Find the area of the triangle with vertices P(1,5, −2), Q(0, 0, 0) and R(3, 5, 1). NOTE: Enter the exact answer. A =

Q: Find the area between the curves y = e-0.7x and y = 1.5x + 1 from x = 0 to x = 1.

A: Explanation of the answer is as follows

Q: (c) I² +4 3x³+4x² - 4x [3 -dx

A: Here we have to find the integral.

Q: CHECKPOINT 3.14 √ √ Rewrite the integral evaluate the integral). x³ √25x² dx using the appropriate…

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Q: Solve the initial value differential equation: (x² + 1) + 3xy = 3x where y(0) = 2

A: Given Differential equation,x2 + 1dydx + 3xy = 3xandy0 = 2

Q: Find the general solution to the following problems: 1. (D² + 4D + 5)y = 50x + 13 e³x 2. (D² - 1)y =…

A: 1. Its AE is: D2+4D+5=0 D=−4±16−202=−2±i Thus  CF​=e−2x(c1​cosx+c2​sinx) Here X=50x+13e3x Lets find…

Q: ∞ Σ (-1)kk sin k=1 Let ak> 0 represent the magnitude of the terms of the given series. Identify and…

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Q: 3. Use polynomial division to show that the general expression for the factors of the difference of…

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Q: 1 2. S- 9y²+64 dy

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Q: Your friend is having difficulty answering the following question. List the steps, both…

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Q: problem for x as a function of t. Solve the initial-value dx (t² − 10t + 21) = 1, (t > 7, x(9) = 0)…

A: The given equation is;  (t2-10t+21)dx/dt =1 (t>7, x(9)=0)

Q: Use the second derivative test to find the location of all local extrema in the interval (0, 2π) for…

A: Here we have to find the local extrema.

Q: Calculate the first eight terms of the sequence of partial sums correct to (-1)^-1 n! 1 2 لیا A 5 N…

A: Topic:- sequence and series

Q: . Find the solution of the differential equation. 25y’’-20y’+4y=0 theme: repeated roots; order…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i - 8j as…

A: Suppose ABCD is the parallelogram with AB=i+j & BC=i-8j. So, the diagonals are AC and BD.

Q: The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a…

A: Given: The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams)…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: We first need to find complementary solution Auxiliary equation is given by m3-2m2-m+2=0…

Q: =(4,-1, 7) along b = (6, 6, -7) and the vector component of v Find the vector component of v =…

A: Given vector,v = 4, -1, 7b = 6, 6, -7Vector component of v orthogonal to b.

Q: Use the fact that the volume by the vectors u, v and w is of a tetrahedron with adjacent edges given…

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Q: Find cube roots of -64i. Graph each cube root as a vector in the complex plane

A: To find the cubic roots.

Q: ∞ Σ (tan ¹5k-tan-1 (5k-5)) k=1 ∞ The series Σ (tan k=1 -1 -1 5k - tan (5k- -5)) can be tested for…

A: Given :∑k=1∞tan-15k-tan-15k-5

Q: Does the series (-1)k +1_ k=1 6 k +4 converge absolutely, converge conditionally, or diverge? Choose…

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Q: A test requires that you answer either part A or part B. Part A consists of 9 true-false questions,…

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Q: Determine whether the following statement is true or false. ƒ(x) − ƒ(1) x - 1 If lim- x→1 O True…

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Q: Give the reference angle for 8= O 5 T 12 O 07T 12 O None of these It has no reference angle TT 12 7π…

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Q: 9. lim (e* + x)²/™ x48

A: Let's evaluate limit.

Q: f(x) Find the extrema and possible points of inflection (if any exist) of In x X

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Q: 12. Solve the problem with given initial value. y’’-6y’+9y=0, y(0)=0,  y’(0)=2 theme: repeated…

A: To find out the solution.

Q: Find y as a function of a if y(0) = 7, y'(0) = 10, "(0) = 36, "(0) = 0. y(x) = 0 y(4) 12y" +36y" =…

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Q: 1. Determine the number of degree and the end behaviours of the polynomial y = (x + 5)(x − 1)(x +…

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Q: 3. Evaluate S dA where R is the region between y = 2x and y² = x³ lying to the R left of x = 1.

A: Let's evaluate double integral.

Q: Sketch the region enclosed by the given curves, y = 3x² and y = x² + 4. Find the area of the region.

A: Given curves are y=3x2 and y=x2+4.

Q: 10. S 1 √√x+ ³√x dx

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Q: Find the solution of the given initial value problem 88y" +19y"+y = 0, y(0) = -5, y'(0) = 6, y"(0) =…

A: To find out the particular solution.

Q: Suppose that f(5) = 1, f '(5) = 7, g(5) = −8, and g'(5) = 9. Find the following values. (a) (fg)'(5)…

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Q: A charge to rent a saw per day or a fraction of a day Fixed Cost $5 variable cost $10 1 1/3 = 2…

A: We have to find the total cost for 113 days.

Q: Σ k=1 3k! k Choose the correct answer below. A. The series converges absolutely. B. The series…

A: The given series is: ∑k=1∞3kk!kk Now, it is a positive term series. So, it is either absolutely…

Q: dx 2- sin x

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Q: x² + y² =a²

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Q: Verify the identity. sin 5x √√2 (sin x- cos x) Write the left side in terms of a sum or difference…

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Q: Use the point on the line and the slope of the line to find three additional points that the line…

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Q: Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. B= C= a= A b…

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Q: Find the indefinite integral. (Use C for the constant of integr √(x-8 - 8)² dx

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Q: 198 5k Σ 4 k=1 7k +3 loose the correct answer below.

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Q: Evaluate using Reduction Formula 1. f cos7x dx 2. f sin³x dx cos x x dx n cos-1x sinx + 1 sin" x dx…

A: We use the given formula for sine to evaluate the given integral. But the given formula for sine is…

Q: Question 2 Choose the correct answer. The average rate of change of the function f(x) = x² + 1 from…

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Q: Use the Law of Sines to solve the triangle. Round your answers to two decimal places. C = O a = b= A…

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Q: f(x) = In (x) + In (25-x²), (0,5)

A: 1st derivative test

Q: A ship is just off the shore of New York City. A sighting is taken on the Statue of Liberty, which…

A: Given  Height = 305 feet  Base = 950 feet  We need to find the angle of elevation

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

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