Saturday
September 5, 2015

Posts by Reiny


Total # Posts: 30,726

Algebra
sometimes it helps if you just relate the problem to a specific numerical case. e.g. supposed you were asked how far a car going 60 km/h would go in 3 hours. the answer is clearly 180 km What did we do to get 180 ? we multiplied 3 by 60 so if the time is y hours instead of 3 ...
September 4, 2015

Math
tree : shadow = 12 : 6 = 2 : 1
September 4, 2015

Algebra
yup
September 4, 2015

Math
This is a sneaky question, f(x) = (x^2+3x+2)/(x+2)*tan(π*x) = (x+1)(x+2)/(x+2) tan(πx) = (x+1)tan(πx) the vertical asymptote is caused by the tan(πx) part, recall that tan90° is undefined, and 90° = π/2 radians or (1/2)π so if x = 1/2 we ...
September 4, 2015

Algebra
no, the correct choice is B , which says in a simplified way that xy = yx notice the two factors are switched
September 4, 2015

math
Using the factor theorem , I tried x = ±1, ±2, ±4, and it worked if x = -4 so by synthetic division: 4x^3 + 32x^2 + 79x + 60 = (x-4)(4x^2 + 16x + 15) = (x-4)(2x+5)(2x+3) (x-4)(2x+5)(2x+3)=0 x = -4, or x = -5/2, or x = -3/2 and sure enough -5/2 + (-3/2) = -...
September 4, 2015

MATH
better form would be to place the equal sign in front of each new line You also have errors -3(x + 3)- 2(x + 4) = -3x - 9 - 2x - 8 = -3x - 2x - 9 - 8 = -5x - 17
September 3, 2015

math
I cannot decipher your text on my Mac - instead of creating the symbols, state them in words e.g 56 degrees for 56° in your second question, where is X ? Is it on some line?
September 3, 2015

Algebra
5x+2y according to your definition of x and y shows me that each adult ticket costs $5 and a student's ticket costs $2. for 5x + 2y = 220 the x-intercept is 44 , the y=0 the y-intercept is 110, the x = 0 Meaning: if no students show up, then the number of adult that went ...
September 3, 2015

algebra
assuming that letters may be repeated, and no words formed are restricted .... number of plates = 3x26x26x26x26 = 3(26^4) = ...
September 3, 2015

math
your are in quad II drop a perpendicular to the x-axis and draw your right-angled triangle cosØ = x/r secØ = r/x remember : r^2 = x^2 + y^2 = (-5)^2 + 5^2 = 50 r = 5√2 secØ = 5√2/-5 = -√2
September 3, 2015

Math
just use your decimal let x = .232323... 100x = 23.232323... subtract them: 99x = 23 x = 23/99 so 5.2323.... = 5 23/99 or 518/99 check with your calculator to verify it to be correct.
September 3, 2015

Alg 2
You did not indicate what your choices are
September 3, 2015

algebra 2
ahhh, so you mean 2|3x-5| - 8 = 8 then 2|3x-5) = 16 |3x-5| = 8 3x-5 = 8 or -3x+5 = 8 3x = 13 or -3x = 3 x = 13/3 or x = -1
September 3, 2015

Mat
210= 3*7*2*5
September 3, 2015

Math
list them, then add them up
September 3, 2015

Math
follow my previous solution, except we cannot start with a 0
September 3, 2015

Math
possible numbers: single digits: 1 2 3 double digits 12 13 23 21 31 32 triple digits: 123 132 213 231 312 321 Can you add them up ?
September 3, 2015

Math
I will assume that the interest is 7.5% per annum compounded quarterly. (The interest period must coincide with the payment period for our formula to work) i = .075/4 = .01875 n = 20 payment = p p(1 - 1.01875^-20)/.01875 = 38000 I get p = 2296.02
September 3, 2015

raj english school
one rotation covers 63π cm so 200 rotations will cover .... ?
September 3, 2015

Geometry
I meant to say: in a vertical line (early morning senior moment)
September 3, 2015

Geometry
radius = 3 (easy to see since the given point and the centre lie in a horizontal line) C = 2πr = 6π units
September 3, 2015

math
no, you multiplied instead of dividing 15 - 2 1/3 = 12 2/3, (you had 12 3/4) "He cut the remaining cloth into equal pieces" -- assuming you meant 2 equal pieces , it should have said that. There could have been 3 equal pieces, or 45 equal pieces , or .... 12 2/3 &...
September 3, 2015

typo - Math
oops, 1/5 hr = 12 minutes, not 20 minutes so 1 hour, 12 minutes
September 2, 2015

Math
mechanic' rate --- 1/2 assistant's rate --- 1/3 combined rate = 1/2 + 1/3 = 5/6 time at combined rate = 1/(5/6) = 6/5 hrs or 1 hour 20 minutes
September 2, 2015

math
Your period is not correct If the temp is 36° at 4:00am and 56° at 4:00pm you only have 1/2 a period. Doesn't the temperature have to come back down at 4:00am so you should have 2π/24 or π/12 so try: Temp = -10 cos (πt/24) + 46
September 2, 2015

math! please help!
This looks almost identical to the one I answered here http://www.jiskha.com/display.cgi?id=1359417542
September 2, 2015

Math
I assume that x ---> 1 Use Hopital's Rule = limit 500x^499/1 = 500(1) = 500
September 2, 2015

Maths
rigorous method: 1/9 = 20/180 3/2 = 270/180 4/5 = 144/180 19/20 = 171/180 , 180 being the LCD so what do you think? (of course the answer was obvious, since 3/2 is the only fraction greater than 1)
September 2, 2015

MATH
2^8 x 16^3 x 64 = 256 x 4^6 x 4^3 = 4^4 x 4^6 x 4^3 = 4^13
September 2, 2015

MATH
= (1/x)^-1 = x
September 2, 2015

MATH
taking your typing at face-value, since you have no brackets N = a-b^a - b, for the given values = 2 - 2^2 - 2 = 2 - 4 - 2 = -4
September 2, 2015

math
looks like you are multiplying a term by 2 to get the next one, so .....
September 1, 2015

Math
12 = 4*3 16 = 4*4 20 = 4*5 24 = 4*6 = 4*2*3 perfect squares come in pairs of equal factors so we need 4*4*25*9 = 3600
August 31, 2015

Math
looks to me like n^2 - 6 = 5770 n^2 = 5776 n = √5776 = 76 76 rows
August 31, 2015

Math, trigonometry
did you make your sketch ? looks like tan 4.25° = 47/x x = 47/tan4.25° calculator time ...
August 31, 2015

additional maths
I don't know if you are the same person, but this question is a cut-and-past of http://www.jiskha.com/display.cgi?id=1422453360 areas are measured in cm^2 , not cm^3 I cannot understand 2 cm2 ´ s -1
August 30, 2015

Math
for each rotation, the wheel travels the circumference of the circle, so find the circumference of the circle for the distance of one rotation, and ... - how many rotations do you have ?
August 30, 2015

Maths
The model had measurement of 4/25 m by 6/25m = .16 m by .24 m = 16 cm by 24 cm area = (16)(24) cm^2 = 384 cm^2 or area of actual room = 400 cm by 600 cm area = 240000 cm^2 but areas are proportional to the square of the sides, so divide by 25^2 or 625 to get 384 cm^2
August 30, 2015

Math
first of all, I am sure you meant y=1/2x-2 Secondly, is it y=(1/2)x-2 ? , the way you typed it or y=1/(2x)-2 ? or y=1/(2x-2) ? See how critical those brackets are ?
August 30, 2015

equation
You must be referring to the 2nd term of (3^-x)^4 + (3^-x)^-3 = 81 notice in the previous line it was 3^(3x) which is (3^x)^3 or (3^(-x))^-3 Steve substituted 3^x, I substituted 3^-x, our equations reflect that No, logs will not work here, since you have to take the log of a ...
August 30, 2015

equation
I did similar what Steve did, and agree with him Steve asked you to improve your typing of the equation, but this does not change things. I will assume you meant: 9^(-2x) + 3^(3x) = 81 which becomes 3^(-4x) + 3^(3x) = 81 (3^-x)^4 + (3^-x)^-3 = 81 let 3^-x = t so we have: t^4+ ...
August 30, 2015

Trigonometry/ please help!
oops, forgot the 7, thanks Steve
August 29, 2015

Trigonometry/ please help!
you are right, S = 4 cos (πt/2) does not pass through the origin. Perhaps you meant, where does it cross the t - axis? in that case 4cos(πt/2) = 0 we know cos(π/2) = 0 so πt/2 = π/2 t = 1 or t = -1 we also know that the period of your function is 2&#...
August 29, 2015

Calculus
looks good to me http://www.wolframalpha.com/input/?i=plot+y+%3D+xsecx%2C+y+%3D+%28%CF%80%E2%88%9A2%2F4+%2B+%E2%88%9A2%29x+%2B+%CF%80%E2%88%9A2%2F4+-+%28%CF%80%E2%88%9A2%2F4+%2B+%E2%88%9A2%29%28%CF%80%2F4%29
August 29, 2015

Calculus
y = x secx , point is (π/4 , π√2/4) dy/dx = x secx tanx + secx = secx(x tanx + 1) so at the given point: slope = √2( (π/4)(1) + 1) = π√2/4 + √2 so using y = mx + b π√2/4 = (π√2/4 + √2)(π/4) + b solve ...
August 29, 2015

alegbra 2
from first principles, the directrix is y = 7 let P(x,y) be any point then PF = PD, where D is the vertical distance from P to the directrix √( (x-6)^2 + (y-1)^2 ) = √(x-x)^2 + (y-7)^2 ) square and expand x^2 - 12x + 4 + y^2 - 2y + 1 = y^2 - 14y + 49 x^2 - 12x - 44...
August 29, 2015

Calculus
y = √x (x^3 + 1) dy/dx = x(1/2) (3x^2) + (1/2)x^(-1/2) (x^3 + 1) = (1/2)(x^(-1/2)) (6x^3 + x^3 + 1) = (7x^3 + 1)/(2√x) you are correct, but you need brackets around the denominator, or else it is only divided by 2
August 29, 2015

Math
One mile = 5280 ft = 5280(12) inches each rotation of the smaller wheel = 32π inches number of rotations = 4264.5(5280)(12)/32π = appr 2,687,716 each rotation of the larger wheel = 54π inches number of rotations = 4264.5(5280)(12)/(54π) = appr 1,592,721 ...
August 29, 2015

Math
I agree with your method and with your answer
August 29, 2015

math
look at all the variations of your question in the Related Questions below
August 29, 2015

math
amount added ..... x L solve for x, .6(80) + 0.0x = .5(80+x) 48 = 40 + .5x x = 16
August 29, 2015

maths
missing information
August 29, 2015

algebra
I will assume that letters can be repeated. So for your first letter you can only choose from 3 letters. Number = 3x26x26 = ....
August 28, 2015

calculus
SA = 4πr^2 d(SA)/dt = 8πr dr/dt subbing in our values d(SA)/dt = 8π(3)(-2) = -48π you differentiated volume, it asked to find the rate of change of the surface area. So you need to differentiate surface area
August 28, 2015

Math
The odds of rolling two dice for a sum greater than 9 are 6:30, or 1 : 5 so the probability of greater than 9 is 1/6 The probability of less than or equal to 9 is 5/6 Make sure to understand that "odds" and "probability" are not the same thing. I don't ...
August 28, 2015

Math
The concept of odds is slightly different from probablity the odds in favour of some event = prob of the event happening : prob of the event NOT happening so, prob of direct hit = .2 prob of no direct hit = .8 odds in favour of no direct hit = .8 : .2 = 8:2 = 4 : 1
August 28, 2015

Math
I will assume you meant: (x^2-y^2)/(x-y)^2 , those brackets are important = (x+y)(x-y)/(x-y)^2 = (x+y)/(x-y) , x≠y
August 28, 2015

Pre-algebra
Irrational means "not a ratio" or not a fraction. the fact that you wrote it as 7/8 , .......
August 27, 2015

Math
I will assume that point C is supposed to be on the curve y = x^2 and that point (1,1) stays constant. label the points: A(1,1), B(0,b) and C(c,c^2) , since y = x^2 slope of AB = (b-1)/-1 or 1 - b slope of AC = slope of AB = (c^2 - 1)/(c-1) then (c^2 - 1)/(c-1) = 1-b c^2 - 1...
August 27, 2015

pre-calculus
the 15 would be the number of units of height he would climb every minute You don't say what units, but I would assume h(t) is in metres. the graph would be increasing, that is, it would rise to the right. h(1000) makes no physical sense even though you get a mathematical ...
August 27, 2015

Math
let the distance be d km time on first trip = d/320 time on return trip = d/480 d/320 + d/480 = 5 the LCD is 960 3d/960 + 2d/960 = 5 5d/960 = 5 d/960 = 1 d = 960 (in Montreal they would use km and km/h, not miles and mph)
August 27, 2015

ALBEBRA
simplest way to explain: the mosaic is 3 ft by 5 ft or 36 inches by 60 inches for a total area of 2160 square inches each time covers 6x12 or 72 square inches number of tiles = 2160/72 = 30 tiles or since the length is 60 inches, we can stand 10 tiles in the first row. it is ...
August 27, 2015

Math
the outcomes you want are (3,6) or (6,3) there are 36 possible outcomes, so the prob(of your event) = 2/36 = 1/18
August 27, 2015

calculus
amount = c (2^(t/10)), where t is in minutes and c is the initial amount so when covered by 50% .... .5 = 1 (2^(t/10) take log of both sides log .5 = log 2^(t/10) log .5 = (t/10)log 2 t/10 = log .5/log2 = -1 t = -10 So it was covered to 50% 10 minutes ago, or at 11:50 am when ...
August 27, 2015

Algebra
rate of old pump = tank/7 rate of new pump = tank/5 combined rate = tank/7 + tank/5 = (5tank + 7tank)/35 = 12tank/35 combined time = tank/(12tank/35) = 35/12 = 2 11/12 hours = 2hours and 55 minutes
August 27, 2015

math
If you entered it the way you typed it above, I noticed you left out the variable for time it should be y = -1020/7 x + 1020 or try : y = (-1020/7)x + 1020 checking, for now, x = 0, x = 0 + 1020 = 1020, checks! for 7 years from now, x = 7 y = (-1020/7)(7) + 1020 = 0 , checks!
August 27, 2015

Geometry
multiply each term by 3 3by + 2 = 3c 3by = 3c - 2 divide both sides by 3b y = (3c-2)/(3b)
August 27, 2015

Algebra
you did not finish at the end 3x(x^2-9y^2/(3x(4x+12y)) is correct, notice the brackets at the denominator = 3x(x-3y)(x+3y)/((3x)(4)(x+3y)) = (x-3y)/4 , x ≠ 3y looks like choice #1, if you had included the brackets
August 27, 2015

math
we know that 2lw + 2lh + 2wh = 184 or their hint: lw + lh + wh = 92 there would be an infinite number of solutions, e.g. let w = 4, l = 8, then 4(8) + 8h + 4h = 92 12h = 60 h = 5 so length = 8, width = 4, and height = 5 check: 4*8 + 4*5 + 8*5 = 92 let w = 1, h = 6 l + 6l + 6...
August 27, 2015

equation on tangent of a curve need help
In x^2.y^3+y^2.x^4+4x^2-14=0 I will assume you are using the "." as a multiplication symbol Usually we use the * symbol x^2(3y^2)dy/dx + y^3(2x) + y^2(4x^3) + x^4(2y)dy/dx + 8x = 0 dy/dx(3x^2 y^2 + 2x^4 y) = -2x y^3 - 4x^3 y^2 -8x dy/dx = (-2x y^3 - 4x^3 y^2 - 8x)/(...
August 27, 2015

math analysis
Just like in numerical fractions, you will need a common denominator , which would be (x-5)(x-3) so we get ( (x+3)(x-3) + 5(x-5) )/((x-5)(x-3)) = (x^2 - 9 + 5x - 25)/(x^2 -8x + 15) = (x^2 + 5x - 34)/(x^2 - 8x + 15)
August 24, 2015

Maths
s + r = 494 ---> s = 494-r (3/5)r/(s-57) = 2/3 9r/5 = 2s - 114 use substitution 9r/5 = 988 - 2r - 114 9r/5 = 874 - 2r times 5 9r = 437 - 10r r = 230 s = 264
August 21, 2015

Math
why not just take the √ of both sides as it stands (x-2)^2 = 49 x-2 = ± 7 x = 2 ± 7 = 9 or -5 you had x^2 - 4x - 45 = 0 which would have factored to (x-9)(x+5) = 0 x = 0 or x = -5
August 12, 2015

Calculus
draw a right-angled triangle (side view) mark the base as 80, and the height of the balloon as h a) you want to know how fast the balloon is receding, so we are talking about how fast the hypotenuse is changing. let the hypo be x x^2 = 80^2 + h^2 2x dx/dt = 0 + 2h dh/dt, but ...
August 12, 2015

Calculus
http://www.jiskha.com/display.cgi?id=1439263714
August 12, 2015

algebra 2
I find that changing everything to sines and cosines usually works well for these type of problems unless you recognize one of the standard formulas. LS = sin^2 x (1 + cos^2 x/sin^2 x) = sin^2 x (sin^2 x + cos^2 x)/sin^2 x , forming a common denominator = sin^2 x (1/sin^2 x...
August 11, 2015

@ Steve - Math
I ain't touching that one :)
August 11, 2015

Maths
Make a sketch. the line from the centre hits the chord at its midpoint and you have a right-angled triangle. You can use Pythagoras. r^2 = 3.3^2 + 5.6^2 = 42.25 r = √42.25 = 6.5
August 11, 2015

math
The way your question is worded makes no sense You must have meant this: done by Steve last year http://www.jiskha.com/display.cgi?id=1397894767
August 11, 2015

eua high school
surface area of a graph???
August 11, 2015

Calculus
done, look at your previous post
August 11, 2015

calculus
to be at rest, v = 0 4t^2 - 1 = 0 4t^2 = 1 t^2 = 1/4 t = 1/2 let the displacement be s s = (4/3)t^3 - t + c assume that when t = 0 , s=0 , then c =0 s= (4/3)t^2 - t when t = 1/2 s = (4/3)(1/4) - 1/2 = 1/3 - 1/2 = -1/6 the object is 1/6 m to the "left" of O
August 11, 2015

Calculus
y = 1 - cos^2 x y = 1 - (cos x)^2 dy/dx = -2cosx (-sinx) = 2 sinx cosx or sin (2x)
August 11, 2015

yale high school
your number when divided by 4 leaves a remainder of 3 when divided by divided by 5, leaves a remainder of 2 numbers which fit the first case: 7 11 15 19 23 27 31 35 39 numbers which fit the 2nd case: 7 12 17 22 27 the least number would be 7, but I have a feeling they are ...
August 11, 2015

math
your equation factors to (w-4)(2w + 13) = 0 so w = 4 or w = -13/2, which makes no sense so the width is 4 and the length is 2(4) + 5 or 13
August 11, 2015

please help urgent
For your second, the 15-year plan i = .0775/12 = .00645833.. n = 15(12) = 180 p( 1 - 1.00645833^-180)/.006458333 = 300000 I got p = 2823.83 you had the same, good job As to your last question, you cannot just add up the payments. e.g. a payment of $500 made today does not have...
August 10, 2015

please help urgent
I will do the first, you do the 2nd i = .085/12 = .00708333.. n = 30(12) = 360 payment = p PV = p(1 - (1+i)^-n)/i 300000 = p(1 - 1.00708333^-360)/.007083333) 300000 = p(130.0536..) p= 2306.74
August 10, 2015

Maths
I don't know your notation of 100/-
August 10, 2015

Urgent math
This is an arithmetic series where a = 40000 , d=1900 you want sum(10) sum(10) = (10/2)(2(40000) + 9(1900)) = 485500 What you found is how much he made in the 11th year.
August 10, 2015

Calculus
make a sketch let the distance of the man from the lamp-post be x let the length of his shadow be y by ratios: 5.5/y = 10/(x+y) 5.5x + 5.5y = 10y 5.5x = 4.5y times 10 55x = 45y 11x = 9y 11 dx/dt = 9 dy/dt 11(8) = 9 dy/dt dy/dt = 88/9 ft/s or 9 7/9 ft/s --> rate at which the...
August 10, 2015

Math
Did you post this question under the name of Fay? http://www.jiskha.com/display.cgi?id=1439188422 a(1) = 1 a(2) = 3 a(1) + 6 = 3(1) + 6 = 9 a(3) = 3 a(2) + 6 = 3(9) + 6 = 33 a(4) = 3 a(3) + 6 = 3(33) + 6 = 105 a(5) = 3 a(4) + 6 = 3(105) + 6 = 321
August 10, 2015

Calculus
What about it ?
August 10, 2015

Math
It should be clear to you that the 37.313 is the number of quarter years, and if I divide that by 4 I would get years 37.313../4 = 9.33 years rounded to 2 decimal places
August 10, 2015

Math
i = .075/4 = .01875 1. n = 4(3) = 12 amount = 3000(1.01875)^12 = 3749.15 2. 3000(1.01875)^n = 6000 , where n is the number of quarter years 1.01875^n = 2 take logs of both sides and use use of logs n log 1.01875 = log 2 n = log 2/log 1.01875 = appr 37.313 = 37.313../4 or appr ...
August 10, 2015

Algebra
7% = .07 , not .7 like you had That was your major mistake. a) equation: n(t) = 1900 e^(.07t) b) if 2005 ---> t = 0 then 2010 ---> t = 5 n(5) = 19000 e^(.07*5) = 26962 I don't understand how you could possible think that 5 foxes would be correct. there were 19000 ...
August 10, 2015

logarithms maths
Nothing to solve, I don't see an equation Are you simplifying? Do you mean log x + log(x+n) - log(x/n) ??? Do you know your basic rules of logs ? if so, then log x + log(x+n) - log(x/n) = log( x(x+n)) - (logx - logn) = log( x(x+n) - logx + logn = log( x(x+n)(n)/x) = log( n...
August 10, 2015

Math sequences
you have a geometric series with a = 1 and r = 4/5 sum(n) = a(1 - r^n)/(1-r) > 4.9 1(1 - (4/5)^n)/1/5 > 4.9 1 - (4/5)^n > .98 (4/5)^n < .02 suppose we let .8^n = .02 log .8^n = log .02 n = log.02/log.8 = 17.53 testing: if n = 17 , sum(17) = (1 - .8^17)/.2 = 4.8874...
August 10, 2015

statistics and probability
-2(y-3)= 5y-29 -2y + 6 = 5y - 29 -7y = -35 y = 5
August 10, 2015

a math
For this to work you must mean (cotx-1)/(cotx+1) = sec(2x) - tan(2x) LS = (cosx/sinx - 1)/(cosx/sinx +1) multiply top and bottom by sinx = (cosx - sinx)/(cosx + sinx) RS = 1/cos(2x) - sin(2x)/cos(2x) = (1 - 2sinxcosx)/(cos^2 x - sin^2 x) = (sin^2 x + cos^2 x - 2sinxcosx)/((...
August 10, 2015

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