i just bought a new iPad 10th generation, and an apple pencil 2nd generation. Do they work together?

No. The iPad10 is compatible with the first generation Apple Pencil. Here is Apple’s definitive compatibility list for Apple Pencil and iPad:

Apple Pencil compatibility - Apple Support

The second generation Apple Pencil is only compatible with iPad models that feature an inductive/magnetic charging dock that is explicitly designed for pairing/charging the second generation Pencil. 

The iPad10 does not have an inductive charging dock - principally as the front-facing camera has been relocated to the centre of the long-edge of the screen - and now occupies the internal cavity that might otherwise house the inductive charging dock components. As such, the iPad10 instead supports the first generation Apple Pencil that is paired and charged via the iPad’s USB-C port.

For pairing and charging, the first generation Pencil requires use of special USB-C/Lightning Adapter; this adapter is included within the box of new first generation Pencils. If purchased directly from Apple, a new Pencil will include the adapter. Older stock, purchased from other retailers, may not include the Adapter.

For owners of existing first generation Pencils, or for purchasers of old-stock Pencils, the special adapter is available as an accessory:

• USB-C to Apple Pencil Adapter

https://store.apple.com/uk/xc/product/MQLU3ZM/A

Unfortunately, no. That model of iPad uses the first generation Apple Pencil, and requires a “special” adapter to charge it.

No, the 10th gen iPad is the last one to only be compatible with the first gen pencil (the one with the lighting connecter on the end)