take a look

The word "look" is very general. It can mean to look for a long time, a short time, carefully, absent-mindedly, or in many other ways. "Take a look" is more specific. It means to look at something for a short period, usually for a specific purpose.

You can ask someone to take a look at something that needs to be fixed, or for something that's important for them to see. Here's another example from a science classroom. The teacher tells the class to look at something in the textbook:

Everybody take a look at the picture on page 46. This is a model of what a strand of DNA looks like.

an in-depth (something)

Doing something "in-depth" means that you do it in a really careful and detailed way. Here are some things that you can do "in-depth":

• write an in-depth explanation
• listen to an in-depth description
• conduct an in-depth scientific study

a process

A "process" is a repeatable series of steps or actions. For example, a doctor might have a specific "process" for doing a surgical operation.

Businesses often have processes for each of the different things that they do. Workers are supposed to "follow" the processes.

determine (something)

To "determine" something means to figure it out. You "determine" facts or conclusions. For example:

Police have not yet determined the cause of death.

I've determined that the next camera I buy should be a Canon T3i

The word "determine" is more formal than "figure out".

(something) managed to (do something)

People use the phrase "manage to ___" to talk about things that weren't likely, but happened anyway. In the example above, the boss doesn't understand why the mistake happened, so she asks how it "managed to happen".

Here's another example of using "managed to" to talk about doing something which wasn't likely:

But I've managed to do OK.