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log x - log y = a

log y - log z = 15

log z - log x = -7

Add the last two equations

log y - log z  = 15

log z  - log x = -7

______________

log y - log x =  8     multiply through by -1

log x - log y   =  -8     =   "a"

To find the common ratio, divide the second term by the first term....so.....

    -4/9 / 5/6  =   -4/9 * 6/5 =  -24 / 45 =  - 8 / 15   =  common ratio

It doesn't = "infinity"   [ this is what many calculators show ]

It would be better said that it is "undefined"

The tangent ratio is  y / x

But, at 90°, y will = r, but x = 0......and since we cannot dvide by 0, then thr tangent is undefined at 90°

The graphs of a function f(x)=3x+b and its inverse function f^-1(x) intersect at the point (-3,a). Given that b and a are both integers,

what is the value of a?

Hey CoolStuffYT thanks for all the help you give everyone!! Have a Happy New Year!!! My resoulation is to eat fast food less. Whats yours?

The initial investment must be a typo.  Even 1 year of 5% interest on 70k is 3.5k which is much larger than 1451.25

I'll assume OP meant 7000

\(P_1 = x,~P_2 = 7000-x\\ I = P_1 r_1 N + P_2 r_2 N = (0.1)3x + (0.05)3(7000-x) = 1451.25\)

\(1050+0.15x = 1451.25\\ 0.15x = 401.25\\ x = 2675\\ 7000-2675 = 4325\\ \text{so \$2675 was invested in the 10% account and \$4325 was invested in the 5% account}\)

This forms an arithmetic series as follows:

First term =788, Number of terms =25, Common difference =-32

SUM = N/2 * [2*F + D*(N - 1)]

SUM = 25/2 *[1,576 + (-32 * 25 - 1]

SUM = 12.5 *[1,576 + (-32 *24]

SUM = 12.5 *[1,576 - 768]

SUM = 12.5 *[808]

SUM =10,100

Same graph.....from Desmos.....

ok thank you

Here's a graph on EP's response: 

I might have to change it, took quite a while!

Sub in the poitns given:

3 = 2^2 + 2b +c     and

3 = 4^2 + 4b +c       Now solve for c   (Multiply first equation by -2  then add it to the second equation....you'll find c = 11)

Nice work, MathToo !

Thank you! 

Oh...I forgot....you wanted a + b + c

This  is

3  + 3/2 + 3/2  =

3 + 3  = 

6

Thank you! Do I have to add the x-intercept to it? So, 3 + that value?

x =  2y^2 - 6y + 3

The x intercept is easy....let y = 0    and x =  3

To find the y intercepts, let x =  0    and we have

2y^2 - 6y + 3 =  0

Using the quadratic formula, the y intercepts are

y =      [ 6 ±  √ [ 36 - 24] ] / [ 2 * 2 ]   =  [ 6 ±  √12] / 4  = [ 6 ±  2√3] / 4  =  [ 3 ±  √3] / 2

Yes! 16/7-4/7=12/7. Thank you!

It's the derivative of  2x^2 + 6    =   4x

Anchoring P at the top of the circle and letting Q be the next point on the circle clockwise from  P

R  can  then  be  located at any  5 of of the remaining points on the circle

So.... angle PQR can take on 5 possible values

Can you explain where the 4x came from please thanks very much

We don't need to worry about the denominator with the quotient rule

Remember that the quotient rule is  ....   (f / g)'  =   [f' g -   f g'] / [ g^2 ]

f = 3(x - 1)^2  =  3x^2 - 6x + 3

g = 2x^2 + 6

So....

The numerator is 

(6x - 6)(2x^2 + 6)  -  (3x^2 - 6x + 3) (4x)   =  0

6 ( x - 1) * 2 (x^2 + 3)  -  3(x - 1)^2(4x) = 0

12(x - 1) (x^2 + 3) - 12x(x - 1)^2  =  0

12(x - 1)  [ (x^2 + 3) - (  x(x - 1) ]  = 0

12 (x - 1) [ x^2 + 3 - x^2 + x]  = 0

12(x - 1) (x + 3 )  = 0

Setting both factors to 0 and solving for x produces the two stationary x coordinates of  x = 1    and x = - 3

And f(-3) = 2

So....the other stationary point is (-3, 2)

Yep...go with tertre's answer.....I  didn't interpret this one properly...!!!!!

so to solve the system should i use simultaneous equation?

i solved it with my graphical calculator but i believe i am expected to show some working out and i cant do 4 at once yet 

thank you for helping