Find the unit tangent vector t(t) at the point with the given value of the parameter t. r(t) = t2 − 3t, 1 + 4t, 1 3 t3 + 1 2 t2 , t = 4.

T(t) = [1/144 , 1/180 , 1]

Step-by-step explanation:

if the parametric curve is

r(t) = t² − 3t, 1 + 4t, 13*t³ + 12* t²

then r'(t) = [ x'(t) , y'(t) , z'(t) ]

therefore

r'(t) = 2t - 3, 4 , 39* t² + 24t

at t=4

r'(4) = 2*4 -3 , 4 , 39*4² + 24*4 = 5 , 4 , 720

also the modulus of the r'(4) vector is

| r'(4) | = √(5²+4²+720²) ≈ 720

thus

T(t) = r'(4) / | r'(4) | = 5/720 , 4/720 , 720/720 = 1/144 , 1/180 , 1

T(t) = 1/144 , 1/180 , 1

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.