Show that, given the three angles A, B, and C of a triangle and one side, say a, the area o the triangle is [ABC] = a² sin B sin C 2 sin A Note: [ABC] refers to the area of triangle ABC.

Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

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Q: Test for convergence / divergence. Find the limit if result is convergence.

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines

Q: A real estate firm estimates that the value of a certain property will be given by the function V…

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Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: Determine whether the series k=1 3\k-1 converges and if so, find its sum.

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Q: Solve using Variation of Parameters (D² + 1) y = tan x O y = c₁ cos x + c₂ sin x − cos x ln(secx +…

A: The objective is to find the general solution using variation of parameter.

Q: Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 5π/4…

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Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A: We have to find the area of the given region.

Q: Sort St Question 2. Evaluate the following integral region). Show all your work! cos(x²) dx dy. Make…

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Q: find the general solution of the given equation. y''+2y'+6y=0

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Q: 4. Let sinx = Ź (-1)" x²n+) 2n+1 n=d ♦ a) Find a paver series for xsinx, Differentiate the power…

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Q: If f (x) = x(x - 1)³, then which of the following statements is correct? f(x) has a maximum point at…

A: We have to select the correct statement from the given statements.

Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: To find the dimensions that minimize the amount of metal needed to make the can.

Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

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Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

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Q: B. Find the general form of the equation of the tangent line to the given curve at the indicated…

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Q: 1 вхось xа(1 — x)bdx - = 6xº1 Bx®1 - x)dx /0

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Q: Determine the area of the region bounded by x=3+y^2, x=2-y^2, y=1 and y=-2. *

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Q: 1) If y = (x-a)√2ax-x² + a² sin-¹(*), then y' = 2√/2ax - x² a a is constant. 2) If f(k)= k√a²-k² +…

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Q: 2. If g(x)=√√3-x and f(x) = x³ +1 evaluate the following: gof(-1) b. (g-f)(2)

A: Given, g(x)=3-xf(x)=x3+1

Q: 4. x² + y² = 25 at point (3,4) 2

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Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±7), vertices: (0,…

A: We have to solve above hypobola question

Q: If the present value of an item is P and we experience an inflation rate of r for t years, what will…

A: solving the problem by finding the value of the future value.

Q: - 6 = ₁6 -X

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Q: A. Find the derivative of each of the following functions. 1. f(x) = 5x -9 2. (x)=-6x +3 3. /(x)=x²…

A: In this question, we need to find the derivative of the given functions. Note : Please note that as…

Q: x = 1. 2. Find the derivative of f(x) = 3x² - 5x at x = 1 using the formula f'(x) = lim f(x)-f(xo)…

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Q: Use the chain rule to find where st the pieces: z = x²y + xy², x=3-t³, y=3-t6

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Q: EX 4: a) Determin the value of A and B for wich the vector field x4 F (X₁y₁z) = Axluze + B By ² z 5…

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Q: Consider the function f(x,y)=-2x²+12x-6y²+4y+4xy+24. (a) Find the partial derivatives of f(x,y).…

A: As per guidelines, I can answer maximum three sub parts of a question. To know rest, please repost…

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y=√x,…

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Q: Given that sin(0)= TT 3 and 2 <0<π what is the exact value of cos(20)?

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Q: Solve the DE using laplace transformation: y''(t)-y(t)=4cos(t); y(0)=0, y'(0)=1 the answer should…

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Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

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Q: It is known that for a function f(x), f'(1) = 0 and f" (1) = -0.5. What does the Second Derivative…

A: This question can be solved using the concept of second derivative test.

Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: The equation P=25sin(2πt)+90P models the blood pressure, P, where tt represents time in seconds.…

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Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.8q +800, what profit can be…

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Q: A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics…

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Q: Let T : R² ⇒ R³ be a linear transformation such that T([ 1 ]) = = 8 [][]) ([ 13 0 What is T -1 and T…

A: Concept: A linear transformation is a feature from one functional area to some other that takes into…

Q: Find the general and Singular Solution o the Following differential equation yLny = xyP+ P²

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: A population grows according to the model, 1400 e 0.06t where A is the population t years after the…

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Q: 1 x² + y² = 4

A: Given: 1x2+y2=4

Q: 8 9 - 4e²™ dx Please approach doing this integral by hand with the following steps: First, make a…

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Q: You deposit $1500 in an account with 5% annual compound interest. Complete the following, assuming…

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Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A: Given  Population in 2000 = 45,000  Population in 2010 = 65148

Q: Graph a vector, opposite to the given vector, that has an initial point at the origin.

A: In order to graph the opposite vector we need have one more point along with the origin.

Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…