f a rock is thrown upward on the planet Mars with a velocity of 7 m/s, its height in meters t seconds later is given by y = 7t − 1.86t^2. (Round your answers to two decimal places.)

Estimate the instantaneous velocity when t = 1.

the velocity is dy/dt = 7 - 3.72t

plug in the value of t=1

To estimate the instantaneous velocity when t = 1, we need to find the derivative of the given height function y = 7t - 1.86t^2 with respect to time.

The derivative of a function represents its rate of change with respect to its independent variable (in this case, time). In other words, it gives us the velocity at any given time.

To find the derivative of y = 7t - 1.86t^2, we can use the power rule of differentiation:

1. Take the derivative of the term 7t: The derivative of a constant multiplied by a variable t is just the constant itself. So, the derivative of 7t is 7.

2. Take the derivative of the term -1.86t^2: We apply the power rule here. The derivative of t raised to the power of n, where n is a constant, is n times t raised to the power of (n-1). In this case, the exponent is 2, so the derivative of -1.86t^2 is -1.86 * 2t^1 = -3.72t.

Combining the derivatives of the two terms, we get:

dy/dt = 7 - 3.72t

Now we can substitute t = 1 into the derivative equation to estimate the instantaneous velocity:

dy/dt = 7 - 3.72(1)
= 7 - 3.72
= 3.28 m/s

Therefore, the estimated instantaneous velocity when t = 1 is approximately 3.28 m/s.