Find the unit tangent vector at the given value of t for the following parameterized curves. r(t)= ⟨7–√e^t,3e^t,3e^t⟩

, for 0≤t≤1
; t=ln 2

Step-by-step explanation:

Given :

We first have to differentiate of equation

Now to get a unit tangent vector at the given value of , we put in equation

                   [∵]

Now to get a unit tangent vector , we will divide our vector by its magnitude. So let's first find the magnitude.

Now we can find the our unit tangents vector.

Hence,

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

you