Tuesday

February 21, 2017
Total # Posts: 37,719

**Math**

let the tens digit be x, and the unit digit be y So the number is 10x + y, the number reversed is 10y + x 10x+y - (10y+x) = 9 9x - 9y = 9 x - y = 1 or x = y+1 ** 2x = 7y-8 sub in ** 2(y+1) = 7y - 8 2y + 2 = 7y - 8 -5y = -10 y = 2 The number is 32 check: the number reversed is ...

*January 1, 2017*

**math(geometric series)**

2nd term is 3/2 --- ar = 3/2 sum of all terms is 8 a/(1-r) = 8 divide the first equation by the 2nd equation: (ar) / (a/(1-r)) = (3/2) / 8 r(1-r) = 3/16 r - r^2 = 3/16 3 = 16r - 16r^2 16r^2 - 16r + 3 = 0 (4r - 1)(4r - 3) = 0 r = 1/4 or r = 3/4 check for r = 1/4 a(1/4) = 3/2 a...

*December 31, 2016*

**math(A.P/G.P)**

Shall I assume that 2% p.a C.I means 2% per annum compounded instantaneously ? the amount = 55 e^.02t if 2005 ---> t = 0 then 2015 --- t = 10 amount = 55 e^(.02(10)) = 67.177 crores (is 1 crore equal to 10 million? I see one answer as 6700, but that would not match your ...

*December 31, 2016*

**Algebra**

for 1st series: first term is a, common difference is d sum(n) = (n/2)(2a + d(n-1)) for 2nd series: first term is b, common difference is e sum(n) = (n/2)(2b + e(n-1)) (n/2)(2a + d(n-1)) / (n/2)(2b + e(n-1)) = (7n+1)/(4n+27) (2a + dn - d)/ (2b + en- e) = (7n+1)/(4n+27) 8an + ...

*December 31, 2016*

**Math**

The way you typed it, and following the order of operation ... 100-100/100-100 = 100 - 1 - 100 = -1

*December 29, 2016*

**mathematics**

look at the second part of this post http://www.jiskha.com/display.cgi?id=1482579345

*December 24, 2016*

**maths**

No zero in single digit numbers For double digit numbers: 10, 20 .. , 90 ---> 9 of them triple digits: using 2 zeroes: 100, 200, 300, 400, 500 --- 10 of them using 1 zero: case 1: the zero in 2nd place = 5 x 1 x 9 = 45 case 2: the zero in 3rd place = 5 x 9 x 1 = 45 total = ...

*December 24, 2016*

**MATH**

The change is caused by the term -3x Since you are "decreasing" x by 2 we sub in x = -2 so y = 42 - 3(-2) = 42 + 6 thus the change is 6

*December 24, 2016*

**ellipse**

alternate solution for B: let's "move" everything to standard position using (x,y) ---> (x+1, y-2) centre (-1,2) ---> centre (0,0) F(-1,5) ----> focus( 0, 3) , so c = 3 P(5,6) -----> P' (6, 4) b^2 = a^2 + c^2 = a^2 + 9 starting equation: x^2 /a^2...

*December 24, 2016*

**ellipse**

A) centre at (-2,3) --> (x+2)^2 /a^2 + (y-3)^2 / b^2 = 1 focus at (-2,7) implies the ellipse is vertical and c = 7-3 = 4 vertex is (-2,10) , so a = 10=3 = 7 and a^2 + c^2 = b^2 7^2 + 4^2 = b^2 = 65 (x+2)^2 /49 + (y-3)^2 / 65 = 1 B) centre (-1,2) ---> (x+1)^2/a^2 + (y-2)^...

*December 24, 2016*

**algebra**

I see 2c^3 as a common factor = 2c^3(a^2 - 7b + 16d^2)

*December 22, 2016*

**math**

a1 = 13 a2 = 15 = a1 + 2 a3 = 17 = a2 + 2 ... an = an-1 + 2 , n > 1

*December 22, 2016*

**small correction - QUADRILATERAL MATHS**

For the last method, I meant to say : " list the coordinates of the quadrilateral counter-clockwise starting with any point in a column. "

*December 22, 2016*

**QUADRILATERAL MATHS**

There are several ways to do this: 1. If you join AC, you have a right-angled triangle ABC. Find the length of AB and BC and use area = (1/2)base x height for its area. Find angle D by using the slopes of AD and CD, find the lengths of CD and AD , then area of triangle ACD = (...

*December 22, 2016*

**math**

look at the last 4 answers below under Related Questions.

*December 22, 2016*

**math**

Sketch your three intersecting circles, V, B, and T place 20, 10 and 6 in the "only" part of the circles. Place 4 in the intersection of all circles. Place x in the remaining parts of the circle. Add up all the parts: x + x + x + 4 + 20 + 10 + 6 = 70 3x + 40 = 70 3x...

*December 22, 2016*

**calculus**

looks like a homework dump. Five questions without showing us any of your starting steps or any indication where your problems lie with these questions.

*December 21, 2016*

**calculus**

find the derivative, set that equal to zero and solve for x sub back into original f(x) to find the matching y values. also find the end values of f(-2) and f(4) , then decide which are your max/mins.

*December 21, 2016*

**calculus**

let the two numbers be x and y xy = 16 y = 16/x Let S be the sum of their squares S = x^2 + y^2 = x^2 + 256/x^2 = x^2 + 256x^-2 dS/dx = 2x - 512x^-3 = 2x - 512/x^3 = 0 for a min of S 2x = 512/x^3 2x^4 = 512 x^4 = 256 x = ±4 then 16/±4 = ±4 the two numbers ...

*December 21, 2016*

**math**

Or did you notice that each of the given numbers is one more than the perfect square, that is 2 = 1^2 + 1 5 = 2^2 +1 10 = 3^2 + 1 17 = 4^2 + 1 thus: term(n) = n^2 + 1

*December 21, 2016*

**math connections**

solve -4n + 7 + 2n=1 ---> -2n = -6 n = 3 solve 4(y-4)=8 divide by 4 y-4 = 2 y = 6

*December 21, 2016*

**Math**

let the distance traveled by car X be x km let the distance traveled by car Y by y km their paths form a right-angled triangle. Let the distance between them be D km D^2 = x^2 + y^2 2D dD/dt = 2x dx/dt + 2y dy/dt dD/dt = (x dx/dt + y dy/dt)/D at the given case: x = 60, y = 80...

*December 20, 2016*

**math**

effectively he gains 10 m every 2 minutes but for the last 10 m he does not have to rest 1 minute to reach his goal. That is, at the end of 2 minutes, he has gone 10 m 4 minutes, he has gone 20 m ... 36 minutes, he has gone 180 m Since he can swim 20 m per minute, he will ...

*December 20, 2016*

**pre calculus**

Ok, Meredith, after doing this one for you http://www.jiskha.com/display.cgi?id=1482199382 surely you can follow the same steps for this one.

*December 19, 2016*

**Business Finance**

ummmhhh, for 5 years, for 2 years, for 20 years ??? The question is incomplete.

*December 19, 2016*

**Business Finance**

You did not state the time period

*December 19, 2016*

**math**

Prob(sum of 2) = 1/36 prob(sum of 3 ) = 2/36 prob(sum of 4) = 3/36 prob(sum of 5) = 4/36 prob(sum of 6) = 5/36 prob(sum of 7) = 6/36 ... sum of 8 = 5/36 ... sum of 9 = 4/36 ... sum of 10 = 3/26 ... sum of 11 = 2/36 ... sum of 12 = 1/36 notice the sum of these prob's is 1 ...

*December 19, 2016*

**Maths**

I will do the first one, you do the other two in the same way. let the width be x let the length be 2x, notice x : 2x = 1 : 2 2(x) + 2(2x) = 30 5x = 30 x = 6 sides are 6 cm and 12 cm, with an area of 72 cm^2

*December 19, 2016*

**business math**

i = .055/365 = .000150684 amount after 21 days = 6000(1.000150684)^21= 6019.01 So what interest did she earn ?

*December 19, 2016*

**Write the system of equations as an augmented matr**

-4 -1 | -6 -8 -5 | -6

*December 19, 2016*

**Pre calculus**

recall: sinØ = y/r and cosØ = x/r so: r= 5/(sin theta +2cos theta) r = 5/(y/r + 2x/r) r = 5/((2x+ y)/r) r = 5r/(2x + y) 1 = 5/(2x+y) 2x + y = 5 <----- a straight line proof: http://www.wolframalpha.com/input/?i=polar+plot+r%3D+5%2F(sin+theta+%2B2cos+theta)

*December 19, 2016*

**data management gr.12**

Your question is perfectly suited for this applet http://davidmlane.com/normal.html Just enter your data

*December 19, 2016*

**pre calculus**

Steve has the correct equation. I don't know why my 8 was dropped in my 3rd last line, just careless.

*December 19, 2016*

**pre calculus**

from your previous question, recall sinØ = y/r --> y = rsinØ cosØ = x/r --> x = rcosØ (x-4)^2+y^2=16 (rcosØ -4)^2 + r^2sinØ = 16 r^2 cos^2 - 8rcosØ + 16 + r^2sin^2 Ø = 16 r^2 (cos^2 Ø + sin^2 Ø) - rcos...

*December 19, 2016*

**data management gr.12**

See the webpage I gave you in your other post

*December 19, 2016*

**Trigonometry**

tan(Ø - 30) = -5 we know tan 78.69° = +5 and since the tangent of our given angle of Ø-30 is negative it must be quadrants II or IV Ø-30 = 180-78.69 = 101.31 Ø = 101.31+30 = 131.3° ir Ø-30 = 360 - 78.69 = 281.3 Ø = 311.3°

*December 19, 2016*

**Engineering Mathematics-I**

First you need the intersection (2x^2)^2 = 4x 4x^4 - 4x = 0 x(x^3 - 1) = 0 x=0 or x = 1 see: http://www.wolframalpha.com/input/?i=y%3D2x%5E2+,+y%5E2%3D4x effective height = ?(4x) - 2x^2 = 2 x^(1/2) - 2x^2 area = ?(2 x^(1/2) - 2x^2) dx from x = 0 to 1 = [ (4/3)x^(3/2) - (2/3)x^...

*December 17, 2016*

**Maths**

original fraction ----- 5x/2x new fraction: (5x+5)/(2x-2) I can't make out what 15 4 is supposed to be. Once you have decided, set that equal to (5x+5)/(2x-2) , looks like you would just cross-multiply to solve

*December 17, 2016*

**Math**

width --- 5x length ---8x (5x)(8x) = 169 40x^2 = 169 x^2 = 169/40 x = 13/?40 width is 65/?40 = appr 10.28 length is 104?40 = appr 16.44 check: area = (65/?40)(104/?40) = 6760/40 = 169 ratio = (65/?40) : 104/?40) = 65 : 104 = 5 : 8

*December 16, 2016*

**math-circles**

The areas of two circles are proportional to the square of their raddi so r1^2 / r2^2 = 9/4 r1/r2 = 3/2 r1 = 3r2/2 also r1 = r2 + 2 Thus: 3r2/2 = r2 + 2 3r2 = 2r2 + 4 r2 = 4 then r1 = 6 the larger radius is 6 units check: area of larger = 36? area of smaller is 16? ratio of ...

*December 16, 2016*

**Math**

sequence is : 3/4 , 1/4, 1/12, 1/36 = 27/36 , 9/36, 3/36, 1/36, ... = (1/36){ 27, 9, 3, 1, ......} can you see the pattern in 27, 9, 3, 1, .... ??

*December 16, 2016*

**maths**

volume of original sphere = (4/3)? R^3 volume of each of the 1000 smaller ones = (4/3000)? R^3 = (1/750) ? R^3 let the radius of the smaller be r 4/3 ? r^3 = (1/750) ? R^3 r^3 = (1/1000) R^3 r = R/10 surface area of smaller = 4? r^2 = 4? R^2/100 = ? R^2/25

*December 16, 2016*

**Math**

first number ---- x 2nd number ----- x+5 x + x+5 = 57 carry on

*December 16, 2016*

**Math algebra**

A quick check with your notes or textbook would have shown this to be a clear case of the distributive property.

*December 16, 2016*

**precalculus**

#1 term(5) = C(8,4) (2x)^4 (-4)^4 = 70(16x^4)(256) = 286720 x^4 <-------- B general term of (a+b)^n: term (k+1) = C(n,k) * (a)^(k-1) * b^k #2, correct

*December 16, 2016*

**math**

4/9 b^6 = (2/3 b^3)^2

*December 16, 2016*

**calc**

x/8 - (2/9)y dy/dx = 0 dy/dx = (x/8) / (2y/9) = 9x/(16y) at (4?2,3), dy/dx = 36?2/(48) = 3?2/4 equation: y - 3 = (3?2/4)(x - 4?2) clean it up to whatever form is needed. Proof: http://www.wolframalpha.com/input/?i=plot+(x%5E2%2F16)-(y%5E2%2F9)%3D1+,+y+-+3+%3D+(3%E2%88%9A2%2F4...

*December 15, 2016*

**Physics- Car moving with speed of 22 m/s...**

acceleration --- (-a) velocity = -at + c when t = 0, v = 22 22= 0+c ---> c = 0 v = -at + 22 when t = 6.5, v = 0 0 = -6.5a + 22 a = 22/6.5 = 44/13 distance = d = (-1/2)a t^2 + 22t + k d = (-22/13)t^2 + 22t + k when t = 0, d = 0, so k = 0 when t = 0 , d = 0 when t = 6.5, d...

*December 15, 2016*

**algebra**

(4.2*10^2)(4.2*10^5) = 17.64 x 10^7 = 1.764 x 10^8

*December 15, 2016*

**algerbra**

h(t) = -16t^2 + 96t 144 = -16t^2 + 96t t^2 - 6t + 9 = 0 (t-3)(t-3) = 0 t = 3

*December 15, 2016*

**math**

After giving .3x of the flowers to her sister Fariza has .7x of them left over giving (4/7) to her brother leaves her with (3/7)(.7x) (3/7)(.7x) = 45 .3x = 45 x = 150 she kept 45/150 or 30% of them for herself She had 150 of them the sister got (.3)(150) or 45 the brother got...

*December 15, 2016*

**math**

What Ms Sue is saying is .... y = 3x + 3

*December 15, 2016*

**Calculus**

Ok, so the second derivative is negative and you know that if the 2nd derivative is negative the function is concave downwards. Of course you should recognize that we are dealing with a quadratic function, a parabola, which opens downwards for all values of x

*December 15, 2016*

**MATH HELP PLEASE**

For any number to be divisible by 9, the sum of its digits must be divisible by 9 So far we have a sum of 16, so we need a 2 21258 is divisible by 9 Surely you know how to do the other two questions.

*December 15, 2016*

**Zee school , math subject.**

What is the area of the original sheet ? What is the area of one of the squares to be cut out? How many of those cut-out squares are there? What is left over after we cut them out? ... etc. I'll wait for your reply and check your answers.

*December 15, 2016*

**Math grade 6, ratio**

number of oranges --- x after give-away number of oranges = x-10 number of pears = 24 and he had twice as many pears as oranges 24 = 2(x-1) 2x - 2 = 24 x = 13 ratio of oranges : pears = 13 : 24

*December 15, 2016*

**Math grade 6, ratio**

current count: boys --- 4x girls ---- 3x 4x = 3x + 6 x = 6 there were 24 boys and 18 girls after 2 girls are added, new ratio is 24 : 20 = 6 : 5

*December 15, 2016*

**math**

let the 3 numbers be x, x+1, and x+2 2(x+2) + x = 4(x+1) - 15 solve for x, then sub into my definitions

*December 15, 2016*

**Math grade 6, ratio**

Number of stamps for david -- 4 x number of stamps for Tim = 3x after give-away, Tim has 1.5x David has 5.5x ratio of Tim : David = 1.5x : 5.5x = 1.5 : 5.5 = 15 : 55 = 3 : 11

*December 15, 2016*

**Math**

Don't repost the same question without looking at your previous one http://www.jiskha.com/display.cgi?id=1481770968

*December 14, 2016*

**Pre-calculus**

Cannot make out your typing what does "cos \theta" mean ? is it r = -5( 2cosØ + sinØ) ??? if so, here is the graph: http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+-5(+2cos%C3%98+%2B+sin%C3%98) certainly not a line

*December 14, 2016*

**Math**

3x^4 + 4x^3 =0 x^3(3x+4) = 0 x = 0 or x = -4/3 looks like two x-intercepts f ' (x) = 12x^3 + 12x^2 = 0 for a max/min of f(x) 12x^3 + 12x^2 = 0 x^2(12x + 12) = 0 x = 0 , f(0) = 0 x = -1, f(-1) = 3 + 4(-1) = -1 looks like (-1, -1) is a minimum , and we will consider (0,0) ...

*December 14, 2016*

**The Value of an Annuity**

You do these kind of questions, you MUST know the basic formulas. I used Amount = payment( (1+i)^n - 1)/i I you don't know this, how can you possibly handle this topic of annuities?

*December 14, 2016*

**The Value of an Annuity**

i = .067/4 = .01675 n = 140 P(1.01675^140 - 1)/.01675 = 800,000 p = ..... b) multiply p by 140 c) subtract 800,000 - answer to b)

*December 14, 2016*

**Math**

let the sides by 17x by 2x ( ---> ratio is 17x : 2x = 17 : 2 ) 34x^2 = 136 x^2 = 136/34 = 4 x = 2 sides are 17(2) by 2(2) or 34 by 4

*December 14, 2016*

**math**

18x^2=420-6x You now have a quadratic equation 18x^2 + 6x - 420 = 0 3x^2 + x - 70 = 0 (x + 5)(3x - 14) = 0 x = -5 or x = 14/3 since x> 0, x = 14/3 so the sides are 6(14/3) or 28 and 3(14/3) or 14 so the perimeter is 2(28+14) = 84 ft check: 18x^2 = 18(14/3)^2 = 392 420 - 6x...

*December 14, 2016*

**precalculus**

see your previous post under anonymous

*December 14, 2016*

**precalculus**

see reply when you were "anonymous"

*December 14, 2016*

**Algebra**

9x^2+ 25y^2 =225 divide each term by 225 x^2/25 + y^2/9 = 1 ellipse, with a = 5 and b = 3 domain: -5 ? x ? 5 range: -3 ? y ? 3

*December 14, 2016*

**can you check my answers precalculus**

Please give yourself a "nickname" and stick with it. That way I can check for your previous posts. I recall just answering that one.

*December 14, 2016*

**Math**

thord te ????? "The eleventh term of an A.P.with positive terms is four times its third term" ---> a+11d = 4(a+2d) a+11d = 4a + 6d 5d = 3a d = 3a/5 "the product of thord te and eleventh term is 256" I will read that as third term (a+2d)(a+11d) = 256 a^2...

*December 14, 2016*

**precalculus**

Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) P(k+1) = Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6(k+1) + 1 = Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6k + 7) "What is the first step when writing a proof using mathematical induction? " Test to see ...

*December 14, 2016*

**Math | Algebra**

amount of brand A needed --- x lb amount of brand B needed ---- 20-x lb .25x + .2(20-x) = .23(20) .25x + 4 - .2x = 4.6 .05x = .6 x = 12 State your conclusion

*December 14, 2016*

**math**

What's the question? If you want the maximum height: the vertex will tell you how high it went and how long it took to reach that height. the t of the vertex is -64/(-32) = 2 seconds h(2) = -64 + 128 + 192 = 256 ft above the ground (the vertex was (2, 256) when will it hit...

*December 14, 2016*

**algebra**

5,100,000 = 5.1 x 10^6 (notice I moved the decimal 6 places)

*December 14, 2016*

**precalculus**

I think this link nicely fits with your problem, carefully study the 3 steps I used to do an induction problem. The problem is the same as your #4 http://www.jiskha.com/display.cgi?id=1481512314 #1. I don't like your notation, did you mean P(k+1) and P(k) ? or Pk+1 and Pk ...

*December 14, 2016*

**Math**

no, why would you divide by 3? you correctly converted the square feet to square yards by dividing by 9, and your cost was in square yards. your cost is $610.50

*December 14, 2016*

**precalculus**

http://www.jiskha.com/display.cgi?id=1481565350

*December 14, 2016*

**algebra**

well, first lets get rid of those nasty fractions ... multiply the first by 10 6x = 5y + 110 or 6x - 5y = 110 ** 3x + 8y = 13 <--- I assume yours was a typo double the 2nd: 6x + 16y = 26 *** subtract *** from ** -21y = 84 y = -4 sub back into 3x+8y=13 to find x

*December 14, 2016*

**Math - Algebra (Percents and Ratios)**

number of people in stands --- x number who were parents = (3/4)x) of those 4/7 were moms total moms = (3/4)(4/7)x = (3/7)x percentage of moms = (3/7)x / x = 3/7 = appr 43%

*December 14, 2016*

**algebra**

I will show you the first one .... ?50 = ?25*?2 = 5?2 general method: Factor your number so that one or more factors are perfect squares. e.g. ?720 = ?9*?16*?5 = 3*4*?5 = 12?5 Show me what you did for the 2nd question

*December 14, 2016*

**pure math**

Did you mean (1 - x/2)^(1/5) ? Are you studying the binomial theorem?

*December 14, 2016*

**math**

You are welcome

*December 14, 2016*

**math**

Yes, it would be because of the repeated multiplication by .88 suppose we show a few steps after 1 km : Pr = 1013(.88) after 2 km : Pr = 1013(.88)(.88) = 1013 (.88)^2 after 3 km : Pr = 1013(.88)^2 (.88) = 1013 (.88)^3 etc , for after x km : Pr = 1013 (.88)^x

*December 14, 2016*

**One step inequalities**

x - 9 ? 27

*December 14, 2016*

**precalculus**

Steve had done the above steps for you, see the first of the Related Questions for you. First, it might help if you looked at the graph http://www.wolframalpha.com/input/?i=polar+plot+r%3D8cos(3%C3%98) Steve told you: |cos 3Ø| ? 1 so |8cos 3Ø| ? 8 | r | ? 8 , so ...

*December 14, 2016*

**Math**

Take a small rectangular piece of paper, such as a business card, hold a finger on the end of the longer side and rotate the card. What do you notice ?

*December 14, 2016*

**Probability**

first of all listing the choices of digits 444 --- can be arranged in 1 way 442--- can be arranged in 3 ways 443--- can be arranged in 3 ways 422--- can be arranged in 3 ways 433--- can be arranged in 3 ways 423--- can be arranged in 6 ways 222--- can be arranged in 1 way 223...

*December 14, 2016*

**Math**

weight of empty basket --- x weight of 1 pear ---------- y x + 30y = 11.2 x + 18y = 7 subtract them: 12y = 4.2 y = .35 sub back: x + 18(3.5) = 7 x = 4.2 Each pear weighs 350 g and the basket ways 4.2 kg so basket with 7 pears = .......

*December 14, 2016*

**maths**

total expenses = 2030+4900+3150 = .... so 2x + 3x + 4x = total above find x, sub back into 2x, 3x, and 4x

*December 14, 2016*

**Algebra**

Athena's age is expressed as a function of the cousin's age, so it is usually easier to define the domain Four years ago: let the cousin's age be x then Athena was 2x-5 present: cousin ---- x+4 Athena ----- 2x-5 + 4 or 2x - 1 x+4 = 3(2x-1) - 18 x+4 = 6x - 3 - 18 25...

*December 14, 2016*

**maths**

done http://www.jiskha.com/display.cgi?id=1481713097

*December 14, 2016*

**Math**

Prob(a 6) = 1/6 , prob(not a 6) = 5/6 so in 5 tosses you want that 3 times Prob(of your event) = C(5,3) (1/6)^3 (5/6)^2 = 10(1/216)(25/36) = 125/3888 or appr .03215

*December 14, 2016*

**precalculus**

Steve said: http://www.jiskha.com/display.cgi?id=1481636669 and this: http://www.jiskha.com/display.cgi?id=1481653351 Make use of it please

*December 13, 2016*

**business**

amount = 2000 ( 1.05^40 - 1)/.05 = ....

*December 13, 2016*

**math**

hina gets ---- x rina gets ----- 3x - 100 x + 3x-100 = 300 4x = 400 x = 100 Hina would get 100 and rina would get 3(100) - 100 or 200

*December 13, 2016*

**precalculus**

umhh, what part of the solution I gave you yesterday did you not like? http://www.jiskha.com/display.cgi?id=1481597953

*December 13, 2016*

**I THINK I FIGURED IT OUT!**

Another simple way to look at it: 24 ----> 6 , so it was reduced by a factor of 1/4 what is (1/4) of 18 ????

*December 13, 2016*

**I THINK I FIGURED IT OUT!**

NOPE, look at my last reply to your previous post

*December 13, 2016*

**a.p.**

ok, your turn use your definitions

*December 12, 2016*