Tuesday
September 30, 2014

Posts by Reiny


Total # Posts: 27,188

math
breadth --- x length ---- 1.2x 2(x+1.2x) = 88 x+1.2x = 44 2.2x = 44 x = 20 area = x(1.2)x = 1.2(20^2) = 480 m^2
July 27, 2014

correction - calculus 2
∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 should be ∆x = (6-1)/10 = 5/3 , so ∆x/3 = 5/30 = 1/6 and the 5/3 in front of the big brackets should be 5/30 or 1/6
July 26, 2014

calculus 2
I assume that you know the formula .... in case you don't, here is the method http://www.mathwords.com/s/simpsons_rule.htm ∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 interval = (6-1)/10 = 1/2 then we have (5/9)[ f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4...
July 26, 2014

calculus 2
fix your equation first
July 26, 2014

math
since the function is linear, the slope must be constant for any pair so (12-a)/(1-0) = (b-12)/(2-1) 12-a = b-12 24 = a+b
July 26, 2014

Math
number of increases of one unit of money (pesos ? or dollars ?) be n price = 10+n number sold = 200-10n revenue = R = (10+n)(200-10n) = 2000 + 100n - 10n^2 completing the square = -10(n^2 - 10n + 25 -25) + 2000 = -10(n-5)^2 + 2250 vertex is (5,2250) price should be 15 max ...
July 26, 2014

math
so -9x^2 + 9x + 5 = 0 9x^2 - 9x - 5 = 0 Don't see any obvious facors, so let's use the formula x (9 ± √261)/18 = appr 1.4 or -.4 looks like d)
July 26, 2014

Calc
let each of the 2 equal sides by x let yeach of the 3 equal sides by y xy = 1,500,000 y = 1500000/x let the length be L L = 2x + 3y = 2x + 4500000/x dL/dx = 2 - 4500000/x^2 = 0 for a min of L 2x^2 = 4500000 x^2 = 2250000 x = 1500 then y = 1500000/1500 =1000 so L = 2(1500) + 3(...
July 25, 2014

math
Since no choice of 3 points forms a straight line, you are simply finding the number of ways to choose 3 of the 5 points, which is C(5,3) or 5!/(3!2!) = 10
July 25, 2014

good observation - Trigonometry
Bosnian, thanks for catching that The question used feet as its units, and I just did the math without really thinking about that height. I think the linear units should have been metres and not feet. Both of our numerical values were correct, you also had 171.7 I recall ...
July 25, 2014

Trigonometry
I use a slightly different method. In my sketch , I labeled the top of the monument P and the bottom Q By properties of the sum of angles in a triangle, in triangle ABP , angle A = 32°, angle ABP = 142, and angle APB = 6° using the Sine Law: BP/sin32 = 55/sin6 BP = ...
July 25, 2014

Math
I made a sketch, letting the top of the building A I drew in the tower, called the top P and the bottom Q I drew a line from A to B, AB parallel to the ground thus QB = 16 , the same height as the building. We now have two right angled triangles, ABP and ABQ in triangle ABQ, ...
July 25, 2014

maths
I know math is heavenly, but triangles have angels ?? If the smallest angle is x, then the largest is 5x If they are in AP, then the middle angle must be 3x (note: 3x - x = 5x - 3x , using the common difference relationship) then x + 3x + 5x = 180 9x = 180 x = 20 the angles ...
July 25, 2014

math
pieces on disc = 3 + 4 + x = x+7 prob of picking one of the 4 ballads = 4/(x+7) but we are told 4/(x+7) = 1/4 x+7 = 16 x = 9
July 24, 2014

Math 221*revised*
This is a poorly worded question. " y=x+4 and the parallel must past through this given point (-7, 1) " y = x+4 does not pass through (-7,1) and you cannot make it do it, unless you change its slope or y-intercept. If you merely want a new line which is parallel to y...
July 24, 2014

MATH
He can use the 2 pennies in 3 ways, take none, take 1 or take 2 He can use the 3 nickels in 4 ways, take none, take 1, etc the dime in 2 ways, and the quarters in 3 ways total number of ways = (3)(4)(2)(3) = 72 but that includes taking none of any coins, so number of ways to ...
July 23, 2014

Math
1. find what percentage of the trip Keith drove, then his wife must have driven the remaining percentage 2. 1.5J = (1/2)K 3J = K divide by K 3J/K = 1 divide by 3 J/K = 1/3 3. with radius r, area = πr^2 reduce radius by 10% ---> new radius = .9r new area = π(.9r)^2...
July 23, 2014

MATH
What choices did you pick? Where are your difficulties? I will do the first one, you try the others If A is 125% of B ----> A = 1.25B B = (1/1.25)A = .8A so B is 80% of A
July 23, 2014

Algebra
When it hits the ground , h(t) = 0 , so -16t^2 + 40t + 5 = 0 16t^2 - 50t - 5 = 0 Now solve this quadratic using the method that you learned. One of the answers will be negative, you would reject that one.
July 23, 2014

math
8 hrs, 15 minutes = 315 minutes total minutes available for the experiments = 8(315) = 2520 minutes 84 experiments take 2520 minutes 1 experiment takes 2520/84 or 30 minutes
July 23, 2014

geometry
areas of similar figures are proportional to the square of their sides area1 : area2 = 3^2 : 9^2 = 9 : 81 = 1 : 9
July 23, 2014

math
You must have meant: area is 2x^3+5x^2-x-6 if so, then it factors nicely into (x-1)(x+2)(2x+3) and the width of 2x^2 + x - 3 factors to (2x+3)(x-1) then (2x^3+5x^2-x-6) ÷ (2x^2+ x-3) = (x-1)(x+2)(2x+3)/( (2x+3)(x-1) ) = x+2 or you could do a long algebraic division as ...
July 23, 2014

algebra 2
Is this supposed to be the solution to finding the inverse of y = 1/3x - 5 ??? I suggest a 2-step process 1. interchange the x and y variables ----> x = 1/3y - 5 (you had that) 2. now solve this new equation for y x = 1/3y - 5 x+5 = 1/3y times 3 3x + 15 = y so f^-1 (x) = 3x...
July 22, 2014

Algebra
what do you think ? I just answered it for you in your previous post
July 22, 2014

Algebra
I would say it is A it simplifies to -x + 3 = 0 , which is linear and not quadratic. If you force the issue and make it look like a quadratic, it would be 0x^2 - x + 3 = 0 so a=0 , b=-1 and c = 0 BUT, in the formula we are dividing by 2a which in this case would be dividing by...
July 22, 2014

math
if AP , then d = 2k/3 - k = 2k/3 - 3k/3 = -k/3 term 6 = a+5d = k + 5(-k/3) = -2k/3
July 22, 2014

Math
2160 = 2*2*2*2*3*3*3*5 1344 = 2*2*2*2*2*2*3*7 1440 = 2*2*2*2*2*3*3*5 HCF = 2*2*2*2*3 = 24 2. let their income be x x/10 + x/3 + x/5 + 1320 = x times 150 , the LCM 15x + 50x + 30x + 198000 = 150x 198000 = 55x x = 3600
July 22, 2014

algebra
(3+2x)^5 = 3^5 + 5(3^4)(2x) + 10(3^3)(2x)^2 + 10(3^2)(2x)^3 + 5(3)(2x)^4 + (2x)^5 =243 + 810x + 1080x^2 + 720x^3 + 240x^4 + 32x^5 by simple observation that a negative base raised to an odd exponent is negative .... (3-2x)^5 = 243 - 810x + 1080x^2 - 720x^3 + 240x^4 - 32x^5 (3+...
July 22, 2014

algebra 2
use your formula for S(n) S(n) = a(r^n - 1)/(r-1) 405 = a(3^4 - 1)/(3-1) 405 = a(81 - 1)/2 405 = 40a a = 405/40 = 81/8
July 22, 2014

math
8+4+2+1+1/2+1/4+...+1/32 = 1/32 + 1/16 + ... + 4 + 8 sum = ∑ 2^(n - 6) for n= 1 to 9
July 22, 2014

math
sum(n) = (n/2)(first + last) sum(11) = (11/2)(1+6) = 77/2
July 22, 2014

math
volume = lwh = 18(3)(1/3) = 18 cubic feet
July 22, 2014

coordinate algebra
I don't see any choices, but it would have to be c = 4h
July 22, 2014

trigonometry
write it as y = -3sec 2(x-π/6) period = 2π/2 = π no vertical translation phase shift π/6 units to the right
July 22, 2014

Maths
a = b+2 c = b-11 )a+b+c)/3 = 70 a+b+c = 210 b+2 + b + b-11 = 210 3b = 219 b = 73 a = 75 c = 62 check: (73+75+62)/3 = 70 all looks good
July 22, 2014

Math
the wonders of Wolfram http://www.wolframalpha.com/input/?i=pattern+%2831%2C30%2C27%2C22%2C15%29 actual work did you notice that consecutive differences are -1, -3, -5, -7 ? this forms an arithmetic sequence, so a quadratic will act as the defining function. let the sequence ...
July 22, 2014

Algebra
e.g. x^2 - 6x = 0 add 9 to both sides x^2 - 6x + 9 = 9 (x-3)^2 = 9 x-3 = ±3 x = 3 ± 3 = 6 or 0 check: by factoring, x(x-6) = 0 x = 0 or x = 6 , as above
July 21, 2014

Algebra
I betcha I can solve any quadratic equation by completing the square.
July 21, 2014

math
#2 number of green = x number of marbles after 5 reds are added = x+5 prob of picking red = 1/7 5/(x+5) = 1/7 x+5 = 35 x = 30 there were 30 marbles
July 21, 2014

math
#1 g/(b+g) = 1/3 3g = b+g b = 2g (g+1)/(b+g+1) = 3/7 7g + 7 = 3b+3g+3 4g - 3b = -4 4g - 6g = -4 g = 2 then b = 4 , which is choice d. #3 1 million is an even number all prime numbers are odd, except the first one, which is 2, thus even so we have the sum of 999,999 odd numbers...
July 21, 2014

math
looks like a typo in both functions. is it f(x) = x+2 or f(x) = -x+2 ? same for the other one.
July 21, 2014

Alegbra
If the expression is as you typed it, then -9x - 13x+7 is indeed equal to -22x + 7 and it is your professor who is in error.
July 21, 2014

Algebra
I will assume you meant to type 9(/x-1)*7/(x-3) which is 63/( (x-1)(x-3) ) or 63/(x^2 - 4x + 3)
July 21, 2014

math
Make a sketch and set up your ratio. I get height/(30+25) = 20/30 height = 55(2/3) =110/3 ft or 36 ft, 8 inches
July 21, 2014

math
dimes in box A originally --- x dimes in box B originally --- y case 1: after 25 moved from A to B box A has x-25 box B has y+25 but x-25 = y+ 25 ----> x = y + 50 case 2: after 100 dimes moved from B to A box A has x+100 box B has y-100 but (x+100)/(y-100) = 7/2 7y - 700 = ...
July 21, 2014

Trigonometry
No need for trig, just use a simple ratio ... height/60 = 5/10 height = 60(1/2) = 30 ft (did you notice the height of the man is 1/2 of his shadow, then the height of the pole must be 1/2 its shadow, or 1/2 of 60, which is 30 )
July 21, 2014

Trigonometry
done, see your other post above
July 21, 2014

statistics
prob defective = .05 prob of good = .95 So we want the prob that all are good = .95^14 = .48776... prob of at least one is defective = 1 - .48776.. = appr. .512 The 8000 does not enter the picture, since we have the percentage if we used it then we could proceed as follow ...
July 21, 2014

Algerbra 1
again, you should type it as (y+5)/(x^2 + 4y - 32) , the way you have it, the only division is 5/y^2 = (y+5)/((y+8)(y-4)) so which values would make the denominator zero ?
July 21, 2014

algerbra 1
According to your given choices, I suspect you meant 2/( x(x-3) ) so the restrictions are, x = 0 x = 3 namely, those values which make the denominator zero, thus resulting in an undefined answer.
July 21, 2014

math
This is the best there is for these kind of questions Just fill in the data http://davidmlane.com/hyperstat/z_table.html
July 20, 2014

Math 221
2 < y and 7 ≥ y 2 < y and y ≤ 7 or 2 < y ≤ 7
July 20, 2014

mat/117
Use the formula like I showed you in your other post
July 20, 2014

mat/117
-3x^2+3x+9=0 x^2 - x - 3 = 0 x = (1 ±√13)/2
July 20, 2014

Algebra
The wording is poor. Did you mean: " The numerical value of the area of the rectangle is 25 more than the numerical value of 4 times the width" ? if so, then ... width --- x length -- x+4 x(x+4) = 4x + 25 x^2 + 4x = 4x + 25 x^2 = 25 x = 5 The width is 5 units (length...
July 20, 2014

Algebra
slope = (4 -(-9))/(-3 - (-2)) = 13/-1 = -1 Surely you must have the definition of slope in your notes or in your text.
July 20, 2014

Algebra
x - y ≥ 2 -y ≥ -x + 2 y ≤ x - 2 draw the line y = x-2 and shade in the region below the line. Since the line is included, make it solid (had it been y < x-2, you would have drawn a dotted line to show it is excluded.)
July 20, 2014

Math
double the first: 6x - 2y = -24 x + 2y = -18 add them: 7x = -42 x = -6 back into the second: -6 + 2y = -18 2y = -12 y = -6 x = -6 , y = -6
July 20, 2014

Algebra
I would use substitution, from the 1st: y = 5x-18 sub into the 2nd: -4x - 2(5x-18) = -6 -4x - 10x + 36 = -6 -14x = -42 x = 3 y = 5(3)-18 = -3 x=3 , y = -3
July 20, 2014

College math
let each of the two equal sides be x let the single side by y then y+2x = 5500 y = 5500 - 2x area = xy = x(5500-2x) = -2x^2 + 5500 Since you labeled it "college" math, I will assume you know Calculus d(area)/dx = -4x + 5500 = 0 for a max of area 4x = 5500 x = 1375 y...
July 20, 2014

stats
must be an old-type "crank on the wall" from The Waltons era .... anyway .... I will assume that none of your 6 digit numbers can start with a zero, and that numbers may be repeated, so we can't have a number with no 8 prob of no 8 = 8 x 9^5/(9x10^5) so prob that...
July 19, 2014

math
i = .105/12 = .00875 n = 12(30) = 360 payment ( 1 - 1.00875^-360)/.00875 = 130000 payment = $1189.16
July 19, 2014

Math
In 1959 the inch was internationally defined in terms of the centimetre 1 inch = 2.54 centimetres So if you want any precision you have to go back to that basic definition. c) 80 in = 80(2.54) cm = 203.2 cm = 2.032 metres once you have converted to any of the metric units, the...
July 18, 2014

math
cost of computer = .8(825) = 660 original amount of money --- x 12x/100 + .25(88/100)x +1320 + 660 = x 34x/100 - x = -1980 66x-100x = -198000 x = 3000 check: car repairs = .12(3000) = $360.00 leaves --- 2640.00 food = .25(2640) = 660 amount to parents = 1320.00 computer = 660 ...
July 18, 2014

math
Using proper algebra: number of lights --- x white = x/2 red = (1/3)(x/2) = x/6 blue = 4 yellow = 10 x/2 + x/6 + 4 + 10 = x times 6 3x + x + 6(14) = 6x 84 = 2x x = 42 42 lights in total check: whites = 21 leaves 21 red = (1/3)of 21 = 7 sum = 21 whites + 7 red + 4 blue + 10 ...
July 18, 2014

typo - math
just noticed a typo should have said: if 3 decimal places divide by 1000 but you probably figured that out anyway.
July 18, 2014

math
1. count the number of decimal places, in this case there are 2 divide by 100 -----> 12/100 2. reduce the fraction to lowest terms 12/100 = 3/25 (if 1 decimal place, divide by 10 if 2 decimal places, divide by 100 if 3 decimal places divide by 100 etc e.g. .2568 = 2568/...
July 18, 2014

Math 221
Third time for this question. Surely your text or notes must have your "Cowling's Rule" state and explained. Since I have no idea what it is, .......
July 17, 2014

math
288π , not 268 TT = appr 904.78 cm^3
July 17, 2014

math
volume of a cylinder is π r^2 h you are given r and h, take it from here.
July 17, 2014

math
volume of given tank = (45)(70)(10) cm^3 = 31500 cm^3 number of packages = 31500/3000 =10.5 but since we probably can't buy half a package, there will be 11 packages needed
July 17, 2014

math
according to your wording of the problem, term(n) = √term(n-1) - 2 or √term(n-1) = term(n) + 2 square both sides term(n-1) = term(n) ^2 + 4term(n) + 4 for n = 3, term(3) = 1 term(2) = 1^2 + 4(1) + 4 = 9 term(4) = √term(3) - 2 = -1 so we can't go any ...
July 17, 2014

math (xi)
looks like the definition of dy/dx for y = secx we know dy/dx = (sec x)(tan x) so lim [sec(x+h)-sec x]/h h>0 = (secx)(tanx)
July 17, 2014

math
sum of 20 = 10(2a + 19d) = 10(2a - 38) = 20a - 380 sum of 22 = 11(2a + 21d) = 11(2a - 42) 22a - 462 22a - 462 = 20a - 380 2a = 82 a = 41 first term is 41
July 17, 2014

math
1960 ---> term10 = a + 9d = 2400 1990 ---> term40 = a + 39d = 600 subtract them 30d = -1800 d = -60 then a + 9(-60) = 2400 a = 2940 sum40 = 20(2(2940) + 39(-60)) = 70800
July 17, 2014

Calculus Help!
let the number of additional dollars be x new price = 7.5+x number of tickets sold = 1500 - 95x Revenue = (7.5 + x)(1500-95x) = 14250 + 787.5x - 95x^2 d(Revenue)/dx = 787.5 - 190x = 0 for a max of Revenue 190x = 787.5 x = 4.14 ticket price = 7.5+4.14 = $11.64 number of tickets...
July 16, 2014

math
5(3^2) + 3(3)(-3) - (-3)2 = 45 - 27 - 9 = 9
July 15, 2014

Math
2[-3(2x+4)+8(3x-2)] = 2[-6x-12+24x-16] = 2[18x-28] = 36x - 56
July 15, 2014

Math
suppose the radius of the original cone is r then the base area of the original is πr^2 Now, the radius of your half-size cone is r/2 so the base area = π(r/2)^2 = πr^2/4 = (1/4) πr^2 Thus the base area of the scaled down cone = 1/4 of the base area of the ...
July 15, 2014

statistics
Find the z-score of each. The one with the higher z-score is a "better score"
July 14, 2014

math
You must mean 6 square root of 3, or 6√3 let each side be 2x then x^2 + (6√3)^2 = (2x)^2 x^2 + 108 = 4x^2 3x^2 = 108 x^2 = 36 x = 6 So each side is 12 units long
July 14, 2014

Math
with replacement: prob = (13/52)(13/52)(26/52) = 1/32 without replacement: prob = (13/52)(12/51)(24/50) = 12/425
July 14, 2014

algebra
Katie's share ---- x Brandy --------- 2x Steph-----------x-3 x + 2x + x-3 = 56 4x = 59 x = 14.75 Katie --- $14.75 Brandy --$29.50 Steph---$ 11.75 check: 14.75+29.50+11.75 = 56 All is good.
July 14, 2014

Math
Fraction of female drivers = 48/106 = 24/53 So according to this experimental data number of female drivers = (48/106)(190 million) = appr 86 million
July 14, 2014

Calculus 2
yup, didn't see that perfect square
July 14, 2014

Calculus 2
let y = x^5/10+1/(6x^3) here is a picture of y = x^5/10+1/(6x^3) from 3 to 6 http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E5%2F10%2B1%2F%286x%5E3%29+from+3+to+6 arc length = ∫√( 1 + (dy/dx)^2) dx from 3 to 6 dy/dx = x^4/2 - 1/(2x^4) (dy/dx)^2 = x^8/4 - 1/2 + ...
July 14, 2014

Alegbra
slope of #1 is 7 slope of #2 is .... -3y = 21x + 7 y = -7x - 7/3 to be perpendicular, the slopes would have to be opposite reciprocals of each other that is, the 2nd would have had to have a slope of -1/7 no, they are NOT perpendicular
July 14, 2014

Math
first conditions: x+4 ≥0 ---> x ≥ -4 and 3x+10 ≥0 ----> x ≥-10/3 so we know that x ≥ -10/3 case 1: x+4 = 3x+10 -2x = 6 x = -3 case 2: -x-4 = 3x+10 -4x = 16 x = -4 , also no good, because of above restriction So x = -3 check: if x = -4 LS...
July 13, 2014

Math
case 1: 1-x = 2x-5 -3x = -6 x = 2 case 2: -1+x = 2x-5 -x = -4 x = 4 x = 2 or x = 4 but by definition of absolute value, 2x-5 ≥ 0 2x ≥5 x ≥ 5/2 so x = 4
July 13, 2014

Math
The width of 12 m governs the value of x We must have 12 - 2x > 0 x < 6 the square garden must have sides less than 6 m each.
July 13, 2014

Math
What part don't you understand ? there are 25 skittles, of which 15 are green so prob of green = 15/25 = 3/5 since you are returning the one you picked, the second prob is the same as the first so prob(2green) = (15/25)(15/25) = (3/5)(3/5) = 9/25
July 12, 2014

RE: ALGEBRA
Improvement over your last post. 25x^2 - 10x = 0 5x(5x-2) = 0 5x = 0 ---> x=0 or 5x-2=0 ---> x = 5/2
July 12, 2014

Algebra
I suspect a typo, your wording indicates that it should have been a quadratic. the way you have it ... 25^2 - 10x = 0 625 = 10x x = 625/10 = 125/2 or 62.5
July 12, 2014

Math
prob(2 green) = (15/25)(15/25) = 9/25
July 12, 2014

math
argggh, what kind of a texbook would mix metric with non-metric units ?? anyway ... 20 inches = 20(2.54) cm = 50.8 cm one rotation would cover 2π(50.8) cm or 319.1858. (I stored it on calculator) 150 km/h = 150(1000)100)/3600 cm/s = 4166.666.. cm/s number of revolutions...
July 12, 2014

math
cost of one item --- x .2x = 16 x = 16/.2 = 80 So two items without tax would cost 160
July 12, 2014

maths
good question, Olivia, since if 3x+3 = 0 we would have 0/(6y+1) = 3 0 = 3 which would be nonsense. Jonel was just "lucky" to get the correct answer, since x = -1 works in the simplified equation x = 6y but not in the original equation.
July 12, 2014

maths
from the given equation, 18y + 3 = 3x+3 18y = 3x x = 6y then 7x/3y = 42y/(3y) = 42/3 = 14 =
July 12, 2014

Math
width = 2x+2 length = 4x + 4 2(2x+2)(4x+4) = 216 2(2)(x+1)(4(x+1) = 216 4(x+1)^2 = 54 take √ of both sides 2(x+1) =√54 = 3√6 x+1 = 3√6/2 x = 3√6/2 - 1 = appr 2.67 the pool is 7.35 m by 14.70 m check: 2(7.35)(14.7) = 216.09 , not bad
July 12, 2014

silly typo - Math
the third last line of the solution should of course be (x-2)^2 = 28 and the conclusion line: can't have a negative side, so x = √28 + 2
July 12, 2014

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