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Q: The “triangular” region in the first quadrant bounded by the x-axis, the line x = 4, and the hyperbo...

A: Given,

Q: A bird flies from its nest 5 km in the direction 60° north of east, where it stops to rest on a tree...

A: A bird flies from its nest 5 km in the direction 60° north of east, where it stops to rest on a tree...

Q: Find the volume V of the described solid S. A right circular cone with height 7h and base radius 4r ...

A: Given that height of right circular cone is 7h and the base radius is 4r.

Q: describe the given set with a single equation or with a pair of equations. The circle in which the p...

A: sphere of radius 5 centered at the origin is given by:

Q: Match the polynomial function with its graph: [A] through [H]

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

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval nota...

A: Consider the provided function,f(x) = (x+8)/(square root x)The rational function is continuous every...

Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: Find an equation for the set of points equidistant from the a. xy-plane and yz-plane. b. x-axis and ...

A: a) Let (x,y,z) be such point that xy-plane and yz-plane are equidistant from it.Distance of (x,y,z) ...

Q: I need help evaluating a derivative of a function at the point (pi/2,18pi)

A: We have given

Q: Evaluate the limit, if it exists:

A: LCM of (x+h)^2 and x^2 is x^2*(x+h)^2.Simplify the numerator using LCD.

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at (a, 0...

A: (a)

Q: Write inequalities to describe the sets in Exercises 45–46. 45. The half-space consisting of the poi...

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

Q: In a psychology experiment, a person could memorize x words in f(x) = 3x2 − x seconds (for 0 ≤ x ≤...

A: a person could memorize x words in f(x) seconds where

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

A: Click to see the answer

Q: Find parametric equations for the circle x2 + y2 = a2, using as parameter the arc length s measured ...

A: The given equation of circle is,

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...

Q: In Problems 11–14 verify that the indicated function is an explicit solution of the given differenti...

A: Verify that the given function is an explicit solution of the given differential equation. Find an a...

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c. zx-pla...

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Ex...

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

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: find an equation for the line tangent to the curve at the point defined by the given value of t. Als...

A: Click to see the answer

Q: Evaluate the indefinite integral. +32 sin(x33) dx

A: Given:

Q: In Exercises 1–3, give a geometric description of the set of points in space whose coordinates satis...

A: To describe the geometric curve satisfied by the equation.

Q: Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 = 3...

A: Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 = 3...

Q: Find a vector of magnitude 3 in the direction opposite to the direction of v = (1/2)i - (1/2)j - (1/...

A: Given,

Q: Find the distance from the point (4, 3, 0) to the a. x-axis b. y-axis c. z-axis

A: To determine the distance of the point from,Part (a) x-axisPart (b) y-axisPart (c) z-axis

Q: slove the differential equation y′ = xy ln x ln y

A: Given:

Q: Exercises 1–4 give equations of parabolas. Find each parabola’s focus and directrix. Then sketch the...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

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: Mixtures 9. Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds...

A: Let the amount of salt in the tank at any time t is given by A(t).So the rate at which the amount of...

Q: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft deep, is fu...

A: Given: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft deep...

Q: What is a parabola? What are the Cartesian equations for parabo-las whose vertices lie at the origin...

A: Explanation:

Q: How do you reindex a series? Why might you want to do this?

A: Any series can be reindexed without changing its convergence.

Q: Find parametric equations for the semicircle x2 + y2 = a2, y> 0, using as parameter the slope t =...

A: Click to see the answer

Q: Solve the inequality. Write your answer in interval notation. |5x - 4| ≤ 7

A: Click to see the answer

Q: Solve the differential equations in Exercises 1–4. 1. x dy /dx + y = ex, x> 0 2. xy′ + 3y = sin x...

A: Consider the provided differential equation,

Q: I need to compute each limit. I have attached the problem as a photo.

A: Given:

Q: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: What are the basic facts about a. sums, differences, and products of power series? b. substitution o...

A: (a) The basic facts about sums, differences, and products of power series.

Q: Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. L...

A: For the given function to determine its behaviour at a critical point x=a, use second derivative tes...

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

A: Problem 1:Recall the following fact.

Q: In the function: f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?

A: Given function is,

Q: How would I evaluate this indefinite integral?

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

Q: What is an infinite sequence? What does it mean for such a se-quence to converge? To diverge? Give e...

A: Infinite sequence: