User = }= * 3 – 5 2t to parameterize the equation: y t+ TI t²³ + +²2² +

Q: Find the domain of vector r(t) and find the limit as t goes to 0 of vector r(t)

A: According to question,Given vector,rt = 2-t, et-1t, lnt+1

Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 400mi/h and…

A: Let ditance along east = x distance alond north = y Given dxdt = -400dydt = -200

Q: 5) d²y dy +6 dx² dx +9y=4exp(-3x), y(0)=3, y'(0) = 2

A: The given differential equation is: d2ydx2+6dydx+9y=4e-3x, y0=3, y'0=2 So, we can also write as:…

Q: (r, 0) = (2, 110°) What is the sum of x and y?

A:

Q: Solve for x. log3(x-4)= 5 X = (Separate answers by a comma.) If the answer is radical use sqrt(5) to…

A:

Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A:

Q: Find the area bounded by the curve y = 3e and y = 3e x = 2. and the ordinates at x = 1 a

A:

Q: What is the value of cos-¹ (-¹)? Enter your answer in the box.

A: To find:- cos-1-12

Q: Find an equation for the tangent plane to the surface z + 4 = xy cos(z) at the point (4, 1, 0).…

A:

Q: Take a standard 8.5 in. by 11 in. page of paper. You're going to cut square corners of equal size…

A: According to question,We have,Dimension of paper : 8.5 in. × 11 in.

Q: The vectors u, v and w are shown in the diagram below. 80° V 40° Given Jul = 6, |v| = 8 and [w] =…

A:

Q: Evaluate the integral and check your answer by differentiating. 4x6 / 2² +10²-1 dr == +C

A:

Q: slope

A:

Q: #5 y = √² x Volyne find 5 254≤ Votate y-axis

A: 5. The given data is: y=x3y3=x,      2≤y≤5  Find the volume rotate about y-axis.

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 300e-x² - 3y²-72² where T is measured…

A:

Q: Explain why the columns of an n x n matrix are linearly independent when the matrix is invertible.…

A: Solution: To prove that the columns of an n x n matrix are linearly independent when the matrix is…

Q: A balloon is rising vertically above a level, straight road at a constant rate of 5 ft/sec. Just…

A:

Q: Evaluate the integral and check your answer by differentiating NOTE: Enter the exact answer. / [²…

A:

Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A:

Q: x=-2-5i und w = 4 + 9i a = x x+w x-w -x w X W 4 W - Χ · |x| = x + |w||

A:

Q: 9. 7-6-5-4-3-2 -3-2-1\0/ 1\2/3 익

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 3. Show that there are no tangents to the curve f(x) = 9x³ + 2x² that are parallel to the line 2y +…

A:

Q: The volume V of a right circular cylinder is given by V = r² h, where r is the radius and h is the…

A: Sol:- To find the rate of change of V with respect to r, we need to take the derivative of V with…

Q: 62. Let S be the collection of all sets with at most 5 elements. Then: A. An element of S is a set…

A: Sol:- Option A is correct: An element of S is a set with 1, 2, 3, 4, or 5 elements.

Q: Suppose the temperature in degrees Celsius over a 10-hour period is given by T(t)= -12 + 5t+31. a)…

A:

Q: Need help with the following problems: 1. Solve this differential equation: e^t (dy/dt) = y^2,…

A: we do only first part of multiple questions (1)  et(dydt)=y2y(0)=-14∫etdt=et+c∫tndt=tn+1n+1+c

Q: Show that f(x, y) = e³x sin 3x satisfy Laplace's equation.

A:

Q: 4. The fish population, p, in a lake can be modelled by the function p(t) = 15(t² +30) (t + 8),…

A: p(t)=15(t2+30)(t+8)rate of change of fish population is d dt(p(t))d dt(tn)=ntn-1

Q: 5) Use mathematical induction to prove that Σ(2¹)=2+(n-1)2+¹ 7-1

A: Prove the equation

Q: Find the area of the region under the given curve from 1 to 2. y = 9 x³ + 3x .3

A:

Q: Problem #7: Find the arc length of the parametric curve x = 5+18r², y = 2+12³, 0≤t≤1. Problem #7:…

A:

Q: The United States population in 1800 was 5,308,000 and in 1900 was 76,212,000. Assume t = 0 in 1800…

A: The united states population in 1800 was 5,308,000 and in 1900 was 76,212,000. Assume t=0 in 1800…

Q: (C) (E) (G) -1.5 -1.0 -0.5 1.5 1.0 0.5 1 2 -1 0.5 1.0 1.5 2 (F) (H) 2 1 0.5 -5 1.0 1 1.5 1 2

A: Note:- According to guideline we can do maximum 3 sub parts so i am solving here first 3 sub parts.

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A:

Q: 6. For each series determine if it converges or diverges, and if it converges find its sum: (a) Σ 8.…

A:

Q: e the integral using 1

A:

Q: 16. Determine the vector equation of each line.

A: a) Since the line is parallel to the y-axis, its direction vector is ?=[0,1,0] . The line passes…

Q: 10. Two ships leave the harbor at the same time. One ship is traveling at 14 miles per hour on a…

A: From the data  after 3 hours first ship travel = 14*3=42 mi2nd ship travel = 12*3=36 mi

Q: Find the Laplace transform of f(t) = 4 + 3t – 5t² — 2(t-1) a. (6s²-s-10)/s³ b. (6s² + s-10)/s³ c.…

A: Here we have to find the Laplace transform.

Q: 3. Let (an) and (b) be sequences. Suppose that (an) converges to 0. (a) Using the definition of…

A:

Q: Find the derivative of the function. y = In 7x OA. dy 1 dx 7x ㅎㅎ ㅎ증 중증 중증 OB. dy OC. dy dx = dx X =…

A: To find the derivative.

Q: 4. Find the critical points of the function f(x, y) = 2x² - y² +3. Does the function attain maxima…

A:

Q: 1. Determine f'(x) and DO NOT simplify. f(x) = 2x³7x² + 3x - 1 a) c) f(x) = -3√x 2 b) f(x) =…

A: To determine f'x and to do not simplify. (a) fx=2x3-7x2+3x-1 (b) fx=5x2-3x (c) fx=2x2-3x

Q: A 12-ounce soda is roughly 12 centimeters tall by 6 centimeters wide. Convert the volume to cubic…

A: Please see the below picture for detailed solution.

Q: 3. What is the exact value of the trigonometric expression? 2π 3 7π 4 tan sin - sec (-7)

A: Given tan( -2π3 )sin( 7π4 )- sec( -π )

Q: 3. Find the equilibrium point for the demand and supply functions for the Ultra-Fine coffee maker.…

A: Solution is given below:

Q: Select the situations that could be modeled by tangents and circles. a knife that cuts a circular…

A: The given data is: Select the situations that could be modeled by tangents and circles

Q: Solve the equation dy-5y-te'y = 0, y (1) = 1. Let y be the solution of the initial value problem.…

A: Given differential equation:- tdydt-5y-t163ety13=0

Q: Problem #8: Find the area enclosed by the curve x(t) = -9r. y(t)=√r and the y-axis. Enter your…

A:

Q: Graph the function.. y=4 cot 2xx- To draw the graph, plot two consecutive asymptotes. Between those…

A: Given: y=4cot2πx-π2+2