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#2 Re: Help Me ! » Review » 2017-09-14 18:04:27

Not quite -- if
were 4, then you'd have
You want
so there should be an
appearing somewhere in your answer. For example, what expression, when squared, gives you
?

#3 Re: Help Me ! » Circumferences and Arc Length » 2017-09-13 08:10:06

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?

#4 Re: Help Me ! » Review » 2017-09-13 07:39:36

would be
, and
would be
. What could
and
be, then?

#5 Re: Help Me ! » Difference of squares » 2017-09-11 19:40:52

Hi Thompsonnn,

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

#6 Re: Help Me ! » Review » 2017-09-05 23:33:46

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?

#7 Re: Help Me ! » Help FAST! » 2017-09-03 22:49:05

Yes, I agree with that.

#8 Re: Help Me ! » Help FAST! » 2017-09-03 20:22:46

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).

#9 Re: Help Me ! » Help FAST! » 2017-09-03 19:52:48

Deduce from the first statement that
divides
, which gives you a small number of possibilities to test against the second statement. (
of them, to be precise.)

#11 Re: Help Me ! » Solving Quadratics by Factoring and Graphing » 2017-08-31 08:51:33

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

#13 Re: Exercises » What is 0^0 » 2017-08-30 04:53:27

Hi Samuel.lagodam,

Welcome to the forum. Why would that be?

#14 Re: Help Me ! » Solving Quadratics by Factoring and Graphing » 2017-08-28 06:47:42

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

#15 Re: Help Me ! » PreCalc Problems » 2017-08-27 19:02:46

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

#16 Re: Help Me ! » PreCalc Problems » 2017-08-27 08:18:29

You could use the equation
with your known values of
and
with
, as detailed in post #2. This gives you a quadratic, which you can then solve to obtain the answer to the second part of that question.

#17 Re: Help Me ! » PreCalc Problems » 2017-08-27 07:46:11

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?

#18 Re: Help Me ! » Solving Quadratics by Factoring and Graphing » 2017-08-27 07:07:23

The quadratic equation
has solutions
and
This is because when you replace
with
into the equation, you get:

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?

#19 Re: Help Me ! » Are these two rings equal? » 2017-08-27 07:03:27

Yes, and there are two inclusions you need to prove. The inclusion
is clear. For the reverse inclusion, note that
has inverse
So you know now that both
and
are elements of the ring
, and so any
-linear combination of these also belongs to the same ring. Deduce that
must therefore belong to the ring (as some linear combination of those two elements) and do the same for
. This proves the reverse inclusion, and thus, these rings are in fact the same. (By the way, if you've done any Galois theory, you could also use the fact that
since both radicals are trivially algebraic over
, and then use the tower law.)

For the second question, try assuming that
and derive a contradiction.

#21 Re: Help Me ! » Solving Quadratics by Factoring and Graphing » 2017-08-24 20:05:02

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?

#23 Re: Help Me ! » Why is it called f(x+Δx)? » 2017-08-22 08:50:38

The first point is
. The second point is
.

#24 Re: Help Me ! » Solving Quadratics by Factoring and Graphing » 2017-08-21 20:16:53

That is what happens when you expand the brackets, but what are the solutions to the quadratic equation
? (Think back to questions 10-12...)

#25 Re: Help Me ! » Solving Quadratics by Factoring and Graphing » 2017-08-21 01:36:25

Here's a quick way to factor
We want to find two numbers such that:

-They add to make
, and
-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?

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