Sunday
November 23, 2014

Posts by Reiny


Total # Posts: 27,929

Algebra/Math
f(x) = 3x + b f^-1 (x) = (x - b)/3 (-3, a) lies on both so f(-3) = -9 + b = a f^-1(-3) = (-3-b)/3 = a (-3-b)/3 = -9+b -3-b = -27 + 3b 24 = 4b b = 6 then a = -9+6 = -3 a = -3, b = 6 check my arithmetic
November 6, 2014

Calculus-Newton Method Approximation
1/ 3(x^3) + 1/2(x^2) + 1 = 0 times 6 2x^3 + 3x^2 + 6 = 0 let y = 2x^3 + 3x^2 + 6 dy/dx = 6x^2 + 6x according to Newton's method newx = x - y/y' = x - (2x^3 + 3x^2 + 6 )/(6x^2 + 6x) = (6x^3 + 6x^2 - 2x^3 - 3x^2 - 6)/(6x^2 + 6x) = (4x^3 + 3x^2 - 6)/(6x^2 + 6x) using my ...
November 6, 2014

Math/Algebra
let's find their intersection points 1+x^2+x^3 = 3-x^2+x^3 2x^2 = 2 x^2 = 1 x = ± 1 if x = 1, y =1+2+1 = 3 if x = -1, y = 1 + 1 - 1 = 1 They intersect at (1,3) and (1,1) so what is the difference between their y values ?
November 6, 2014

Algebra
√((x-2)^2 + (y-7)^2 = 13 square both sides and expand x^2 - 4x + 4 + y^2 - 14y + 49 = 169 x^2 - 4x + y^2 - 14y = 116 but x = 10+2y sub that into the first equation (10+2y)^2 - 4(10+2y) + y^2 - 14y = 116 100 + 40y + 4y^2 - 40 -8y + y^2 - 14y = 116 5y^2 + 18y - 56 =0 (y-2...
November 6, 2014

Math
So we are going to need those intercepts, the x - intercepts are easy x = 3 or x = -2 for the y-intercept, let x = 0 y = (-3)^2 (2) = 18 so the points of the triangle are (3,0), (-2,0) and (0,18) so the base of the triangle is 5 and the height is 18 area = (1/2)(base)(height...
November 6, 2014

statistic
a) prob(red) = .546 prob(not red) = .454 prob(exactly 5red) = C(12,5) (.546)^5 (.454)^7 = appr .153 b) prob (green) = .395 prob(not green) = .605 prob(at least 3 green) = prob(3green) + prob(4 green) + ... + prob(12 green) =1 - prob(0 not green) - prob(1 not green) - prob(2 ...
November 6, 2014

math
c is wrong 3^3 = 27 , so 27 is a perfect cube.
November 6, 2014

geometry
what is 8/9 yards ?
November 6, 2014

Math
I suspect you meant: c(t) = 9 - 90 000 (1/ (10 000 + 3t) ) I will also assume that c(t) is in kg/m^3 then 6 = 9 - 90 000 (1/ (10 000 + 3t)) 90000(1/(10000+3t)) = 3 30000 + 9t = 90000 9t = 60000 t = 6666 2/3 minutes ? check my arithmetic
November 6, 2014

Trigonometry
Did you make your sketch? Mine is triangle ABC with angle A = 55° angle C = 22°, and angle B + 103° then it is just a matter of the sine law: AC/sin103 = 300/sin22 I got AC = appr 780 miles
November 6, 2014

geometry
There would be an infinite number of such triangles. What part of the instructions are you having difficulties with ?
November 6, 2014

Maths
make your sketch draw a horizontal line from the top of the shorter pole to the other pole. You now have a right-angled triangle with base 12 m, height 18-13 or 5 m You should recognize the common 5,12, 13 right-angled triangle, if not c^2 = 12^2 + 5^2 = 169 c =√169 = 13
November 5, 2014

Algebra
adults --- x children -- y seniors --- z x+y+z = 895 , #1 14x +11y + 8z = 10514 , #2 translation of: "If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 295" ---> x+y > 2z by 295 x+y = 2z + 295 x + y - 2z...
November 5, 2014

Trig
"A playground slide starts 107cm above the ground and is 250cm long" Trusting my English grammar somewhat, you made "slide" the subject of your sentence, and you said it is 250 cm long. Thus 250 is the hypotenuse. tanØ = opposite/adjacent sinØ...
November 5, 2014

Trig
Assuming the slide is a straight line, (most are not) Did you make your sketch? I have the opposite as 107 and the hypotenuse as 250 so sinØ = 107/250 Ø = appr 25°
November 5, 2014

please help, math question
let the width of the matte be x all around so the width of the whole picture = 10+2x and the length is 15+2x area of whole picture = (10+2x)(15+2x) area of picture = 10(15) = 150 area of matte only = (10+2x)(15+2x) - 150 so (10+2x)(15+2x) - 150 = 150 150 + 20x + 30x + 4x^2 - ...
November 5, 2014

Algebra 2
let x be the larger then the smaller is 96-x x - (96-x) = 17 x - 96 + x = 17 2x = 113 x = 56.5 larger is 56.5 , the smaller is 39.5 check: difference = 56.5-39.5 = 17 , yup!!
November 5, 2014

Vertex, Focus, & Directrix of Parabolas
Just did this for Kayla http://www.jiskha.com/display.cgi?id=1415240099
November 5, 2014

Math
x( 1 - 1.02^-11)/.02 = 1700 x( 9.786848.. = 1700 x = $ 173.70
November 5, 2014

Algebra II
writing it in terms of y first of all 48y = x^2 - 12x + 276 or 48y = x^2 -12x + 36 - 36 + 276 48y = (x - 6)^2 + 240 y = (1/48) (x-6)^2 + 5 so the vertex is (6,5) the x of the focus is the same as that for the vertex so x = 6 for y = (1/48)x^2 - (1/4)x + 23/4 the y of the focus...
November 5, 2014

Math HELP!
What did we do to the 7 to make it a 2 ? looks like we subtracted 5 What did we do to the -3 to turn it into a 5 ??? so (x,y) ---> (x-5, ..........) I am sure you can get this
November 5, 2014

math
I did this same problem 2 years ago http://www.jiskha.com/display.cgi?id=1352760453 Looks like this teacher is just recycling the same problems
November 5, 2014

Math
for any parabola of the form y = a(x-h)^2 + k , the vertex is (h,k) and the axis of symmetry is x = h so in your case ......
November 5, 2014

math
it should not be too hard to actually list them Q-D-N 0 0 6 0 1 4 0 2 2 0 3 0 1 0 5
November 5, 2014

Finance
what is 1000(1.07)^20 ?
November 5, 2014

trigo
distance covered by both wheels must be the same ... with radians, arclength is simply rØ so 24Ø = 60(12) Ø = 30 radians
November 5, 2014

Algebra
Don't know what you want to "solve" You have a cubic function, are you graphing it? are you finding intercepts? ??
November 5, 2014

Probability
prob(right) = 1/4 prob(wrong) = 3/4 if passing grade is 8/10, then I will pass if I get 8/10 or 9/10 or 10/10 prob of that = C(10,8)(1/4)^8 (3/4)^2 + C(10,9)(1/4)^9 (3/4) + (1/4)^10 = appr .00041 check my arithmetic
November 5, 2014

college statistics
C(12,3) = 12!/(3!9!) = 220 Added attraction: Google Pascal's triangle look at the row: 1 12 66 220 495 .... here is a good one.. http://ptri1.tripod.com/
November 5, 2014

algebra
Your answers make no sense to me. How did you get these?
November 4, 2014

algera
find the derivative, set it equal to zero and solve.
November 4, 2014

algebra
You left your answer choices blank. What did you get?
November 4, 2014

Calculus
BUT, the given point is not on the curve, so what you did is bogus. look at your sketch, the point (0,-4) is below the parabola. Draw the two tangents, you will see that it touches the curve at two different points, one in the first quad, the other in the 2nd quad. Let the ...
November 4, 2014

Calculus
y' = 18x^2 + 5 we want 18x^2 + 5 = 4 18x^2 = -1 x^2 = -1/18 but that is not possible since the square of anything has to be positive, so there is value of x making this equations true thus there is not slope of 4 thuse there is no such tangent
November 4, 2014

Calculus
dy/dx = 6x^2 - 6x - 6 = 0 for a horizontal slope x^2 - x - 1 = 0 x = (1 ± √5)/2 = appr 1.618 or -.618 you are correct, but all it asked for is the values of x (did you know that the first answer x = 1.618.. is the "golden ratio " ? )
November 4, 2014

Calculus
correct
November 4, 2014

math
look at one of the 6 congruent triangles the base of it must be 78/6 = 13 area of one of them = (1/2)base x height = (1/2)(13)(11) = 143/2 square inches so the whole hexagon is 6(143/2) = 429 inches^2
November 4, 2014

math
adults --- x children --- 3x 7x + 3(3x) = 6000 16x = 6000 x = 375 so 375 adults and 1125 kids for a total of 1500 sold
November 4, 2014

Math
cost per quart for orange --- x cost per quart for grapejuice -- x-1 (5/2)(x-1) + (3/2)x = 12.5 times 2 5(x-1) + 3x = 25 8x = 30 x = 3.75 x-1 = 2.75 orange juice costs $3.75 per quart and grape juice costs $2.75 per quart
November 4, 2014

math
I am 100% sure it was measured in feet. Looks like Sandy is a kid or a short junior. The stick should come to your chin with skates on, and to about your nose without skates on.
November 4, 2014

algebra
number of dimes --- x number of nickels --- 2x 10x + 5(2x) = 120 20x = 120 x = 6 So 6 dimes and 12 nickels
November 4, 2014

Algebra
I have a feeling you meant f(x) = (x+5)/3 or is it the way you typed it ? confirm please
November 4, 2014

math
looks like plain ol' Pythagoras to me y^2 + 2.8^2 = 10.5^2 y^2 = 102.41 y = √102.41 = appr 10.12 m
November 4, 2014

Algebra please help
since a 2 ounce bag is 1/3 of a 6 ounce bag, I predict it will cost one third of $3.60.
November 4, 2014

Algebra please help answer
clearly 9:6 ≠ 4:3
November 4, 2014

algebra
I am assuming that the 2nd shift follows the first shift now: let the number of girls in A be x let the number of girls in B be y after 1st shift: A has x-7 B has y+7 "the number of girls in the classes would interchange" ---> y+7 = x 2nd shift A has x-7 + 4 = x-3...
November 4, 2014

Algebra
Are you sure you don't have any more information, such as an angle ? otherwise, let the third side be y P = 2(3x+2) + y
November 3, 2014

Math: permutation
let's choose the consonants and vowels first No of combinations = C(5,2) x C(2,1) = 10(2) = 20 Since you titled your post "permutations" we now want to arrange these. That can be done in 6 ways each So the number of permutations is 6(20) = 120
November 3, 2014

Math
looks like you are studying the binomial theorem You MUST memorize some basic formulas e.g. for (a+b)^n term(r+1) = C(n,r) (a^r)(b^(n-r)) so for (3x+9)^9 term6 = C(9,5)(3x)^5 y^4 = 126(243x^5)y^4 = 30618 x^5 y^4 b) what is the middle term for (3x + y^3)^8 ? c) let that term be...
November 2, 2014

Math
2.25 = 1(10^8) 1.5^(t/20) since the time would be same for a small country or a large country to increase by 124%, we can ignore the 10^8 take log of both sides log 2.25 = l log 1.5^(t/20 log 2.25 = (t/20) log 1.5 log2.25/log 1.5 = t/20 t = 20(log2.25)/log 1.5 = 40 years 2 = 1...
November 2, 2014

Algebra
Wow, that is the second post in a row that your re-posted before checking if your first posting had been anwered. http://www.jiskha.com/display.cgi?id=1414981217
November 2, 2014

Algebra
Bob did this for you Did you not check back ???
November 2, 2014

Math
from max to min = 254-88 = 166 so amplitude = 84 period = 20 min period = 2π/k 20 = 2π/k k = π/10 let p(t) = 83 cos π/10(t + d) + 171 when t = 0 we want p(0) = 88 88 = 83cos (π/10)cos(0 + d) + 171 -1 = cos (dπ/10) I know cos π = -1 so dπ...
November 2, 2014

Pre-Calc
draw a line from his final position to the centre and complete the triangle all the way around is 2πr = 6π so completed 6/6π or 1/π around the circle angle" Ø/360 = 6/6π Ø = 360/π = 114.59156° cosØ = x/3 and sin&...
November 2, 2014

Math Calc
I will assume that neither A nor B are the right angle, or else why would you ask to find it So tanB = 13/26 = 1/2 angle B = 26.565 then angle A = 63.435° (90 - B) c^2 = a^2 + b^2 = ... you finish it
November 2, 2014

Algebra
You probably meant: f(x) = (2x-1)/(x+5) I will assume that then y = (2x-1)/(x+5) we form the inverse by interchanging x and y x = (2y-1)/(y+5) xy + 5x = 2y -1 now solve this for y xy - 2y = -5x - 1 y(x-2) = -5x - 1 y = f^-1 (x) = (-5x - 1)/(x - 2) so by comparison, a = -5 b...
November 2, 2014

Math
We "solve" equations, yours is not an equation. Did you perhaps want to factor it ?? x^2 - (y^2 + 2y + 1) = x^2 - (y+1)^2 ahhh, a difference of squares ... = (x+y+1)(y-y-1)
November 2, 2014

Algebra
((7-10)+3)-5 ---> (10-7) + 3) - 5) = (-3+3) - 5 ----> (3-(-3)) - 5 = 6-5 ----------> 5-6 = -1
November 2, 2014

Algebra (1)
Is that (y+2)/(y+7) = 11/31 ?? , (looks like ll instead of 11) Are you solving for y ?? if so, just cross-multiply 31y + 62 = 11y + 77 20y = 15 y = 15/20 = 3/4
November 2, 2014

Calculus
when x = 3 f(3) = 1.201 , correct to 3 decimals so the point of contact is (3, 1.201) f ' (x) = e^(-.4x) (1/x) + (-.4) e^(-.4x) ln(18x) f ' (3) = -.380 correct to 3 decimals y - 1.201 = -.38(x-3) y = -.38x + 2.342 better check my arithmetic and button-pushing
November 2, 2014

statistics and probability
fewer than 4 defective ---> 0 ,1,2, or 3 are defective prob(defective) = 5/100 = 1/20 prob(not defective) = 19/20 prob = C(100,0) (1/20)^0 (19/20)^100 + C(100,1)(1/20)(19/20^99 + C(100,2)(1/20)^2 (19/20)^98 + C(100,3)(1/20)^3 (19/20)^97 = .00592.. + .03116.. + .08118...+ ....
November 2, 2014

math
4(x+15) ≥ 120 4x + 60 ≥ 120 4x ≥ 60 x ≥ 15
November 2, 2014

Algebra
let n be the number of pages scanned .02n + 70 ≤ .09n 70≤ .02n or .02n ≥ 70 n ≥ 3500 so 3500 pages is the break-even point so anything greater than 3500 she should rent the scanner, at less than 3500 her old scanner will be better.
November 2, 2014

calculus
arrrgggghhh! Wolfram says: http://integrals.wolfram.com/index.jsp?expr=x%5E2%2F%28%28x%2B3%29%283x%2B4%29%5E%281%2F2%29%29&random=false
November 2, 2014

mathzzzz gkpp
x(1.1)^2 = 12000 x = 12000/1.1^2 = appr 9917.36
November 2, 2014

math
Please use proper English with correct grammar and punctuation in your post. It would make it so much easier to establish what your are trying to say. Furthermore, is there a question such as, "Find x" ? sum of 8 number is x so the average of those 8 numbers is x/8 ...
November 2, 2014

Intermediate Algebra
I assumed that you meant (-9)^(1/2) which is the same as √-9 , which of course is not real vs -(9^(1/2)) which is -√9 which is -3 the ^ is the generally accepted symbol to indicate an exponent, e.g. x^2 is x squared, x^5 is x to the fifth, etc
November 2, 2014

Intermediate Algebra
This only makes sense if you meant √(-9) vs - (√9) remember we cannot take the square root of a negative number, that would be an imaginary or complex answer. but by the order of operation for -√9 we take the square root first, and then make the answer ...
November 2, 2014

Solid Mensuration
Remember that in a cyclic quadrilateral, the diagonal subtends a 90° angle. Since the two diagonals also intersect at 90°, the shorter diagonal must be bisected by the diameter. In my diagram, I labeled the diameter A and B and the point on the circle above AB as C My ...
November 2, 2014

Calculs I
btw, jorge's answer is bogus. I got 27203
November 2, 2014

Calculs I
y(t) = a e^(kt) , where a is the intitial count, and k is a constant, and t is in minutes You have two ordered pairs, (15,16000) and (45,22000) for (15,16000) 16000 = a e(15k) for (45,22000) 22000 = a e^(45k) divide the 2nd by the 1st 1.375 =e^(30k) ln both sides , that is : (...
November 2, 2014

Calculus
k(t)=(t^2-4)^2 = (t^2 - 4)(t^2 - 4) now do as instructed
November 2, 2014

Calculus
let the time after their split be t hrs I see a triangle with sides 10t and 6t and an angle of 120° between them let the distance between them be d miles by the cosine law: d^2 = (6t)^2 + (10t)^2 - 2(6t)(10t)cos120° = 136t^2 + 60t^2 d2 = 196t^2 d = 14t dd/dt = 14 mph...
November 2, 2014

Calculus
2x dx/dt + x dy/dt + y dx/dt + 2y dy/dt = 0 (dy/dt)(x + 2y) = -2x dx/dt - y dx/dt dy/dt(2 + 6) = -4(3) - 3(3) dy/dt = -21/8 the ant is moving DOWN at 21/8 cm/s
November 2, 2014

Calculus
C = 2πr dC/dt = 2π dr/dt A = πr^2 dr/dt dA = 2πr dr/dt you have the values to plug in for both rates.
November 2, 2014

Calculus
dV/dt = πr^2 dh/dt + 2πrh dr/dt plug in the given values SA = 2πrh , are you not considering the ends ? differentiate with respect to t using the product rule like I did for the volume, then plug in the values
November 2, 2014

Calculus
let the length be x inches let the width by y inches A = xy dA/dt = x dy/dt + y dx/dt for the given data... dA/dt = 24(-3) + 15(4) = -12 inches^2/min the area is decreasing at 12 square inches/min P = 2x + 2y dP/dt = 2 dx/dt + 2 dy/dt = 2(-3) + 2(4) = 2 inches/min
November 2, 2014

Math
i = .049/12 = .00408333... n= 15(12) = 180 amount = 10000(1.00408333..)^180 = $ 20,823.63
November 2, 2014

Algebra
notice that for every increase of 1 in the x, the y increases by 2 so slope = 2 or, more formally, take the fist two points (1,1) and (2,3) slope = (3-1)/(2-1) = 2 so y = 2x + b sub in the first point (1,1) 1 = 2(1) + b b = -1 y = 2x - 1 check the remaining points to make they...
November 1, 2014

Algebra
I assume you want it 'simplified' and that you forgot the brackets (8-6i)/(3i) = (8-6i)/(3i) * i/i = (8i - 6i^2)/(3i^2) = (6 + 8i)/-3 or =( -6 - 8i)/3 hint for the second... multiply top and bottom by (4-2i)/(4-2i)
November 1, 2014

Math
simply solve ... .07x + .15(x+1500) = 1545 where x is the amount invested at 7%
November 1, 2014

Maths
Please type your question in proper English. "d" is the common variable for the difference between consecutive terms of an AP and not as a substitute for "the".
November 1, 2014

math
Finding the distance between 2 points and finding the midpoint between 2 points should be part of your repertoire of common and memory-recall-ready formulas if you want to study math for (a,b) and (c,d) Distance = √( (c-a)^2 + (d-b)^2 ) midpoint = ( (a+c)/2 , (b+d)/2 ) ...
November 1, 2014

Algebra
so a#b =(a+b)/2 then ((1#2)#2)#4 = (1.5#2)#4 = 1.75#4 = 2.875 or = 23/8 or ((1#2)#2)#4 = (3/2#2)#4 = (7/4)#4 = 23/8
November 1, 2014

Algebra
P(g(x)) = p(4-3x) = 4 + 2√(4 - 3x + 2) = 4 + 2√(6-3x) remember we cannot take the square root of a negative, so 6-3x≥0 -3x ≥ -6 x ≤ 2 so the largest value of a is 2
November 1, 2014

MATHS
I will need 2 zeros (0 can't be in front) 3 ones 3 twos 3 fours ... 3 sevens 2 eights 2 nines total = 29 for b) we can save the 2 nines, (the 3 sixes will suffice) so they can save 2 cards
November 1, 2014

Maths
Prob(m) = 1/5 prob(S) = 4/5 Possible outcomes in best of three" MM --- (1/5)(1/5) = 1/25 MSM -- ((1/5)(4/5)(1/5) = 4/125 SMM -- ((4/5)(1/5)(1/5) = 4/125 SS ---- (4/5)(4/5) = 16/25 ----> Sue wins SMS -- (4/5)(1/5)(4/5) = 16/125 ----> Sue wins MSS -- ((1/5)(4/5)(4/5...
November 1, 2014

Algebra
πr^2 = 2πr r^2 - 2r = 0 r(r-2) = 0 r = 0 , the trivial answer or r = 2 So the diameter is 4 a/b = 2/3 or 2b = 3a, or b = 3a/2 (a+5)/b = 5/6 5b = 6a + 30 5(3a/2) = 6a + 30 times 2 15a = 12a + 60 a = 20 and b = 3(20)/2 = 30 the fraction was 20/30 y < √x by 4 y...
October 31, 2014

Math
factor is 10^8.8/10^7.1 = 10^1.7 = appr 50 times as strong
October 31, 2014

Math
number of quarters ---- x " he has one more dime than he has quarters" ---> dimes ---- x+1 now for the "value" of coins equation: 25x + 10(x+1) = 115 25x + 10x + 10 = 115 35x = 105 x = 3 etc
October 31, 2014

Width of a square
How can 45/10 = 3.5 ?? 45/10 = 4.5
October 31, 2014

math
You are looking for those values of x, so that y = (x+5)/(x-2) lies above the x-axis first of all, x ≠ 2 or else we are dividing by zero critical values are -5 and 2 investigate x < -5, say x = -10 then y = -/- = + , that's good investigate between -5 and 2, say x...
October 31, 2014

maths
I will assume you meant: 1/( (x+2)(x+3) ) - 1/( (x-4)(x-5) ) what about it? are you simplifying?
October 31, 2014

Math, Can someone check my answers?
all 3 are correct
October 31, 2014

Thanks Steve - Pre Calculous
for keeping an eye on me. I just have to read more carefully, I read it as sinx = 1/4
October 31, 2014

Pre Calculous
my keystrokes on my calculator: 2nd sin .25 = to get 14.478° but the sine is positive in I and II so x could also be 180 - 14.478 = 165.522° there are an infinite number of solutions, just add/subtract 360° to any existing answer to produce more.
October 31, 2014

Math Calc
divide by 7 sinØ = 6/7 Ø = arcsin (6/7) = appr 58.997° Did you use a calculator? my keystrokes: 6 ÷ 7 = 2nd sin = to get my answer
October 31, 2014

Math Arc Length
circumf = 2πr = 2π(4.9) = 9.8π so 360° of arc = 9.8π units and 1° of arc length = 9.8π/360 = 49π/1800 units Maybe they didn't like your decimal, but your answer is correct
October 31, 2014

Calculus
dy/dx = 4x + 5 dy = (4x + 5)dx so for your given data dy= (20+5)(.1) = 2.5 so the other one the same way
October 31, 2014

math
amount poured into canister --- x g amount in canister = 5026 + x amount left in bag = 4157-x g 5026+x = 2(4157-x) 5026 + x = 8314 -2x 3x = 3288 x = 1096 amount left in bag = 4157-1096 = 3061 g
October 31, 2014

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