#1 Cπ/2 ST 0 (8 + 4 cos x) dx

Q: The population of a town is increasing at a rate given by P'(t) = 420.0181 where P is the population…

A: The population of a town is increasing at a rate given by P't=42e0.018t, where P is the population t…

Q: The daily cost (in dollars) of producing LG ultra high definition televisions is given by C(x) = 3x³…

A: NOTE: Refresh your page if you can't see any equations. . the given cost function is  where…

Q: Evaluate the following integrals a) S √1+x-√1-² dx (Hint: Maybe you need to rationalize the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Use the graphs of f and g to answer the following about h(x) = f(2g(x) + 1) -2 -1 y 6 5 4 3 2 1 -2 1…

A: Given hx=f2gx+1

Q: It takes Fena Tailoring 2 hr of cutting and 4 hr of sewing to make a tiered silk organza bridal…

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Q: 3. Find the derivative of each function. Use proper notation, and simplify your answers. Thi…

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Q: D Question 8 In the Four-Step Rule, why is the cancellation of the Ax terms allowed even if Ax→ 0 is…

A: Solution

Q: Free fall. In dropping a stone or an iron ball, air resistance is practically negligible.…

A: Given     Acceleration of gravity, g=9.80 m/sec2=32 ft/sec2 At t=0, v=y'=0

Q: e demand function for math self-help videos is given by 55 -0.2x, and the total cost function to…

A: Given query is to find the marginal profit at x = 20.

Q: Suppose f(x)=4/x-2, f'(5)= ____ Use this to find the equation of the tangent line to the curve…

A: Suppose f(x)=4/x-2,   f'(5)= ____   Use this to find the equation of the tangent line to the curve…

Q: 2. A balloon is released upward from the ground at a speed of 5 m/s. When the balloon was 10 m above…

A: In such type of problem we generally use the pythagoras triangle rule . ie.x2+y2=z2

Q: 19) Find the average rate of change of the function from x₁ to ₂. f(x)=x²-8 x₁ = -3 to x₂ = 5.

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Q: Question 6 Given: y = (16+¹) Z -61² (16+74) 3 √16+t¹ 23 (16+) O (E) None of the choices -21² (16+¹)…

A: Solve for the dy/dt

Q: 5. Find the exact value of each x = [0, 2π) for which sin (2x) = √3 cos (x). Leave answer in exact…

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Q: solve  log10(x+3)-log10 X =1

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: What is the value of k so thate(x-1)=4e²³x-k? dx

A: givenddxek(kx-1)=4ek2x-k

Q: (2xy-3x²) dx + (x² + 2y) dy = 0 2

A: Given differential equation:- 2xy-3x2dx+x2+2ydy=0

Q: TT Evaluate the integral: (2costi+ sint j + 2tk)dt

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Q: G(r)=3r^3/2 + r^5/2 /r  *differentiate the function How do I approach problems like this? Like…

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Q: Make an ORIGINAL EXAMPLE OF "Variable Separable" A) GIVEN B) SOLUTION C) ANSWER D) WITH EXPLANATION

A: Given expression, Solve 1+x2dydx=1+y2

Q: Evaluate f cos³ x(sin x) dx O (sin x) [-sin² x] + C O (sin x)[-sin x] + C O(sin x)2/5 + sin x + C…

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Q: Find given the set of parametric equations dy dx x = csc² (at) and y = cot(at), (a) — cot(at) 1 (c)…

A: The objective of the question is determine derivative by help of parametric equations.

Q: 3. Determine the following limit (tabulate). sin (t-1) lim t1 t²+2t - 3 O-1/4 O ⁰ O None of the…

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Q: Find the general solution: sin 2x tan² x y

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Q: 1. Calculate the following limits (showing all working): log₂ (n) + 2n no log3 (n) + 3n (a) lim √7n7…

A: We have to find the limits.

Q: Solve the DE (6x + y2) dx + y (2x - 3y) dy = 0. Hint: Exact O 3x^3 + xy^2 - y^3 = c O 3x^2 - xy^2 -…

A: Given differential equation:- 6x+y2dx+y2x-3ydy=0

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: The function is given by y = x3-23x2+4 To determine: The derivative of the function.

Q: Solve the problem. Find an equation for the least squares line representing weight, in pounds, as a…

A: Solution: We can directly use here Excel for regression, Step1) Enter data in Excel.

Q: Exponential decay. Subsonic flight. The efficiency of the engines of subsonic airplanes depends on…

A: This is a problem related to exponential function. Please follow the procedure given below.

Q: w = xy + yz + xz, x = r cos 0, y = r sin 0, z = re. Findow, when r = 2,0 = π/2. dw 20

A: Concept: Partial derivative: Let's say we have a function f(x, y) that depends on the values of two…

Q: 9. For each set of equations (part a and b), determine the intersection (if any, a point or a line)…

A: I am attaching image so that you understand each and every step.

Q: Let f(x)=xsin(x)/1+x. Find f'(pi/2).

A: We can find the answer in the below steps.

Q: Solve x dy - y dx = 2x³ dx. O y = x^3 - cx O y^3 - x^3 - cx Oy=x^3 + cx O y^3 - x^3 + cx

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Q: Define g(-5) in a way that extends g(x) = x² - 25 x + 7x + 10 to be continuous at x = -5.

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Q: Find the area of the region that is enclosed by the card 10+ 10 sin 0. OTE: Enter the exact answer.…

A: Topic:- application of integration

Q: Direction : Write the expresion in alebragic form  (9) sin(arc sec x

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored 3.…

A: y=(x^3-6x)(2-4x^3) apply product rule y=uv dydx=udvdx+vdudx

Q: II. Find the equation of the normal line to the curves at the point of tangency, if given.…

A: Given:    Equation of the given curve is    y=x3-x22+5x+1 On differentiating with respect to x…

Q: u 2.) du + (-1/2 − u²)dt = 0 t

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Q: A ball is thrown straight up from the top of a building 156 ft tall with an initial velocity of 72…

A: Given data:- The given value is, h0=156 ft The given value of, v0=72 ft/s The given equation is,…

Q: C(x) = 6x³ 30x² + 80x + 1600 where x denotes the number of thousands of televisions produced in a…

A: Given query is to find average cost and marginal average cost.

Q: 1. A balloon is released from the ground 30 feet from an observer. The balloon rises directly upward…

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Q: The UCSB has 8 squads of badminton players. The UCI team has 5 squads. Every squad from UCSB must…

A: Given query is to find the total number of games.

Q: f(x)=x^3(x+3) *differentiate the function

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Q: A tank with a capacity of 300 L is full of a mixture of water and chlorine with a con- centration of…

A: We need to find amount of chlorine.

Q: Problem 5. Find in two ways: (a) (b) (c) S sin 2x dx Using the u-sub u = 2x. Using the identity sin…

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Q: The system of equations 2x-3y-z = -2, -x+2y-5z = -15, 5x-y-z=6 has a unique solution. Find the…

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Q: Find f''(x). f(x) = (x² + 2) f''(x) =

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Q: let a and b be integers such that 7 divides both a+3b and a-2b. Show that 7 divides a

A: Given 7 divides a+3b and a-2b  Then 7 divides (a+3b)+(a-2b)= a+b  And 7 divides (a+3b)-(a-2b)=5b…