Tuesday
February 21, 2017

Posts by Reiny

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

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