roblem 4.

Q: Evaluate the integral: dw J 2000 5 W8 W8

A: I have stated the used formulas in the solution

Q: The bearing of a ship from a lighthouse was found to be N 18° E. After the ship sailed 5.5 miles due…

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Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: The measurement of the radius of the end of a log is found to be 16 inches, with a possible error of…

A: Suppose r is the radius of the log with the area of the log is given by: A=πr2 So, we have:…

Q: Find the area of the region that lies inside both curves. r = 2 + cos(8), r = 2 - cos(8)

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Q: 2. Find the gradient of the following functions a. F=x²sin(5y) b. F = x¹yz c. F=x³exy + ²x

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Q: (b) x-2º dr

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Q: A company wants to start a new clothing line. The cost to se up production is 35, 000 dollars and…

A: The solution is given below

Q: S tan 520 do

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Q: Consider the following formulas. a sin Be + b cos Be=a2 + b2 sin(Be + C), where C = arctan(b/a) and…

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Q: / dw W8 W8

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Q: Medium. Answer any two questions. 1. Find all three critical points for the function: f(x, y) = x²y…

A: The given equation is;  f(x,y)=x2y-xy+3y2

Q: By using the substitution z = cos y, show that the differential equation dy cot y dx X can be reduce…

A: Given differential equation,dydx - cot yx = e3x cosec y

Q: 1. Find the exact value for: a) sin (377) 2 b) cot (210⁰) c) sec (-765°)

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Q: Prove that if A is an invertible matrix and B is row equiva- to A, then B is also invertible. ation

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Q: QUESTION 1 Consider f(x)=x²+2x+1. Which of the following is true? Of is continuous at all C; given…

A: Let's solve.

Q: Evaluate du/dy at (x,y,z) = (2,2,0) for the function u(p,q,r) = epqcos(r); p = 1/x, q = x2lny, r = z

A: To evaluate dudy at x, y, z=2, 2, 0 for the function up, q, r=epq cosr; p=1x, q=x2 ln y, r=z

Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

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Q: Find the derivative of f(x): z²+2 . Enclose numerators and denominators in parentheses. For example,…

A: Finding f'(x)

Q: y=x^3+5

A: Please refer to the image below

Q: 2. Consider the function: f(x) = ² +⁹ Step 1. Find the critical values of the function. Separate…

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Q: x=-2 of f(x)=√x²-1

A: Above question is solved.

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: Find the area of the surface generated when the indicated arc is revolved about the y -axis. 6. y =…

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Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

Q: Three atoms with atomic radii of 4.0, 5.0. and 6.7 are arranged as in the figure. Find the measure…

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Q: 1²-29x + 5 dx (d) / (z − 4)² (z ² + 3) d (x

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Q: Compute derivative for the of the

A: Given: hx=log2x232x3

Q: Use the comparison theorem with f(x) = 1 √x [₂² to show that 1 X- is divergent.

A: Show that ∫2∞1x-1 is divergent.

Q: (d) tan¹(x)dr

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Q: If sin(0) and is in quadrant I, find the following: 7 Give exact values. No decimals allowed! cos(0)…

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Q: Use the comparison theorem with f(x) = = 1 √x r∞ 1 •√₂ √I-1 to show that is divergent.

A: Solution is given below:

Q: ve the following: y' - x³y² = 4x³, y(0) 4x³, y(0) = 2.

A: We will solve the differential equation

Q: An open-top storage box with a square base has a capacity of 32 m². Find the dimensions that will…

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Q: ∞ A function is a probability density function if it satisfies the following definition: 1: f(t)dt =…

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Q: Determine whether the series below converges or diverges. If the series converges, find its sum.…

A: Expand the given summation

Q: Solve the initial-value problem for x as a function of t . (2t³ − 2t² + t − 1) 12, x(2) = 0 dx dt =

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the critical points and the intervals on which the function f(x) = (x³ - 2x) e* + 8 is…

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Q: QUESTION 1 Find the absolute maximum and minimum values of the function in the given interval. Use…

A: This is a problem related to maxima and minima of the function. please follow the procedure given…

Q: A = 21° 45', a = 9.5, b = 22 se 1: = ° (smaller B-value) Case 2: B = C = C = O X (larger B-value)

A: topic:- trigonometry ratio in triangle

Q: (y³ − 3y + 2)√9+ x²dx + x²dy = 0

A: To find the general solution to the given differential equation.y3-3y+29+x2 dx+x2 dy=0

Q: Suppose f(z) represents the total number of children that have a symptom, and z is the number of…

A: We can answer both the question as below.

Q: Fill in each blank with an angle between 0° and 360° such that sin 200° = sin and cos 200° = COS

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Q: f(x) Suppose that f(x) and g(x) are differentiable functions such that f(7) = 2, f'(7) = 6, g(7) =…

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Q: Find the Consumer's Surplus corresponding to q=900 units. (Do no rounding of results until the very…

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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: Find the x-coordinate of the centroid of the area bounded by y (x² − 9) = 1, y = 0, x = 7, and x = 9…

A: Given: yx2-9=1

Q: if x - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. f(x) = Let f(x)…

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Q: 2. A ball is dropped from a 20-foot building with a constant acceleration due to gravity of 9.8m/s².…

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