Is cycling on this 35mph road too dangerous? I'm thinking of bike commuting to work and there is a stretch of road with no sidewalk and 35mph speed limit.  Is this too dangerous for biking?  I'm not in the best shape so I can't go very fast. This is Hawaii in the United States.
As an experienced cyclist who has been all over the country and even done hundreds of miles on interstates, after finding that location on Google Maps, and checking  how you might conceivably get there, there is absolutely no way in hell I would ever be caught dead there on a bicycle.
How you answer this question is not by taking one isolated photo out of context, but by looking at the totality of how you would get into and out of the location on your bicycle. By doing this, we can quickly see that it would be unwise to use this road, and a serviceable (and far safer) bike path alternative exists.
There are two ways to get there: The first is to exit H-1; your picture was taken where that off-ramp merges with Nimitz Hwy. I won't discuss this further as it would be illegal to cycle there anyway.
The second is to enter Nimitz Hwy from Kamehameha Hwy at Middle St here:

That means you would have to ride in one of the two left lanes, likely in the middle of heavy traffic, from at least there until you merge with H-1 later on up the ramp:

You would be cycling in the lane where this picture was taken, and would then have to cross those two lanes to the right which are full of cars coming off H-1. This is extremely unsafe unless there is virtually no traffic. I might do it at four in the morning. I would not go anywhere near it in normal waking hours.
Fortunately you don't have to. Just to the right is a bike path which runs parallel to this bit of Nimitz Hwy, ending at Peltier Ave. The sidewalk on the right turns into the bike path just after Middle St:

Instead of trying to play Frogger with high speed vehicles up above, I'd use this bike path.
Given that it's pretty much impossible to get to the point in your picture safely, I've omitted the analysis of how to get out safely.