Use what you know about an icosahedron to derive a formula for its surface area. What is the surface area of an icosahedron with edges of length 1 cm?

Q: Solve for the gradient of the given function. f(x, y) = e" sin y + e cos x

A:

Q: Give an outline for a proof of "for any integer r and any positive integer d, if d|(x– 1), then d…

A:

Q: Use the definition of the matrix exponential, given below, to compute eAL, For any n × n matrix A,…

A:

Q: In Exercises 12-19, do an orbit analysis on the given function using a variety of seeds. 12. f(x) =…

A:

Q: L{e?*sinh t}

A:

Q: Observe that 213 = 8192 8191 + 1, and 8191 is prime. Use this data to compute an eight-digit perfect…

A:

Q: Solving liker diff evential eauaTions dy +y = Xe %3D

A:

Q: power factorization

A: Introduction: A number is prime factorised or integer factorised when it is broken down into a set…

Q: 5. Find the real part of the dot product of the vectors u" = (1 – i,1+ i) v° = (5+ i, –3 – i)

A:

Q: Find the simple interest on a loan of P65,000 if the loan is given at a rate of 20% and is due in 3…

A: Since you have posted multiple questions and we can answer one question. So, answering the first…

Q: 3. Suppose that the revenue in selling r tables is equal to 200x – 0.25x2 dollars, and producing a…

A:

Q: LITI Solve the following differential equations of cos(y)·y' + sin(y)=

A:

Q: Consider the linear system X' = AX of two differential equations, where A is a real coefficient…

A: Solution

Q: Let Tv = Av represent the linear transformation T: R2 → R3 where 1 2 A = -2 4 -2 2]

A:

Q: Perform here the preliminaries to perform

A:

Q: Use X = eAtC to find the general solution of the given system. 0 0 0 5 00 X X' = 810 X(t) = %3D

A:

Q: Part of g guaßly comnl pagram, the gherg,sefs mmalayfured Zojebél Clalme „ Company are subjectd p a…

A:

Q: Calculate the flow in the field F along the path C. Flow means line integral F = y 2 i + z j  + x…

A:

Q: Z1 = 3 + 4i Z2 = 5 – 31i Z3 = 8+ 2i Reduce to a + bi form 1. z1 + Z2 + Z3 2. Z1 * Z2 Z1 * Z2 Z3 3. –…

A:

Q: 2ea

A:

Q: y" – 4y' + 4y = (12x² – 6x)e2*

A:

Q: Consider the voter profile shown on the right. Number of Voters Ranking a>b>c (a) Which alternative…

A:

Q: Find the Laplace transform of the function f(t) = e4 using direct integration. Show your solution.…

A: Given  f(t) = e2t

Q: The point (17, -9) is translated to the point (6, 2). Select the description of the translati 5 A 9…

A: Given that the point (17, -9) is translated to the point (6, 2)

Q: 1. Evaluate and find the real part: 1 1+i

A:

Q: Solve the following PDE: а. у иху +и %3D 0 a²u a2u + at2 = 0 b.

A: Solution :-

Q: 10. Write the binary number (1000110), in decimal and write the decimal number 327 in binary.

A:

Q: What is the area of the region bounded by the graph of r = 4 sin 2θ

A: What is the area of the region bounded by the graph of r = 4 sin 2θ

Q: What is the area of the region bounded by the graph of p? = 16cos20? Choose two (2) correct answers.…

A:

Q: Find the Fourier Series for the following functoin fx) on the interval -12 X < l. Please Show all…

A:

Q: 5. Let R be a commutative ring with identity. Let f: R[x] → R be defined by f(p(x)) = Eo ai, where…

A:

Q: Consider the Matrix.   1. Diagonalise the matrix A, that is, find PDP^-1 2. Calculate the matrix…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the work done by F over the curve in the direction of increasing t. Work means line integral F…

A:

Q: 14.

A: The given matrix is A = -1-201

Q: For the Venn diagram below, what would best describe the variance explained by x1 in a multiple…

A:

Q: af(x,yz) -

A:

Q: Using Modified Euler's Method, approximate the initial value problem for various values of x given…

A:

Q: 1 Solve the following integral differential equation y (t) - f (t- B)?Y(8)dB = t, y(0) = -1 Select…

A: Using laplace transform of convolution product f*g. L{f*g}=L{f} L{g}

Q: (c) Show that the differential equation ry" – 3y + ry = 0 has a general solution of the form y(x) =…

A: Given data xy''-3y'+xy=0we know y"=d2ydx2  &amp; y'=d2ydx2we can write the…

Q: Find the ordinary generating function for the sequence 1,1,1,1,0,0,0...(Hint: it is a polynomial.)

A:

Q: 2y" + 6y" +y-5y-7 0 is a homogeneous equation. O Cannot be determined O True O False

A: The solution is given as

Q: 680 The logistic growth function f(t) = describes the population of a species of butterflies t…

A:

Q: Observe that 213 = 8192 = 8191 + 1, and 8191 is prime. Use this data to compute an eight-digit…

A: We have given relation 213=8192=8191+1, where 8191 is prime. We need to calculate an eight digit…

Q: Express (-2/3+ j2) in rectangular form.

A: Rectangular form of the given complex number

Q: 10z? + 7z – 12

A:

Q: What is the differential equation whose solution represents the family y = Ae3x + Bxe3X+Ce4x? O…

A:

Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.  F…

A:

Q: A set of data has a normal distribution with a mean of 100 and a standard deviation of 15. Find the…

A:

Q: Determine the vector field of F. F(x, y) = 6i – 2j

A: The general form of a vector-valued function in two dimensions is given by F=F1i+F2j, where F1 and…

Q: Is a function Continuous ?why? integrable anod

A: