Melody

Thanks asinus, it is always nice to see you here :)

Hi Irondome,

Her is your graph.

the first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728. find r and n.

\(a=2 \qquad T_n=486\qquad S_n=728\\~\\ ar^{n-1}=486 \qquad \frac{a(r^n-1)}{r-1}=728\\ 2*r^{n-1}=486 \qquad \frac{2(r^n-1)}{r-1}=728\\ r^{n-1}=243 \qquad \frac{(r^n-1)}{r-1}=364\\ \)

\(\frac{r^n}{r}=243 \qquad \qquad r^n-1=364r-364\\ r^n=243r \qquad\qquad r^n=364r-363\\ 243r=364r-363\\ 363=121r\\ r=3\\~\\ 3^n=243*3\\ 3^n=3^6\\ n=6\\ so\\~\\ n=6\qquad and \qquad r=3\)

what is the product of (3-4i) and (7-3i)?

\((3-4i)(7-3i)\\ =3(7-3i) -4i(7-3i)\\ =21-9i -28i+12i^2\\ =21-37i+\;\;\;\;12*-1\\ =21-37i\;\;\;\;-12\\ =9-37i\\\)

if i make £141.10 a week how long would it take for me to make £77,000

77000/141.10 = 545.7122608079376329  weeks

545.7122608079376329/52 = 10.4944665539988006327 years

that is 10 and a half years :)

Since there are no brackets, this reads as 

9-3/1 over 3 + 1 =

9-(3/1) over 3 + 1

= 9-  3/3 +1

= 9 -  1  +1

=9

Which best compares the slopes and y-intercepts of the linear functions f and g, where f = 1/3x + 3 and g is shown in the table below?

x1234

g(x)36912

Is this part of a multiple choice question?

the gradient of f(x) is 1/3      the gradient of g(x) is 3         That is the positive reciprocal       f(x)=(x/3)+3

The y interecept of f(x) is 3    and the y intercept of g(x) is 0                                                  g(x)=3x

I sam not really sure what answer is being sort here.   

Here is what the graphs look like

That is a good question.

I expect you already know the answer ;)

It's 60km/hour.      :))

Hi Cleopatrx,

It is a cool username you have there :)  Welcome to the forum:)

I am on my phone so this is not the best way to explain.

I looked for a fomula that linked number to cost. It is pretty silly because it keeps getting dearer.

Anyway if you square the number and multiply by 3 you get close to the cost.

If you then add 15 and subtract the production number it works out exact.

So

C= 3x^2 + 15 -x

C = 3x^2 - x +15

When x=5

C = 3 × 25 - 5 +15

C = 75 

Find the gradient of the radius that touches the tangent.

The gradient of the tangent is the negative reciprocal.

Use the point and the gradient to determine the equation.