Find the center and radius of the sphere with equation (x − 2)² + (y + 1)² + (z + 6) Center: Radius:

Q: Two sides of an oblique triangle are measured to be 3 and 4. If the angle θ between the two sides…

A: According to question,Given sides of triangle are 3 and 4,anddθdt = 0.04 radianssec

Q: x5 (26 + 6)6 This can be transformed into a basic integral by letting Consider the indefinite…

A:

Q: (4-6) Determine the area bounded by: 4. y=x³-4x and y = x² + 2x

A:

Q: Evaluate the integral. f5sinxcos(cosx)dx -5cos(sinx) + C sin(cosx) 5 5sin(cosx) + C −5sin(cosx) + C…

A: Topic - indefinite integral We are given∫5sinxcos(cos(x))dxwe know thatddxcosx=-sin xand…

Q: A particle moves along line segments from the origin to the points (3, 0, 0), (3, 5, 1), (0, 5, 1),…

A:

Q: 3. Find the equation of the tangent line to the curve x² + 2y² = 9 at the point (1, -2). Write your…

A:

Q: 5. The elevation of a path is given by f(x)=x²³ −5x² +30, measured in feet, where x measures…

A: We have to find the average value.

Q: Find the area of the region bounded by y = x² and y = 2x using horizontal strips and vertical…

A: We have to find the area of the region.

Q: The x-intercept of the tangent line to the curve y = x - 6 / x at the point (3, 1) is:

A: given curve :- given curve is ,y = x-6x then we have to find x intercept of the tangent line to the…

Q: Suppose that an+1 an → 1 as n → ∞. Find the radius of convergence. ∞ n=1 anxn 4"

A: We need to find radius of convergence.

Q: ∞xk Use the power series f(x) = In (1-x) = -Σ, for -1 <x< 1, to find the power series representation…

A:

Q: Ma3. 1. (Two-Part Tariff #2 Cr) The Kiwi company (supplier) has introduced a new device called…

A: given: he Kiwi company (supplier) has introduced a new device called jPad. jPad is sold through Good…

Q: The area of a square is increasing at a rate of 70 centimeters squared per second. Find the rate of…

A: Area of square is increasing at a rate of 70 centimetres squared per second. Side is 7 centimetres.

Q: Consider the following parametric curve. Answer parts a and b. x = 2t, y=t; t = 2 a. Determine dx dy…

A:

Q: Find the slope of the parametric curve x = -3t² +8, y = 6t3, for-co<t<∞o, at the point corresponding…

A: slope is  =dydxand we know that  dydx=dydtdxdtdtndt=ntn-1,   and   dconstantdt=0

Q: 1 1 2 01 3 00-1 (a) Enter X₁, the eigenvalue with algebraic multiplicity one, and then X₂, the…

A: We need to find eigen value and vectors.

Q: Consider the indefinite integral + U a) This can be transformed into a basic integral by letting du…

A: The given integral is: I=∫lnz5zdz   ....1   Use the common derivative. ddxlnx=1x

Q: ²* tF(z) = * sin (8t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). Let Use this…

A:

Q: Confirm that the below limit meets the conditions to apply l'Hôpital's Rule and then solve the…

A: As we know that, The Power Law: ddxxn=nxn-1   To calculate the limit limx→1lnxx7-1.

Q: Consider the differential equation y" - 7 y' +10y = -5 e³t. (a) Find r₁, 2, roots of the…

A:

Q: g(x)= if x < 0 x²-9x if x 20 ax The function g(x) is differentiable for all values of x when a =…

A:

Q: Two sides of an oblique triangle are measured to be 8 and 2. If the angle between the two sides…

A: According to question,Given Sides of triangle are 8 and 2 units.

Q: f(x, y) = 4x² + 5y², P = (-9,2), u = 4i+5j (Duf)p m m

A:

Q: Find the area bounded by the graphs of the indicated equations over the given interval. y=x²-2; y =…

A:

Q: The length of the curve y = 2x^(3/2) between x = 0 and x = 1 is equal to:   (2/27)(10^3/2)…

A:

Q: A sphere of radius R is to be inscribed in a right circular cone of base radius / and height h. Find…

A: In similar triangle,  ratio of corresponding sides are equal.

Q: Convert the rectangular coordinate point (2,-2) to polar coordinate.

A: To convert into polar coordinates

Q: The nth term of a sequence is given. n-1 -2-(--/-)² - ¹ an = (a) Find the first five terms of the…

A:

Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt

Q: Use the indicated formula from the integration table to find the indefinite integral. (Use C for the…

A: Given, ∫1x5+9x2dx

Q: Compute the percent relative error in computing the area of a square whose side is measured with an…

A:

Q: Solve the exponential equation and simplify. Give an exact answer. No decimals. 32x-1 + 2 = 14

A:

Q: Evaluate the indefinite integral. 6dx x ln(2x) + C

A: Given ∫6xln2xdx

Q: lim x →0 In(1+³) x.sin x²

A:

Q: Find surface area generated by revolving the curve a2y  x3=about the x-axis from x = 0 to x = a. a)…

A:

Q: lim x→0 In(1+x³) x.sin x²

A: To evaluate the given limit of function

Q: Obtain the solution. problem (t-2)x- the following initial value of -xc 2(t-2)²

A: Compare with linear differential equations then solve

Q: 2. The function f(x) is defined by the table shown below: Fill in the blanks: (a) f( I f(x) _)=0 -3…

A: The function fx is defined by the table shown below x -3 -2 -1 0 1 2 fx 0 1 2 3 4 5 To…

Q: Linear Differential Equations. Find the general solution. (2x+3)y'=y+√(2x+3)

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with so here we have

Q: dz Find where z = 4 x sin y, and x=t,and y = 5t³. dt'

A:

Q: Find how fast the volume of a parallelepiped is increasing if its edges a, b, and o change at rates…

A: According to question,Given Edge of parallelopiped,a= 5,b = 6,andc =10,Rate of change of It's…

Q: An object moves along the x-axis so its x-coordinate obeys the equation x=at² + bt+c, where a = 15,…

A:

Q: Find nd (25/75 + 7x + 2) dr + C

A:

Q: Find the integral. Show work. fx¹nx dx 25 (51nx-1) + C 1 25 (lnx-1)+C Ox++0 x(51nx-1)+C

A:

Q: Find the sum of the first 14 terms of the geometric sequence shown below. 3, 12, 48, 192, ... The…

A:

Q: Find the arc length of the following curve on the given interval. K|N x=6 sint-6t cost, y=6…

A:

Q: Let f(x, y) = x6y7. Find the linearization L(x, y) of f(x, y) at the point (1, 1). L(x, y) = Find…

A:

Q: Evaluate [² (15²-5, 6r) dr. >

A:

Q: Find the integral. cos³xsin²x dx 1 1 0-sin³x + sin³x + c C 3 1 sin²x - sinx + sinx 5 1 3 1 5 sin²x +…

A:

Q: Find the area of the shaded region. f(x)=x+3 g(x)=x²-3 y ◄||||X -8-7-6-5-4-3-2 ◄||||kty 876543 44 8…

A: The region bounded by the curves fx=x+3 and gx-x2-3. We have to find the area bounded by the curves.