convert the cylindrical (5, pi/3, 2) to rectangular

Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

A:

Q: Let n ≥ 1, x be a real number, and x ≥ −1. Prove the following statement using mathematical…

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Solve ax + by c bx + ay = 1 + 2

A:

Q: Show that the three functions: f₁(x) = ex-8f2(x)= ex, f(x) = 4(2x-2) are linearly dependent.

A:

Q: Find the Laurent expansion of g(z) = (2-1)/[2³3 +32² + 2z] in i) 0 < 2 <1 ii) 3<|2| iii) 0<z +2 <1

A:

Q: Let A = (0,1]-{\n € N}. (a) Find the set Aº of its interior points. (b) Find the set A' of its limit…

A:

Q: 1-x 2+3 Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : = y + 1 = 3 2…

A:

Q: : R³ → R², find its dual map, where (i) 1(x, y, z)=(x-y, y+z), (ii) t(x, y, z) = (x + y + 2z, 2x+y),…

A:

Q: 2. SOLVING HLDECC USING AUXILIARY EQUATION ²+k²x = 0, k is real number; when t = 0, x = 0,= vo. dt…

A:

Q: Let C be the parametric curve defined by [x(t)=t²-t-6, [y(t) = 4t³+31²-6t. Determine the point/s…

A: The general form of a parametric equation of the curve in the xy plane is given by xt=ft and yt=gt,…

Q: convert spherical point to cylindrical (6, pi, pi/3)

A: To find- Convert Spherical point to Cylindrical. 6, π, π3

Q: #1. Let C be a space curve defined by the vector-valued function R(t) = (sint cost, sin² t, √√3t).…

A:

Q: 1. Verify that y = e²x + 3xe²x is a solution of the ODE y" - 4y + 4y = 0. (Show all work when…

A:

Q: Finding the Determinants Using Combined Methods (row operations and cofactor method) -2 -4 A = 1 4 8…

A:

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A:

Q: c) There are three train tracks from village X to village Y and four train tracks from village Y to…

A:

Q: Let A be an n x n symmetric matrix, R be an n xm matrix such that with m ≤n), and let B = R¹ AR (an…

A:

Q: The volume of the solid generated by revolving the region bounded by 1y and y? 04 01 02 0 0…

A:

Q: 5. z = yex+x Iny xey-y lnx

A: Solution : z=yex+xln(y)xey-yln(x) zx=∂z∂x =∂ ∂ xyex+xlnyxey-ylnx-∂ ∂ xxey-ylnxyex+xlnyxey-ylnx2…

Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

A:

Q: Question 1: Show that X is Hausdorff if and only if the set S = {(x,x): x € X} is closed in X X X.…

A:

Q: 0 ] Let Cring complex numbers and M ring from the set of all - matrices of the from (a b) for each…

A:

Q: 5) Give the surface area and the volume of the shape shown. Show all your calculation neatly. a)…

A: Solution: Let distance between two nearest point in the diagram is a Now, there is a smallest cube…

Q: Consider C3 y-1 = 2². a. Sketch the graph of the right cylinder with directrix C3. b. Find the…

A: The curve given is as follows: C3: y-1=z2 (a) The graph of the right cylinder with directrix C3 is…

Q: (D³ + 4D² +9D + 10)y=-24e-* when x = 0, y = 0, y'= -4, y" = -10 ANSWER: y = e-2x + excos (2x) -sin…

A:

Q: Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t= Transpose of A)

A: Let A be a n×n square matrix and Rank (A) = 2

Q: (z-4)2 = 4x2 + 4y2   Find the equation of the generating curve on the yz plane.

A: The equation of the yz-plane is x=0.

Q: Provide all answers to four (4) decimal places. Applying the Gauss-Seidel method in solving the…

A:

Q: using the following: a = 2i + 3j + 6k, b = i - j - k a) find the component vector of a onto b b)…

A: Given a = 2i+3j+6kb = i-j-k

Q: Compute the fifth roots of unity.

A:

Q: 14. If d is a metric on a vector space X‡ {0} which is obtained from a norm, and å is defined by…

A:

Q: 2. During the planning of a birthday party, it is decided that the souvenir will be enclosed in a…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: A lady 1.65 meters tall walks towards a lamp post 2.65 meters high at a speed of 1.5 m/s. How fast…

A: Given: Height of lady=1.65 m Height of lamp post=2.65 m Speed of lady=1.5 m/s To find: Shadow of…

Q: ould you write it out on paper or write each step clearly

A:

Q: Given the quadric surface T: +3y² = z + 3. 3 Find an equation of the traces of T on the planes x =…

A: The general equation of a circle is defined as x2+y2=k, where k is a constant. The general equation…

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A: The quadric equation given is as follows: 4x2-y-32+4z2=4 (a) Rearrange the above equation.…

Q: 9.M.3 A 2 × 2 matrix A is symmetric, and has eigenvalues 3 and -2. A 3-eigenvector is [3]. 5 Find A.…

A:

Q: 20102211 is in base 3 convert it in base 10

A:

Q: 2- Every finite set in any topological space is:

A: every finite set is any topological space is COMPACT

Q: Determine if the function g: RR defined as is analytical og if yes, find its Taylor series. g(x) =…

A:

Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

A: Any vector parallel to the vector: a, b, c is ka, kb, kc, where k is a constant. If two vectors are…

Q: Let S be the quadric with equation 4x² − (y − 3)² + 4z² = 4. What type of quadric is S? Find an…

A:

Q: Estimate how much the value of the function will change f(x,y,z)= ysinx + 2yz if the point P(x,y,z)…

A: If the input of a multivariable function changes its output also changes. The directional derivative…

Q: x² T +3y² = z + 3. Consider the surface T with equation 3 1. Find the equation for the trace of T on…

A: Solution

Q: Solve y"(t)- 2y' (t) + 5y(t) = H(t); y(0) = 0; y'(0) = 1; where H(t) = (t+2,0 ≤t <2 2t - 3,122

A: We have to solve by Laplace transform.

Q: xy(1 + xy²) dx = 1 Ans: + y² -2=2

A: Given ode is ,                                                                   xy(1+xy)dydx = 1…

Q: Q.2. The side of a cube is measured with a possible percentage error of ±2%. Use differentials to…

A: Using differential

Q: 2. Sketch the function and write in terms of unit step function. Hence find the Laplace…

A:

Q: Write down the time measurements on the following analogue stop watches. Give your answe correct to…

A: Given,

Q: Consider the polar curves C1 : r =  4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2)  cos θ as shown in…

A: Given: C1:r=4+322cosθ  C2:r=2−222cosθ To find: a) Area b) Perimeter