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Welcome!

Hi taylorn5683,

Let's start with the formula for the circumference of a circle. If a circle has radius , then its circumference is . So, if a circle has radius , then it has circumference .So if a circle has radius , what must the circumference be?
would be , and would be . What could and be, then?

Hi Thompsonnn,

I responded to this question in your previous thread -- did you see it?

Let's look at the first problem. The easiest thing to do is to get rid of the brackets and then collect all the terms which have the same powers together, like this:

and from there, you can simplify.

For the second question, the difference of squares method says that you can factorise as . We want to try and write in the form . Do you have any ideas for how we could choose and ?What do you think about the third question?

Yes, I agree with that.

Hi Bob,

I was assuming that they meant the multiplicative inverse, yes -- if they meant additive inverse, the problem is very similar (though produces a different answer).

Hi salaisuresh,

Welcome!

It can probably be done in a similar way -- let us know if you have any problems.

Hi Samuel.lagodam,

Welcome to the forum. Why would that be?

Great! But remember to discard one of the solutions, since time cannot be negative.

Yes, and how can you use that to find the maximum height?

Hi Oran,

Have you considered registering an account with us?

Let's start with the first question. We'll work in feet since the question gives us the information in feet, rather than metres. What information do we have?

Let's take the upwards direction to be positive. We're given , , and (that has a negative sign, because gravity acts downwards). So, at a time , suppose that is the height above the ground. We could use the equation here, replacing with (because we start feet above the ground), replacing with , and with . That'll give you a quadratic for in terms of . (You could also get one in terms of , but judging by the question, I suspect this is how they might want you to do it.) How can you then use this equation to find the maximum height?Similarly:

So when we plug and into the left-hand side of , we get -- which means that they satisfy the equation. So we can call them solutions.Does that make sense?

Yes, that's correct.

Thompsonnn wrote:

10. Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

Remember that here we wanted a quadratic equation with factors (x - 3) and (x + 7), because those equal zero when x = 3 and x = -7, respectively.

So a quadratic equation that has solutions x = 3 and x = -7 is (x - 3)(x + 7) = 0.

This time, you're given the quadratic equation (t - 8)(t + 3) = 0.

This has factors (t - 8) and (t + 3).

Can you see which values of t will make those equal zero?

For which values of is equal to ?

The first point is . The second point is .

-They multiply to make .

For instance, -6 and 1 add to make -5, but their product is -6, so that doesn't work.

However, -8 and 3 add to make -5, and their product is -24, so that's the correct combination. Thus, we can factor like this:

Are you able to solve the question from here?