so, (3.75)(4) + (.5)(3.75)(49) or 106.875 radians

that's not the correct answer, so is it just the second part to find the additional angle?

(.5)(3.75)(49) = 91.875 but it too is incorrect, what am I missing?

yes that is wrong.

for displacment, the additional displacement,
d=wi*7+1/2 alpha t^2
where wi is the angular rotation at the end of the first four seconds. I can't find the post which I need to put a number on it, but as I recall, you had an angular acceleration for a time period to get that wf, now a wi.

The angular velocity after 4s is 15r/s

so would it be
15(7) + .5(3.75)(49) = 196.875?

It is! Thanks for your help

To solve the expression (3.75)(4) + (.5)(3.75)(49), let's break it down step by step.

Step 1: Multiply (3.75)(4)
To find the value of (3.75)(4), simply multiply 3.75 by 4. The result is 15.

Step 2: Multiply (.5)(3.75)(49)
To find the value of (.5)(3.75)(49), we need to solve it in the correct order of operations (parentheses first, then multiplication and division from left to right).

First, multiply 3.75 and 49. This gives us 183.75.

Next, multiply the result by 0.5. This gives us 91.875.

So, the correct value of (.5)(3.75)(49) is 91.875.

Step 3: Add the two results
Now that we have the values from step 1 and step 2, we can add them together.

15 + 91.875 = 106.875

Therefore, the correct value of the expression (3.75)(4) + (.5)(3.75)(49) is indeed 106.875.

If you are getting a different result, you might want to double-check your calculations or ensure that you are using the correct values for the given numbers.