“We've been absolutely overwhelmed with orders.”
The small company you work for was featured in an article in the New York Times. Since then, thousands of new customers have started to contact you and buy your products. The number of orders that customers have made is so high that it has been difficult to send out everyone's orders fast enough. You tell a business contact this.
We've been absolutely overwhelmed with orders.
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This is how you describe something that happened to someone, when the effect is still there. In the example above, the speaker's company became overwhelmed, and they are still overwhelmed.
Here's another example. If someone broke into your house and stole things from you, when you call the police you say:
I've been robbed!
The reason you use "have been" is because you were robbed, and you haven't moved anything or cleaned up yet. So your home is still in the "robbed" state. The next day, when you tell people about it, you will say:
I was robbed last night.
"Absolutely" means "completely" or "totally". The differences between these words are very small, but "absolutely" sounds a little bit more formal and more educated.
To be "overwhelmed" means to get so much of something that it becomes a problem. You can become "overwhelmed" with things like e-mail messages, job applications for a position that you're hiring for, parenting responsibilities, homework, etc. For example:
I'm starting to feel overwhelmed. I've got school, band practice, work, not to mention spending time with my boyfriend. I just can't handle it all!
You state the thing that is overwhelming you with the phrase "overwhelmed with ___":
It's easy to get overwhelmed with the amount of work here if you don't have an organized system for handling it all.
You may also hear "overwhelmed by ___". This is more often used to express a positive emotional feeling when something makes you so happy, thankful, or proud that you just can't believe it:
I've been overwhelmed by all the support and help my fans have given me.
I was overwhelmed by the beauty of the Italian countryside.