dy - [ ] (™N - OM) a dA ax ду…

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Q: Answer the following. (a) Find an angle between 0° and 360° that is coterminal with -68°. 23л (b)…

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Q: Let m(x) be the slope of the tangent line to the curve y=x² x³ 2x² + x at the point (x, y). Find the…

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A: The given geometric series :35+925+27125+...The geometric series can be written as:an=3535n-1 where…

Q: Find the area region bounded by the loop of y^2 = x(5-x)^2

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Q: 4. S dx x+√2x+1

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Q: th is the graph of the original function and which is the graph of the derivative? g f is the…

A: Given the query is to find which graph is  function and which one is derivative.

Q: Consider the system of equations x₁ − 2x₂ + 3x₂ = 1 - 2x₁ - 3x₂ - 2x₂ = 3 x₁ - x₂ = 5x₂ = 2 a.…

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Q: Find the partial sum Sn of the arithmetic sequence that satisfies the given conditions. a2 = 7, a5…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. If it…

A: Here,  an=2n+29n     =2n229n     =492n    =4(4.5)n

Q: Calculate[ri(t) r2(t)] and [ri(t) x r2(t)] first by differentiating the product directly and then by…

A: r1(t)=6t i+ 4t2 j+ 4t3 kdr1dt=6 i +8t j +12t2 kr2(t)=t4kdr2dt=4t3 k

Q: Find the area of the region bounded by the given curves. Decide whether integrate with respect to x…

A: Given curves: y=ex, y=xex We have to find the intersection points of both curves Therefore, ex=xex…

Q: 3x²y' = x(5-6y) x = 1; y = 2

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Q: Solve the following Bernoulli’s differential equations 2ydx + x (x^2 ln y - 1)  dy = 0

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Q: Scos2x (2 cos2x-1) dx

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Q: '1+tanx Evaluate the integral 1-tanx dx A In sinx-cosx + C B -In cosx+sinx + C C -In cosx-sinx + C D…

A: Here, to evaluate: ∫1+tan x1-tan xdx

Q: √25x2-4 -dx, 2/5 cosø dø 2/5 sec^2 ødø 2/5 seco tanø dø None of the choices

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Q: Use the given derivative to find all critical points of f, and at each critical point determine…

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Q: x1/2 dx x3/4 + 1 Let x = z8 dx = 8z7dz Is the substitution the most appropriate one? Explain your…

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Q: Use the given derivative to find all critical points of f, and at each critical point determine…

A: Given :

Q: B. Find the equation of the family of curves whose slope at any point (x,y) is given and which…

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Q: 3) Suppose g(t) = 1/t represents the position, in meters from the starting point, of some object…

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Q: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: ck < cre ISP Question af Calculate for the function f(x, y) = x² + y². dr Select the correct answer…

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Q: Construct the truth table for each of these compound propositions: a. (pvq) → (p @q) b. (p^q) → (pv…

A: We have to find the truth table for the given compounded prepositions.

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: Quiz 2.2- Integration by Substitution Evaluate the following and post your answers in the g.…

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Q: 1) Use the definition of the derivative (which involves limits) to calculate g'(x) if g(x) = 3x² 5.…

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Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

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Q: 6.S dx √1+√√x

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