MHB Motion along a straight line by a car

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The discussion revolves around a problem involving motion along a straight line, specifically determining when a car is traveling at 70 mph. Participants clarify that "v(t)" typically represents velocity at time t, but its definition is not provided in the problem, which only defines "s(t)" as the position function. The derivative of the position function, s'(t), represents speed, leading to the conclusion that the correct expression for when the car is going 70 mph is s'(t) = 70. This highlights the importance of understanding function notation and the relationship between position and velocity in motion problems. Overall, the focus is on correctly interpreting the mathematical expressions related to the car's speed.
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Part B of the following problem seems to be fairly straightforward, but I can't seem to understand it properly. I might be overthinking the problem entirely.

Would anyone be willing to help?
 

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(b) asks you to "use function notation" to express the question "When is the car going 70 mph". On the left side of the equal sign you have "v(t)". Were you given that or did you choose it? Often "v(t)" is used to indicate the speed or velocity at time t but there is nothing in the problem that defines v(t). The only thing defined here is s(t). The speed, at time t, is the derivative of that, s'(t). I would answer s'(t)= 70.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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