Given v = (3, –7) and w = (-2, 5), find a. v• w b. w• v c. v• v d. |||

Q: If a = p - q, b = 2pq, and c = p² + q°, show that c2 = a? + b?.

A: Given:a=p2-q2, b=2pq and c=p2+q2To show thatc2=a2+b2

Q: If X = x „then W(x1(t), x,(t)) = 10 Select one: O a. ce- а. O b. ct C. c t? d. ce'

A: We will use basic knowledge of Wronskian for a II order linear homogeneous ODE. WE convert the above…

Q: If ø = Vx + y+ z and ū = 'î + ĵ+ k , then V¢.ũ will be 3 V3 20 2ф

A: Step:-1 Given that ϕ=x+y+z, u→=i^+j^+k^ ∇→ϕ=∂∂xi+∂∂xj+∂∂xk x+y+z ∇→ϕ=12x+y+zi +12x+y+zj…

Q: GIVEN: TV || WY with transversal RS W. MZRUV = (r + 4)(x – 3) R mZWXS = x? 3 3/X FIND: 2.

A:

Q: If ADEF AJKL, DE = 18, EF = 23, DF = 9x – 23, JL = 7x-11,and JK= 3y-21, find the values of x and y.…

A: Given : ∆DEF≅∆JKLDE=18EF=23DF=9x-23JL=7x-11JK=3y-12

Q: Find the value of x and y if ABCD EFGH.

A: Given,           ABCD≅EFGH

Q: Let x = (m, 1, 0,-2)", m> 0 and ||x||2 = V30, then т — Select one: а. 4 b. 7 C. 6 d. 5

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Q: If w 5x2 + 2y2, x = -3s+t, and y = s – 4t, find in terms of s and t. Provide your answer below:

A: Given:   w = 5x2 + 2y2     x = -3s + t      y = 3 - 4t

Q: If f(r, v) = ry – ry", find 7 + ±),-.y-a

A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

Q: RS 9y +3, ST= 3y+ 5, and RT= 16y – 24.

A:

Q: Given v = (7, – 10), w= (-5, 11), and s (-4, –4), find 6(v+2w) –s . 6(v+2w) -s= (O,D)

A: The given values of V , W , S are converted into vector form is shown in the picture ,

Q: if v= 5i-6j and w= xi +8j, Find all numbers x for which ||v-w||=4.

A: Given, v=5 i-6 j and  w=x i+8 j

Q: Show that S is a basis for V = span(S).

A: We are given,  We need to show that S is a basis for V = span(S). In other words, we need to show…

Q: Given u=(3, -2) and v=(-3, 2), determine -4u –v.

A: Given,          u=<3 , -2>  and   v=<-3 , 2>

Q: For x2 + Bx + C = (x + a) (x + b), which of the followingmust be true?(a) ab = B and a + b = C(b) a…

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Q: Given ARWS a ATUV, find the values of x and y. 20 4y +5 29 25 15 (11x-27)

A:

Q: Given that P(X)= P(Y)= and P(XUY)= find 20 20 10 a) P(XnY) b) P(XIY)

A: Given,PX=920PY=720and PX∪Y=710

Q: Find the values of a, b, and c so that det(4) = ax2 + bx+ c. 2 A = -2 -1 -2 -7 3

A: A=x20-2x-1-2-73   and detA=ax2+bx+c

Q: Given that A = 40 + 3ŷ + 2, B = –2â + 42, and C = ŷ+ 42, find: (Ã × B) x Č O a. -50âx-48ây+40âz O…

A: Given vectors are: A→=4x^+3y^+z^  , B→=-2x^+4z^  , and C→=y^+4z^

Q: Find x if mZFDE = x + 68, %3D M2CDE = 146°, and m2CDF = x + 94. %3D D E

A: find x if m∠FDE=x+68

Q: Isaac says that T' will be located at (4, 20). Isabelle says that T' will be located at (4, 12).

A: According to Isaac T' is  at (4,20) According to Isabelle T' is at (4,12)

Q: If z = (1+ iv3)' 100 then find the value of Re(z)/Im(z). a. V3 b. 1/V3 с. 2//3 d. -V3

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Q: Find the values of x, y and z in the figure, where b = 4 and c = 16. (1.5z + b)° (1.5z –c)°%

A: Find the value of x , y and z                 where b=4 and c=16

Q: O Given: m21 = 2x + 10 –+ m22 = 2y + 10 2 m23 = x + 2y Find: m21, mL2, and mz3

A:

Q: Given that A and B are independent with P(A ∪ B) = 0.8 and P(B c ) = 0.3, find P(A).

A:

Q: Given m || n, find the value ofx and y. (2y+17)°/(4x-3)° m (7x+18)° x = y =

A:

Q: Find the value of c if, P(Z < c) = 0.25 а. -0.67 b. -0.0987 c. 0.67 d. 0.0987

A: Given, P(Z&lt;c) =0.25

Q: Let f (x, y, z) = -12x? – y + 5z?. Calculate Vf (0, 5, 6). %3D (Write your solution using the form…

A: Solution

Q: You are given that ||u|| = 1, ||v|| = (би + v) . (и —2v) ? 2 and u • v = -1. What is the value of |

A: Given query is to find the value of indicated vector operation.

Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: Given that D/d = √f + p/f – p, express p in terms of f, d and D

A:

Q: Find a, b, c, d for P(x) : = ax3 + bx? + cx + d if P(1) = 11, b = 3d, a = 2c and P(x) = Q(x) + x+1'

A: Polynomial and remainder

Q: Decide if the statement is true or false, and select the correct explanation. Ifa < b andf'(x) is…

A: Function f is increasing on I if for every a &lt;b in I , f(a)≤f(b) Where I denote integer number.

Q: If z = -0.36, u = 19.162, w = 12.943, find the value of r.

A: Given z = -0.36, u = 19.162, w = 12.943 r = z i^ + u j^ + w k^ |r| = magnitude of r =…

Q: For u(x) = 4x2 - x + 5 and v(x) = 2x + 4, which of the following is correct? a) (u – v)(2) = 11 b)…

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Q: a4)Giveni mel=x,mca=4y ,mL3=ay ,met=2x-yšto. Find: XN,and m25 (minus) 3\4

A:

Q: *:س 6 where The value of she vgiá dà r = |7| Cya g(r) = ! , = xi + yj + zk let And

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Q: Given that A=6-j1 and B=2+j3, find A*B

A:

Q: : Given a r.v.*=2, 3,4,5, then Find the Pif. of X (fw): ,

A: Given that, a  random variable , X = 1,2,3,4,5 We need to find probability function of X i.e f(x)

Q: If t>0 and (3t) – 5(3t) – 14 =0, what is the value of t ?

A:

Q: If A and B are independent and the P(A|B) = 0.4 and P(Bc) = 0.7. Find the P(A ∪ B).

A:

Q: Given ú x ở = (2, 3, – 3), find (ủ – 4v) × (ú + 3v).

A:

Q: Q6: If z = x2 and ad y, then 이렇 이렇 소설 이를 Choose e) others

A: Given problem:- If z=x2 and y=z3/3  To find:- dy/dz

Q: Given v = 21 and w = j, find the following. a) v•w b) v•v

A: We know that i·j=0 and i·i=1. For (a),     v·w=(2i)·j=2(i·j)=2(0)=0

Q: Suppo se fCA) = gl hux). If gce)-3, gʻl2): 4, hl0): 2, and h'(0)=6 find f'c0).

A: we have given function f(x) = g(h(x))g(2)=3g'(2)=4h(0)=2h'(0)=6

Q: (d) Verify that for v= (a, b) E R², P[v]s' = [v]s and Q[v]s = [v]s•.

A: d) First find the matrix P that is the change of basis from S to S'. 1,3=31,2-12,31,4=51,2-22,3…

Q: If x = aPba+r, y = a®b* + P, z = a'bP +q, show that xa -r.y-P.2P-9 =1.

A: x=apbq+r,  y=aqbr+p, z=arbp+q

Q: If r(t) = (3e2t, 3e-2t, 3te2t), find T(0), r"(0), and r'(t) · r'(t).

A: Given

Q: The value of W (x, x², x³) is

A:

Q: Find d.r for r 3 (VAr? - I)

A: