If I had deposited a check of $100,000 at my bank that pays 3.4%,10
days ago, how much would my $100,000 have earned in 10 days?

Hello.

Assuming daily compounding, 10 days' worth of interest on $100,000 would be $93.19.

You can use the calculator on this page:
Compound interest calculator.
http://www.mortgage-investments.com/Mortgage_and_real_estate_Calculators/compound_interest_calculator.htm

Enter:

Principal: $100000
Interest rate per year: 3.4
Time to compound for: 10
Compounding period: 365
Tax rate: 0
Annual inflation rate: 0

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Or you could use Google's calculator:
100000*(1+0.034/365)^10 - 100000 = 93.1897414
://www.google.com/search?hl=en&lr=&q=%28100000*%281%2B0.034%2F365%29%5E10%29-100000&btnG=Search
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search strategy: interest calculator daily compounding

I hope this helps.

Thank you for your prompt explanation!