2.) A small rocket is fired from a launch pad 10 m above the ground. This initial position can be modelled by = <0,0, 10 >. The initial velocity of the rocket is given by v, = < 50,0, 30 > m/s. A crosswind = < 0,2.5, -9.8 > describes the %3D blowing to the north produces an acceleration of 2.5 m/s2. If a(t) acceleration of the rocket, determine the velocity function, v(t), and the position function, r(t) for the rocket. How long after launch does the rocket hit the ground? Round to the nearest second. %3D

Q: Find u - v, u · u, ||v||², (u - v)v, and u - (3v). u = 4i + j - 2k, v = i - 3j + 2k (a) u: v (b) u.…

A: Dot product of two vector is - a→=  a1i^ +  a2j^ +  a3k^ b→=  bi^ +  b2j^ +  b3k^ a→.b→ =  a1 b1 +…

Q: dg 1 дд If g(x, y) = xy + y ln(ry), show that ду + y dr = x+ In(xy). dxðy

A: given: gx,y=xy+yln(xy) we have to show that: ∂g∂y-∂2g∂x∂y-y∂2g∂y2+1y∂g∂x=x+ln(xy)

Q: Let V1 = -1 V2 = 3 20-0-0 B = {V1, V2}. X = 12 Determine whether x € Span {v₁, V2}. If yes, find [x]…

A:

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). u = (2, -2, 4), v = (0,7, 4) (a) 2 (b) 24 U. V U u (c)…

A: Given :u=2,-2, 4v=0, 7, 4

Q: If z = f(u, v), u = g(r, s), v = h(r, t), r = j(s, t), and s= k(t) then dz dž=fu(u, v) [g- (r, s)[j.…

A: Given that we need to check that the statement for the derivative as given below is correct or not.…

Q: Find the line that passes through the point (0, 1) and through the point of intersection of the two…

A:

Q: iven that E(X) = 5, E(Y) = 8, E(X2) = 68, E(Y2) = 75 and rx,y = .35, find the followings. g. Find…

A:

Q: Let u = and v=. (a) Find ||u||. (b) Find u – 3v. -

A: Given: u=1,4,3  and v=2,0,-1

Q: Evaluate f (x + y - z)² dV for the box B with dimension: [0, 8] × [0, 7] × [0, 3]. B (Use symbolic…

A:

Q: If Iz – 2| < 2, then find (x,y) * arg(z),r i5

A:

Q: Find the functionr that satisfies the following conditions. r(t) = (1,31 2); r(1) = (8,7,5) r(t) =…

A:

Q: Find f, f, and f, and evaluate each at the given point. f(x, y, z) = x²y + 2xyz - 8yz, (-3, 1, 3)…

A:

Q: Let A = 0 00 G|5 0 0 0 , u = 1|5 15 10 - 25 and v= g d h Define T: R³ R³ by T(x) = Ax. Find T(u) and…

A: Let and ,Define Then,   and

Q: Find u x v, v x u, and v x v. u = -5i + 3j v = 4i + 5j + 2k (a) u x v (b) v xu (c) V x V

A: The objective of this question is to find the cross products of the given vectors. The cross product…

Q: Let wr₁ (t) = and r₂(t) =. Find (r₁(t)- r₂(t)). O 04t² +6t³ 0312 +8+4 0

A:

Q: (а) Р(0, 1), t %3 /2 t = (b) Р 2 (с) Р( — 1, 0), t%3D (d) Р 2 2 (е) Р(0, — 1), t 3 () P(- (f) Р 2 /2…

A: a. Given point, P(0,1)

Q: R2 2 xy² x² + 1 dA, R = [0,2] x [-4,4] R= Find R

A: Step 1:Step 2: Step 3: Step 4:

Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

A:

Q: Which of the following is the solution of the given system below? X3 + 5x4 = 0, X3 + 7x4 4x1 + 2x2 –…

A:

Q: Using Baye's Theorem, show that if X⊥Y, then I(X;Y|Z)=I(X;Y,Z

A: Using Baye's theorem, show that if X⊥Y, then  IX, Y/Z=IX, Y, Z.

Q: Let r(t) = (a) Find 7 (t). (b) Find Ñ (t). (c) Find K (t)

A:

Q: Show that: х-1 - B(x-1,y+1)= B(x, y)

A:

Q: Find u · v, u· u, ||v||2, (u· v)v, and u · (3v). u = (4, -2, 5), v = = (0, 6, 3) (a) u V (b) (c)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Cov(x,y)=v(y) if x=y True False оо

A: Given problem Given that   Cov( x,y ) = v( y ) if x = y Ans) True First Option

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.