Compute Cixj)xk and un h Find patro of he pMane gog ingi (-i, novmetit tj 4K

Q: Exerca se : A. Describe each of the ff egns, gining ts ordey Cond telling whether it is ordinhar, Gr…

A:

Q: Use De Moivre's theorem to find the following: 4 i. [1+ v3i]" -3 ii. [-1+ v3 i]

A: Given that: i. [1+3i]4 ii. [-1+3i]-3

Q: Solve the with indrial data uiçol=3r r,O) = 0 wave 7.

A: We have to find the solution of given wave equation

Q: Let a = ci + jand b = 2i + 10j. Find c so that a and b are orthogona C = i

A: Given: a=ci+j b=2i+10j.

Q: Calculate the length of the astroid of x + y² = 2 2 X 3 1. S= ←

A:

Q: Qoi Find y if 4+4 Cot zo

A: Given  r = √( 4 + 4cot2θ) To find y

Q: Find the asea enclose by the cuo ves 4= 8-x2 and y=c?

A:

Q: Solve the Divichlet BUP Per an annulus Satisfying Pde: urr +t ur tte Yoo=0 Acr<2, ニo ノ acOc2た

A:

Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

Q: Find the family of orthogonal trageclarnes fo he for

A: Given that            y3 = k x5 Here we have to find the family of orthogonal trajectories to the…

Q: Find the length of the cardioid r = 1 - cos θ.

A: Arc length in polar coordinate is given by:

Q: for tE{0,, 2, ..a} Consider td differrnce equirim

A: For the given difference equation xt+3+4xt+2+xt+!+6xt=16 We need to find the general solution

Q: Let a = ci + jand b = 9i + 36j. Find c so that a and b are orthogonal. %3D

A:

Q: Find all angles between 0 and 2T satisfying the condition -1 Cs x = Separate your answers with…

A:

Q: Find the divectional desivative of div (anadF) he point (1,1,2) in the direction of 3 2 at The -i+…

A:

Q: 2. If AQRS = AXYZ then. QR= RS= LXZY=, State if the trionel

A:

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: Verify that QR and MN are parallel. The length of segment MQ = 1.8, NR = 2, PQ =9 and PR =10. 10 1.8…

A:

Q: Let a = ci + jand b = 2i + 14j. Find c so that a and b are orthogonal. i

A: Given that,a=ci+j and b=2i+14j

Q: Find (1+i)10 using DeMoivre's Theorem

A:

Q: sult. 1. A(5, 8), where A (b, h) =}bh (A computes the area of a triangle with base b and height h.)

A: Put b=5, h=8

Q: find corielation C

A: Calculate Correlation Coefficient r without cov(x,y), Correlation Coefficient r with population…

Q: solve for o earees in a right trimgle, if |lsino -U2-3 inde 11sine Lorrect to 3 decimal 12:3 Give of…

A: We can solve the given equation to find the value of θ as below

Q: he DE. of au staght Linewian tani t Find tove distance from the Abhishek Sinah

A: let the equation of a line be y = mx+c          (1)

Q: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: If v = 3i - 7j and w = -i + 4j, find the magintude of w - v. Round to one decimal place.

A: Given query is to find the magnitude of the following vector.

Q: Let R= (1,5). Calculate the length of OR. %3D

A:

Q: | sec? u du = tan u + C

A: Topic- integration

Q: Find the principle solution of sec(4z) = 2. If there is a distinct solution from the other half of…

A: sinπ3 = 32 and  sinπ-π3=32 cosπ3=12   and   cos2π-π3 = 12 .

Q: If a = 4i + 2j + 4k ,b = -2i + 4j – 3k and č = 4i + 5j. If å + xb is perpendicular to č then find x.

A:

Q: Q/D check if The feanction is Contrnous (2 eaisł find if The Cimił es (メリ/→& 0) mn (2 2. x" +3y…

A: (i) lim(x,y)→(0,0)x3yx6+y2 Let y=mx3. Then, lim(x,y)→(0,0)x3yx6+y2 becomes,…

Q: at.p.(I,.0)..and. the directiun. in. whichit.occurs

A:

Q: Find the tirst B secend dericatices %3D

A: y=7x55-x+8ex Differentiating with respect to x, we get dydx=ddx7x55-x+8ex=75·5x4-1+8ex…

Q: W Given: OWXYZ with diagonals WY and XZ Prove: 21 = 22 2

A: Given: In figure  WXYZ is a rectangle with diagonals WY and XZ. To show: ∠1≅∠2

Q: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

A:

Q: Find the area enclosed by one "leaf" of the three-leaved rose: Bepaal die area wat deur 'n "blaar"…

A: Find the area enclosed by one leaf of r=4cos15θ such that -π30≤θ≤π30

Q: A. ldentify each given pair of angles. GIVEN: x| ly and a is the transversal. a 8 2 1 3 4 . 24 and…

A: 1. ∠4 and ∠8- pair of corresponding angles.∠4=∠8

Q: The diagram below illustrates the construction of PS parallel to RQ through point P. 3/2 Which…

A:

Q: yepriate trigonomic subititution to rewrite the intya) U se in the form E sec'e de

A:

Q: Point K is on line segment JL. Given JL + 10, KL 4r, and JK 2z, determine the numerical length of…

A: Given:Point K is on the line segment JL.JL=x+10 unit, KL=4x  and JK=2xTo find:The numerical length…

Q: Compute the area of the triangle. T = = ||OP x oQ|| = |(36, -36, 36) || = II ト

A:

Q: show thet ® Coule+ AX, {) - A Cou(8iY)

A:

Q: (1) If O is not in Quadraut I and Sec e = V2 , find degres.

A:

Q: O, Solve the foluing differanital equehins -1 Ĉ (-o + g(t)), with ☺ (to) - 0, ? %3D dt

A: In this question we have to find the solution of the ODE.

Q: A space ship travels at 25 miles per hour and traveled continuously for 211 hours. 4 Enter the…

A:

Q: Find w a + bi = Jz, where a and b are real numbers. VE %3D 24+10i

A: It is given that w=z, where z=24+10i. Let w=a+ib where a and b are real numbers. w=z Substitute…

Q: Find the missing part of each probl 1. If OJ = 3, JK = 4, find OK. %3D JK is a tangent

A: