Sunday
May 1, 2016

Posts by Reiny

Total # Posts: 34,401

math - surface area and volume
volume of sphere = (4/3)πr^3 = (4/3)π(9^3) = 972π cm^3 Increase in water volume = 972π radius of cylinder = 7.5 so π(7.5)^2 h = 972π 56.25h = 972 h = 17.28 cm So the water will rise 17.28 cm check my arithmetic
January 31, 2016

surface area and volume
surface area of similar objects varies directly with the square of their corresponding sides ratio of surface areas = 5^2 : 4^2 = 25 : 16
January 31, 2016

Calculus and Vectors
We don't just do your homework or assignment for you. You have posted 4 max/min problems without showing any steps or work or indicating where you difficulties lie. I have done two of them for you. Please show some work or steps before I do any more of them
January 31, 2016

Algebra
Proof-read you post and correct your wording so it can be understood.
January 31, 2016

Calculus and Vectors
let the radius of the can be r cm and its height be h cm given: πr^2 h = 1000 h = 1000/(πr^2) cost = .002(top+bottom) + .001(sleeve) = .002(2πr^2) + .001(2πrh) = .004πr^2 + .002πr(1000/πr^2 ) = .004πr^2 + .002(1000/r) = .002 [2πr^2...
January 31, 2016

Calculus and Vectors
let the width of the whole thing be x m and let the length be y m your sketch should show 3 widths and 2 lengths where 3x + 2y = 54 y = (54-3x)/2 = 27 - (3/2)x area = xy x(27 - (3/2)x) = 27x - (3/2)x^2 d(area)/dx = 27 - 3x = 0 for a max/min of area 3x = 27 x = 9 y = (54-27)/2...
January 31, 2016

Calculus
ln((3x-2)/(x-1))<0 using basic definition of logs .... ln(3x-2) - ln(x-1) < 0 by definition: x > 2/3 and x> 1 so x > 1 , before we even proceed further. but bob found that if we leave it as ln((3x-2)/(x-1)) < 0 we do get a solution of x < 1/2 thus x < 1...
January 31, 2016

solid mensuration
let the height be h √(4^2 + 3^2 + h^2) = √41 square both sides 16 + 9 + h^2 = 41 h^2 = 16 h = 4 volume = length x width x height = .....
January 31, 2016

Maths
number of boys --- 4x number of girls --- 3x given: 4x = 12 x = 3 number of girls = 3x = 9 or , by simple ratio 4/3 = 12/girls 4girls = 36 girls = 9
January 31, 2016

Maths
The way you typed it makes no sense. Did you mean he biked 66 km in 5 hrs ? I will assume that. distance covered at 12 km/h = 12x km distance covered at 16 km/h = 16y km 12x + 16y = 66 6x + 8y = 33 x + y = 5 y = 5-x plug this into the other equation: 6x + 8(5-x) = 33 6x + 40...
January 31, 2016

maths
tens digit --- x unit digit ---- 2x the actual number = 10x + 2x = 12x the number reversed = 10(2x) + x = 21x 12x + 21x = 99 33x = 99 x = 3 the original number was 63
January 31, 2016

maths. It's urgent
The graph of x^y + y^x =30 looks something like this http://www.wolframalpha.com/input/?i=plot+x%5Ey%2By%5Ex%3D30 is there an x-intercept? let y = 0 to get x^0 + 0^x = 30 1 + 0^x = 30 1 + 0 = 30 , false, there is no x-intercept same reason ---> no y-intercept but x+y = 15, ...
January 31, 2016

number pattern
term6 = ar^5 = -243 term3 = ar^2 = 72 divide: r^3 = -243/72 = -27/8 take cube root r = -3/2
January 31, 2016

algebra
use the rules of logs 2logx + log4 = 2 log(x^2) + log4 = 2 log (4x^2) = 2 4x^2 = 10^2 4x^2 = 100 x^2 = 25 x = ± 5, but we cannot take log(-5) so x = 5 test my answer with your calculator
January 30, 2016

Mathematics
1. x^3 - 16x ≤ 0 x(x^2 - 16) ≤ 0 x(x-4)(x+4) ≤ 0 critical values are -4, 0, 4 making a quick sketch of y = x^3 - 16x shows a standard cubic with x-intercepts of 0, ± 4 Where is the curve below the x-axis ? x ≤ -4 or 0 ≤ x ≤ 4 2. (5x/x...
January 30, 2016

Math
a reflection in the y-axis leaves the y's along but changes the x's to their opposites so P(2,-4) ---> P' (-2 , -4) repeat for the other points, then choose your answer
January 30, 2016

math ratios help but explain
I assume these two ratios are supposed to be the same. x:4 = 45:20 x/4 =45/20 times 4 x = 4(45/20) = 9
January 30, 2016

algebra
technicality here from (x+1)^2 we have (x+1)(x+1) so x = -1 or x = -1 same root shows up twice, so they call it a multiplicity of 2 your zeros are correct
January 30, 2016

math
or (4x - 1)(3x - 5) looks "nicer"
January 30, 2016

math
a+b-bc-ac = a - ac + b - bc = a(1 - c) + b(1 - c) = (a+b)(1-c) looks prettier
January 30, 2016

Math
1p + 2s + 2d - 2 = 21.08 but p = 11.7 and s = 11.7/3= 3.90 11.7 + 2(3.9) + 2 d - 2 = 21.08 solve for d, the cost of a drink
January 30, 2016

Math
i = .125/12 = .01041666.. balance after 1 month before payment = 7500(1.01041666.) payment = .05 of balance balance at end of month 1 = 7500(.95)(1.0104166) balance after month 2 before payment = 7500(.95)(1.0104166)^2 payment = .05 of that balance balance at end of month 2 = ...
January 30, 2016

math- HELP!
btw, The Fibonacci sequence was first NOT discovered during a study of rabbits.
January 30, 2016

math
Sum(33) = 6Sum(13) (33/2)(2a + 32d) = 6(13/2)(2a + 12d) but a = 2 33(4 + 32d) = 78(4 + 12d) sove for d
January 30, 2016

College Algebra
x^4-9x^2+20=0 (x^2 - 4)(x^2 - 5) = 0 x^2 = 4 or x^2 = 5 x = ± 2 or x = ± √5 All 4 roots are real, no complex roots
January 30, 2016

math
let B's amount be 6x let C's amount be 11x then A's amount = (3/5)(6x) = 18x/5 6x + 11x + 18x/5 = 1545 continue .....
January 30, 2016

math
Are we supposed to decipher what all that is ? Math is a precise language, and as such needs proper statements and presentation. Sample: let the width be x cm then the length is x+8 cm original area = x(x+8) cm^2 new width = 3x cm new length = x+8 - 9 = x-1 cm new area = 3x(x-...
January 30, 2016

mathematics
change the ratios to more manageable numbers 1/3 : 1/4 : 1/5 = 20 : 15 : 12 = 20x : 15x : 12x so 20x + 15x + 12x = 94 take over ...
January 30, 2016

math
Define the areas as 5x, 6x, and 8x respectively . given: flatC - flatA = 270 8x - 5x = 270 carry on ...
January 30, 2016

math
your last term is not clear is 1/12/16 = 1/(12/16) or = (1/12)/16 they are not the same we generally avoid writing fractions in such triple-decker form
January 30, 2016

math
What is 7(1.88) ?? $1.88 a gallon ? Time to get an up-to-date textbook
January 30, 2016

Mathematics
I will rename them as a , ar, and ar^2 given: ar = a+4 ar^2 = ar+9 ar^2 = a+4 + 9 = a + 13 but we also know that ar^2/ar = ar/a using the property of common ratio (a+13)/(a+4) = (a+4)/a a^2 + 13a = a^2 + 8a + 16 5a = 16 a = 16/5 common ratio = ar/a = (a+4)/a = (16/5 + 4)/(16/5...
January 30, 2016

trigonometry
Purists will argue that to prove the validity of an identity, that is, prove that the equation is true, by using the rules of equations itself is not valid.
January 30, 2016

trigonometry
I usually start these with changing everything to sines and cosines after I test them with some angle that I pick #1. The question should say: 1/(secx - tanx) = secx + tanx Those brackets are critical, the way you typed it, will not work LS = 1/(1/cosx - sinx/cosx) = 1/((1- ...
January 30, 2016

math
So if the content changed from 6/8 full to 3/8, the water was poured out not poured in. So the change is 3/8 of the capacity let that capacity be x litres (3/8)x = 3 x = 3(8/3) = 8 litres so 5 litres will be needed to make the jar full. btw, "how much liter will be needed...
January 30, 2016

algebra
let the unit digit be x let the tens digit be 4x original number: 10(4x) + x = 41x number reversed: 10x + 4x = 14x 41x + 14x = 110 55x = 110 x = 2 the original number is 84 try switching my definition and see what you get
January 30, 2016

grade 12 math
would 4 letters be enough? 26^4 = 459976 , no how about 5 letters ? 26^5 = 11,881,376 , not enough 26^6 = 308,915,776 That will do it. The string must be 6 letters long
January 29, 2016

Calc 1 limits
Look at your first post of this question. since we cannot extend the √ sign, we have to use brackets to show the end of the square root. e.g. is it t√(1+t) ???
January 29, 2016

Calc 1
I am going to go out on a limb and guess that you meant: lim ( √(1+t) - √(1-t) )/t , as t --->0 noting to factor here, you have to rationalize the numerator = lim ( √(1+t) - √(1-t) )/t * (√(1+t) + √(1-t))/(√(1+t) + √(1-t)) = ...
January 29, 2016

Math
you have the division backwards. you have 4 pizzas to be shared by 6 people so 4/6 or 2/3 of a pizza each check: what is 6 times 2/3 ?
January 29, 2016

Limits calc 1
OK THEN let's add up 1/( t√(1+t) - 1/t = (1 - √(1+t)/(t√(1+t) = (1 - √(1+t)/(t√(1+t) * (1 + √(1+t) / (1 + √(1+t) = (1 - 1 - t)/(t√(1+t)((1 + √(1+t) ) = -t/(t√(1+t)((1 + √(1+t) ) = -1/(√(1+t)((1 + &#...
January 29, 2016

Limits calc 1
Still not clear enough if it would be t√1 + t why would they put in that √1 ? it would simply become t(1) + t or 2t is it t√(1+t) ? there is a monumental difference should I guess at Limit (1/( t√(1+t) - 1/t ) , as x ---> 0 ???
January 29, 2016

Limits calc 1
Hard to make out what you mean without brackets for the denominators the way you typed it.... 1/t√1 is just 1/t, remember terms are separated by addition or subtraction so you simply have 1/t + t - 1/t = t I am sure that is not you meant.
January 29, 2016

Math
-15x+3 ≤ -3(4x-7) -15x + 3 ≤ -12x + 21 -3x ≤ 18 x ≥ -6
January 29, 2016

Math
-40 - (-55) = 15 yes
January 29, 2016

Math
cost = x -2 + 25 - 43 cost = x -20
January 29, 2016

geometry
I assume you mean that the dimensions are increased by 75% 2 inch --->2(1.75) = 3.5 3 inch ---> 3(1.75) = 5.25 your choice would have decreased the photo
January 29, 2016

Math, pre-algebra
since V = length(width)(height) 6x^3 - x^2 - 2x must be the product of 3 factors. the first one is obvious, a common factor of x = x(6x^2 - x - 2) and the quadratiac factors to ((2x+1)(3x-2) so which one fits ?
January 29, 2016

Math-fractions
No units were given for the 5/8 a book 5/8 of a foot wide is not very logical, so were the books only 5/8 inches? pretty skinny books. anyway 3 1/2 ft = 42 inches number of books = 42 ÷ 5/8 = 42(8/5) = 67.2 books ??? was expecting a whole number. Check your question.
January 29, 2016

math
franks rate = 1/3 Hanks rate = 1/x combined rate = 1/3 + 1/x = (x+3)/(3x) 1/( (x+3)/(3x) ) = 1 3x/(x+3) = 1 3x = x + 3 2x = 3 x = 1.5 It would take him 1.5 hours
January 29, 2016

Math
I will assume you have a typo in the last equation, and that 2c is 2z double the first: 4x + 4y + 2z = -10 ----> * subtract the end: x = -10 , well , that was lucky 4x + 4y + 2z = -10 x + 3y + 2c = 1 subtract them: 3x + y = -11 sub in x = -10 -30 + y = -11 y = 19 back in ...
January 29, 2016

Math
Use the rules of logs ln 5 + ln (2x) = 5 ln(5(2x)) = 5 ln (10x) = 5 10x = e^5 x = (1/10)e^5 = appr 14.84
January 29, 2016

MATHS
Of course ..... please ignore my reply, looks like I had a senior moment.
January 29, 2016

MATHS
number of hundreds --- h number of tens ------ t h = 6t 100h + 10t = 2440 100h + 60t = 2440 160t = 2440 t = 15.25 ----> not possible Your data is inconsistent.
January 29, 2016

Math
prob(3 hearts ) = C(13,3)/C(52/3) = 286/22100 = 11/850 expectation = (11/850)($50) = $0.647 prob(3 black) = C(26,3)/C(52,3) = 2600/22100 = 2/17 expectation = (2/7)($25) = $2.94 expected return on the game = $3.59 You were right on the $3.60 (difference is roundoff) agree with ...
January 29, 2016

Math
Your E(x) = $12.70 is correct your $1524 is correct I am not familiar with 'standard deviation' in this context
January 29, 2016

Math
We can't see your picture so you will have to describe what DE is
January 29, 2016

Geometry
nope ... distance = √((-2+1)^2 + (1-4)^2 + (3+2)^2 ) = √( 1 + 9 + 25) = √35 = appr 5.92 their choice is 5.9
January 29, 2016

math
Slopes of perpendicular lines are negative reciprocals of each other. One is + , the other is - . Here is a little trick for perpendicular lines If we have some line Ax + By + C = 0 then the line Bx -Ay + k = 0 is perpendicular, that is just switch the coefficients and make ...
January 29, 2016

Calculus
Step 1 in any limit question is to actually sub in the approach value into the expression. If you get 0/0 , you got some work ahead of you If you get (non-zero)/0 , there is no limit If you get a real number, that's it, you are done, that is your answer. So, let's try ...
January 29, 2016

Math
Even not remembering my physics, we can form the equation, since the relationship is given.. R = k L/d^2 25 = k(30)/.75^2 25 = k(30)(16/9) k = 9(25)/((16)(30)) = 15/32 R = (15/32)L/d^2 plug in the 2nd set of numbers 30 = (15/32) L /1.25^2 finish it up by solving for L
January 29, 2016

Pre Algebra
slope = rise/run depends how that information is given in the question.
January 29, 2016

Math
to be an AS, 5p+12 - (7p+2) = 2p-1 - (5p+12) solve for p
January 29, 2016

maths
volume of sphere = (4/3)π5^3 = 500π/3 cm^3 volume of water in tank = (50)(20)(10) cm^3 = 10,000 cm^3 surface area of half the sphere = (1/2)(4π(5^2)) = 50π cm^2 This question does not look complete. It has so much more potential than these 3 straightforward...
January 29, 2016

Pre-Cal
what are doing ? Solving? I see a common factor cosx(sin^2 x + 4sinx + 3) = 0 now I see a trinomial that factors cosx(sinx + 3)(sinx + 1) = 0 cosx = 0 ----> x = π/2, 3π/2 sinx = -3 ----> not possible sinx = -1 ----> x = 3π/2 in degrees: x = 90°, 270...
January 28, 2016

algebra
new length = 140-x new width = 130 - x, just like it said New area = (140-x)(130-x) expand, collect like terms
January 28, 2016

Pre-calculus
Just translate the English into Math ... " the distance a spring will stretch ...varies directly with the force applied to the spring" ---> d = k(1/F) , where d is the distance, and F is the force use the given: d= 9, F = 12 9 = k(1/12) k = 108 thus d = 108/F now ...
January 28, 2016

Calculus
dy/dx = 4x^3 plug in x = 4
January 28, 2016

Math
1*10^-17 ÷ (8*10^-15) = (1/8)*10^-2 = .125 * 10^-2 ---> recognize 1/8 = .125 = 1.25*10^-3
January 28, 2016

geometry
the sum of the two smaller sides must be greater than the largest side to have a triangle so if we cut off x units from each stick 8-x + 15-x = 17-x -x = -6 x = 6 so if we cut off 6 inches, our sticks will form a straight line, so we can cut off 5 inches from each and still ...
January 28, 2016

Math
(4(88) + x)/5 = 90 352 + x = 450 x = 98
January 28, 2016

Math
Make a sketch, so the two squares must be 6by6 each and the rectangle must be 3by6 Wouldn't we just need 2 divisions of 6 m each? or 12 m ? Am I missing something here ?
January 28, 2016

further math
did you mean f(x) = 3 and g(x) = 3x-2 ? then fog = f(g(x)) = f(3x-2) , but f(anything) = 3 = 3
January 28, 2016

MATH
In that case they are wrong 9 – 5(4 – 2) / 3 + 5 ----> https://www.google.ca/?gws_rd=ssl#q=9+%E2%80%93+5(4+%E2%80%93+2)+%2F+3+%2B+5+ 10.66666.... = 10 2/3 = 32/3 < ------ my answer
January 28, 2016

MATH
#1 9 – 5(4 – 2) / 3 + 5 = 9 - 5(2)/3 + 5 = 9 - 10/3 + 5 = 32/3 none of your choices match this. Check your typing #2 is correct
January 28, 2016

Math (Pease Help! 2 questions!)
Welcome
January 28, 2016

Math (Pease Help! 2 questions!)
in general, the probability of some event = number of times that event can happen/total number of possible outcomes so ... you have 2 white and 7 purple prob of purple = 7/9 then prob of white = 2/8 , there are only 8 left since you drew one already. prob(purple, then white...
January 28, 2016

Math
solve the simple proportion 5/4 = h/10
January 28, 2016

Math
No rate of interest is given, thus the question cannot be answered properly
January 28, 2016

Probability #3
prob(red) = 18/38 = 9/19 expected value = (9/19)($1.00) = $ 0.474 how did you get .421 ? I don't know how standard deviation is defined in this context.
January 28, 2016

Math (can you provide me with the working and ans?
The Change in volume = (28)(18)(5) cm^3 = 2520 cm^3 This was caused by the 12 marbles that volume was 12(4/3)πr^3 = 16πr^3 16πr^3 = 2520 r^3 = 2520/(16π) r = (2520/(16π))^(1/3) I got appr 1.69 cm Avg volume = (4/3)π(1.69)^3 = appr 20.22 cm^3 check...
January 28, 2016

trigonometry
not enough info
January 28, 2016

I tried, I really did - Algebra
Don't know what else I can do http://www.jiskha.com/display.cgi?id=1453947294 just translate into Math smallest angle --- x° "One angle in a triangle has a measure that is three times as large as the smallest angle. " second angle = 3x " the third angle ...
January 27, 2016

math
whole trip ---- x km day1 , hiked 1/8 of train, leaving (7/8)x day 2 , hiked 4/7 of (7/8)x leaving (3/7)(7/8)x or (3/8)x to be hiked day3 : (1/3)(3/8)x + 8 = x x/8 + 8 = x times 8 x + 64 = 8x 7x = 64 the trail is 64/7 km check: day 1 they hiked (1/8)(64/7) leaving (7/8)(64/7...
January 27, 2016

analytic geometry
angle between two lines if we know the slopes, m1 and m2 tanØ = |(m1 - m2)/(1 + m1m2)| where Ø is the acute angle slope of first line = 3/7 slope of 2nd line = -5/3 tanØ = (3/7 + 5/3)/(1 - 5/7) = (44/21) / (-2/7) = -22/3 Ø = 180 - 82.23° = 97.77...
January 27, 2016

Calc 1
(6+h)^3 = 216 + 3(36h) + 3(6h^2) + h^3 = 216 + 108h + 18h^2 + h^3 so Limit ( (6+h)^3-216 )/h , as h ---> 0 = lim ( 216 + 108h + 18h^2 + h^3 - 216)/h = lim (108h + 18h^2 + h^3)/h , as h --> 0 = lim 108 + 18h + h^2 , as h --> 0 = 108 check using Calculus as such ... we ...
January 27, 2016

math
Speed of boat with no current --- x mph speed of current ----- y mph Assuming 16 miles each way, time with the current = 1 hr 16/(x+y) = 1 x+y = 16 ----> #1 time against the current = 9 hrs 16/(x-y) = 9 9x - 9y = 16----> 2 you now have two simple equations in 2 unknowns ...
January 27, 2016

Algebra
I did this for you when you were Seymour http://www.jiskha.com/display.cgi?id=1453950266
January 27, 2016

Math help
I prefer these kind of formula in terms of the radius. V = (4/3)π r^3 = 15000 r^3 = 3(15000)/(4π) = 3580.986.. take cube root of both sides r = 12.299 so the diameter = appr 30.6 ft or using your formula: πD^3/6 = 15000 d^3 = 6(15000)/π = 28647.88976 take ...
January 27, 2016

math
x+y = 30 xy = 176 from the firs: y = 30-x x(30-x) = 176 30x - x^2 - 176 = 0 x^2 - 30x + 176 = 0 hint: it factors, if you can't find the factors, use the quadratic formula.
January 27, 2016

Algebra
If we let the width be x m and the length is 6 m more, wouldn't the length be x+6 m ? remember perimeter is twice the width + twice the length take over.
January 27, 2016

AAMU
time at first speed = 2/8 hrs = 1/4 hrs time at 2nd speed = 2/6 hrs total distance = 4 km total time = 1/4 + 1/3 = 7/12 hrs avg speed = 4/(7/12) km/h = 48/7 km/h or appr 6.86 km/h
January 27, 2016

Algebra
I don't understand your notation. Perhaps it comes out different on your own monitor. Your previous post looks just like that too, you just changed the numbers.
January 27, 2016

@ Seymor - Algebra
The purpose of this website is not to homework or assignments as such. We want the students to make an effort to learn how to do the problems. That is why you will usually see some preliminary steps or ideas shown. You had the same type of question a while back and solved it ...
January 27, 2016

Algebra
just translate into Math smallest angle --- x° "One angle in a triangle has a measure that is three times as large as the smallest angle. " middle angel = 3x " the third angle is 10 degrees more than that of the smallest angle" third angle = x+10 Now ...
January 27, 2016

Algebra
I am puzzled ... http://www.jiskha.com/display.cgi?id=1453944021
January 27, 2016

calc 1
I will do the first one: when t = 2 y = 50(2) - 16(4) = 36 when t = 2.5 y = 50(2.5) - 16(2.5)^2 = 25 velocity = (25 - 36)/(2.5 - 2) = -22 repeat for the others, remember you start with t = 2 and add on the given value so for the next one, t =2 and t = 2.1
January 27, 2016

math
b) 4 mill/30s = 3mill/xs 4 mill/ 3 mill = 30 s/x s 4/3 = 30/x 4x = 90 x = 90/4 = 22.5
January 27, 2016

Limits calc 1
You titled it "Limits" but did not present it as a limit question, I will assume it is. it factors lim (x^2 + 6x + 9)/((x^2 + 9)(x^2 - 9) ) as x ----> ? , you don't say, but I will assume it is x ---> -3 = lim (x + 3)(x+3)/((x^2 + 9)(x+3)(x-3) ) = lim (x + ...
January 27, 2016

math
4(3x-1) = 68 continue ....
January 27, 2016

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