Find equations for the line in the plane z = 3 that makes an angle of pai/6 rad with i and an angle of pai/3 rad with j. Describe the reasoning behind your answer.

Q: #12

A: (12)Consider the provided question,

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A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

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Q: How would I evaluate this indefinite integral?

A: Consider the provided indefinite integral,Simplify the given indefinite integral as follows,

Q: Find the angle at which the cardioid r = a(1 - cos u) crosses the ray u = pai/2.

A: Given:

Q: Exercises 53–54 give equations for hyperbolas and tell how many units up or down and to the right or...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

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A:

Q: Marcos traveled for 2 hours and 17 minutes on Interstate 17 as he drove (without stopping) a distanc...

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Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second ...

A: Given:

Q: Find the Cartesian coordinates of the following points (given in polar coordinates). a. (0, pai/2) b...

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts fo...

Q: For approximately what values of x can you replace sin x by x - (x3/6) with an error of magnitude no...

A: The Taylor series for sin(x) can be written as:

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A:

Q: Exercises 49–50 give equations for ellipses and tell how many units up or down and to the right or l...

A: Note: We’ll answer the 49th question since we answer only one question at a time. Please submit a ne...

Q: Solve the homogeneous equations (xe^y/x + y) dx - x dy =0.

A: Find dy/dx from the given equation

Q: Find the area under y = x^3 over [0, 1] using the following parametrizations. a. x = t^2, y = t^6 b....

A:

Q: Find the volume swept out by revolving the region bounded by the x-axis and the graph of x = 2t, y =...

A: Given that x = 2t and y = t(2–t). Obtain the interval of integration as follows.

Q: What is the binomial series? On what interval does it converge? How is it used?

A: Given:What is the binomial series? On what interval does it converge? How is it used?

Q: In Exercises 33–34, find the distance from the point to the line. 33. (2, 1, 3); x = 2 + 2t, y = 1 +...

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question...

Q: y + (2xy − e−2y)y′ = 0

A:

Q: Find the volume swept out by revolving the region bounded by the y-axis and the graph of x = t (1 - ...

A: Given,

Q: 4. Recall that the set of Complex Numbers is defined as C = {z| z = a + ib, where a,b eR and i = v-1...

A: (a)

Q: What happens if you add a finite number of terms to a convergent series? A divergent series? What ha...

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Q: Evaluate the limit, if it esxists. (If an answer does not exist, enter DNE.). lim x°-4I+3 x>3 X-3

A: Factor the numerator.Factor 3 so that the sum of the factors is -4Factors are -3 and -1Write -4x as ...

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A: Given the radius of the circle is 2 and the centered at (0, 0, 0).

Q: What is the second derivative of the function:  f(x) = (9x^2)/ (x^2-49) Please show ALL steps

A: Given function is

Q: f(x) =sqrt16 − x2, g(x) =sqrt x + 2 Find (f + g)(x).

A: Given,

Q: y′=y,y(0)=1

A: Use dy/dx in place of y'Then separate the variables. 

Q: Use Taylor’s formula with a = 0 and n = 3 to find the standard cubic approximation of ƒ(x) = 1/(1 - ...

A: The given function is,

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A:

Q: If u1 and u2 are orthogonal unit vec-tors and v = au1 + bu2, find v. u1 .If u1 and u2 are orthogonal...

A: given u1 and u2 are orthogonal unit vec-tors and v = au1 + bu2,

Q: How can you estimate the error involved in approximating the sum of an alternating series with one o...

A: The alternating series test:

Q: Find the points of intersection of the following pair of curves. 29 X+5 y = ,x3 +3x2 +5, y= 9x2 - 2*...

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Q: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

A:

Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the...

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope...

Q: Find the binomial series for the functions in Exercises 11–13. 11. (1 + x)4 12. (1 - 2x)3  13. (1 + ...

A: As per our norms, I am going to solve only one question as you have posted multiple question so plea...

Q: #1

A: Given differential equation and its solution is

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A: Given,

Q: In Exercises 1–3, a. Identify the equilibrium values. Which are stable and which are unstable? b. Co...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

Q: Find the lengths of the curves in Exercises 25–27. 25. x = cos t, y = t + sin t, 0 <=t<= pai 2...

A: The given curve is

Q: give the eccentricities of conic sections with one focus at the origin along with the directrix corr...

A: 1)Given,e = 1, y = 2 Equation of conic with eccentricity e and directrix y=k corresponding to focus ...

Q: How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N ...

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Q: Use the identity sin^2 x = (1 - cos 2x)/2 to obtain the Maclaurin series for sin^2 x. Then different...

A: It is given that

Q: Let u = 5i - j + k, v = j - 5k, w =-15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)...

A: To determine the vector which are,Part (a) ParallelPart (b) Perpendicular

Q: Find the coordinates of the centroid of the curve x = cos t, y = t + sin t, 0<=t <= pai.

A:

Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: Find the angle between the radius vector to the curve r = 2a sin 3u and its tangent when u = pai/6.

A:

Q: What is the arc length function for a smooth parametrized curve? What is its arc length differential...

A:

Q: I need help finding an equation of the tangent line to the function y= cos(3x) with the point ((pi)/...

A: Given:

Q: In Exercises 9 and 10, find an equation for the line in the xy-plane that is tangent to the curve at...

A:  find an equation for the line in the xy-plane that is tangent to the curve at the point correspondi...

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.