If r(t) = 4e3t, 2e−3t, 4te3t , find t(0), r''(0), and r'(t) · r''(t).

we are given

Calculation of r(0):

we can plug t=0

Calculation of r'(0):

Firstly, we will find derivative

we can simplify it

now, we can plug t=0

Calculation of r''(0):

we can find second derivative

now, we can plug t=0

we get

Calculation of r'(0) · r''(0):

............Answer

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step-by-step explanation:

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|