B)Prove (cose + i sine)" = cosne + i sin ne

Q: Solve the following differential equations of d²y dx² +9y=2e³x +18x+18

A: The given differential equation,      d2ydx2+9y=2e3x+18x+18

Q: To measure a stone face carved on the side of a mountain, two sightings 850 feet from the base of…

A: Height and distance

Q: EVALUATE: IF A = 3i-j-2K FIND: | (A+B) × (A-B)| | (A x B) | & B = 2i + 3; +!

A: We can solve as follows

Q: 2 Q41 x ² dy- (xy + y ² ) dx = o Q4\x

A: The objective of the question is evaluate the differential equation.

Q: Evaluate the integral. (Use C for the constant of integration.) tan³(x) sec(x) dx

A:

Q: Solve the following differential equations of d²y +9y=2e³x +18x+18 dx²

A: First i I have find the complementary function and then particular solution then adding these two…

Q: 17 What is the degree of vertex 4? O 1 ez el V2 V₂ Des

A:

Q: Find the mass and the center of mass of the lamina with density p(x, y) = and occupies the √y x²…

A: Given :ρ(x,y)=yx21≤x≤3 and 0≤y≤4 then

Q: dy Find , given y = log3 dx 10- x 2x5

A: Given y=log310-x2x5⇒y=log3e · loge10-x2x5      Using the property: logab=logac·logcb

Q: Given : y = cot √2x + 1 Find dy dx O csc² √2x + 1 √2x+1 O csc² √2x + 1 2√2x+1

A:

Q: A car purchased for $40,000 depreciates exponentially. After one year, the car is valued at $25,000.…

A: We have to find depreciating after 3 years.

Q: A graph consisting only of a vertex is a complete graph. True False

A: Recall:  The complete graph on zero/one nodes is a trivial graph also known as the null…

Q: Find an approximation of the area y = 16 - x² over the interval [0,4] using L6 (left end point…

A: Use: Area=∆xf(x1)+f(x2)+f(x3)+f(x4)+f(x5)+f(x6)       where ∆x=b-anwhere n= no. of rectangle…

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

A:

Q: Solve:  9 d2y/dx2 - 24 dy/dx +16y = 0;  y(0)=3, y'(0)=3 Write the letter corresponding to your…

A:

Q: Home Work: Solve the following system of equations. 1 -1 2 0 2 -3 1 -4 3 X₂ 14 1 -4 5 -1 X3 -1 4-2…

A: We can solve the given system of equations.

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given…

A: Use derivative concept

Q: Use the Inverse Function Theorem to find (s−¹)' (6) given that s(x)=√√-8x - 4. Note that s(-5) = 6.…

A:

Q: Use logarithmic differentiation to find the derivative of the function. y = (x5 + 2)²(x4 + 4)4 y'(x)…

A: By using logarithmic differentiation to find the derivative of the given function.y=x5+22x4+44

Q: Suppose the revenue from producing (and selling) x units of a product is given by R(x) = 15x-.06x²…

A: To find marginal revenue at production level of 35.

Q: The position function of an object is given by s(t) = 2³-12² + 30t+8, where time, t, is in seconds…

A: The position function of object is given as  s(t) = 2t3-12t2+30t+8  Where 't' time in seconds and…

Q: 1. The simplified form of the logarithmic expression log6 + 2log3 is a. log36 b. log54 c. log81 d.…

A:

Q: While buying a new car, Derek made a down payment of $1,000.00 and agreed to make month-end payments…

A:

Q: ▪ Let L:2 y+3 Z+4 X-2 = = and M: 2x - 3y + z = 6 are line and 2 5 plane and let P be the…

A: First we find the intersection point of line and panel

Q: 4 Find the coefficient of the given term when the expression is expanded by the binomial theorem…

A: Find the coefficient of x2y7 in (2x+3y)9 using binomial expression.

Q: Find the domain of the following function. 1 f(x) = 2 25-x

A: Given function f(x)=125-x2we know that fraction abis defined when b≠0the function is not defined…

Q: 4) 4 6 9 тоон 3 -3 2 -2 0 0 Х2 X3 ХА 44 66 124/

A: The given system of equations,1-13-240-30602095-25x1x2x3x4=-14466124

Q: Find the area of the shaded region. r = 1 + cos 0

A: Here, the given curves are r=1+cos θ & r=3 cos θ First of all find the intersection points of…

Q: The manager of a restaurant found that the cost to produce 100 cups of coffee is $10.55, while the…

A:

Q: The total cost (in dollars) of producing x food processors is C(x) = 1600+50x-0.4x². Find the…

A: Derivative of total cost function gives the marginal cost function

Q: 31 Matrix A =[42],find Eigen values of A².

A:

Q: Determine whether the statement is true or false. True False The equation y' = 4y - 2x + 8xy - 1 is…

A:

Q: 3. (0.002x4 -0.3x² + 4x - 7) dx

A: We need to find,   ∫-1010(0.002x4-0.3x2+4x-7)dx

Q: 4. Express the integral as an equivalent integral with the order of integration reversed. 2√x (a) ff…

A: The process of switching between dxdy order and dydx order in double integrals is called changing…

Q: 2. Which of the following sets of ordered pairs could be part of a linear function? F II (0, 1), (3,…

A:

Q: ind the equation of a line that passes through A(1,-1) and is perpendicular to the line (x,y) =…

A: The equation of a line that passes through A(1,-1) and is perpendicular to the line…

Q: Give the domain and range of the graph shown to the right. Then, use the graph to answer parts (a)…

A:

Q: For the function g(x)=x^2 -2x + 5 estimate for the instantaneous rate of change at x=3. Round to the…

A: For the function g(x)=x^2 -2x + 5 estimate for the instantaneous rate of change at x=3. Round to the…

Q: Determine whether the given sequence converges or diverges. If it converges, calculate its limit. An…

A:

Q: Estimate the slope (slope = rise/run) of the tangent line to the curve.

A: answer is in next step . please give a like !!

Q: Evaluate the following integrals C. [x√x + 1dx

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Here, the given function is: y=f(x)=xx2+4

Q: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed…

A:

Q: () + + C) + () + C) (ع) 77 ساح 0 27

A:

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Explained below

Q: The eigenvalues of the coefficient matrix A are given. Find a general solution of the indicated…

A: Given  A=7716-32-72-113214432-59   λ=-3,5,5

Q: 10-8-8-4 191 6 30 O 45 X 10

A: Topic = Functions

Q: find f'(a) f(t) = 1/(t2+7)

A:

Q: Find , given y = log(ev+x²). dy dx

A: