Posts by Reiny
Total # Posts: 40,197

Algebra
number correct  x number wrong  30x 9x  5(30x) = 18 solve for x 
Calculus
look at the graph http://www.wolframalpha.com/input/?i=y+%3D+x%5E2++1+and+y+%3D+cos(x) and notice the symmetry. So we need the intersection cosx = x^2  1 which you found correctly as ± 1.177 correct to 3 decimals area = 2[integral] (cosx  (x^2 1)) dx from 0 to 1.177... 
Math
original: boys: 80 girls : 95 now: boys = 1.15(80) = ... girls = .8(95) = ... add them up to get the new total. take the difference, percent change = difference/175 , interpret the positive vs negative answer. 
Math
solve for x , the price of the car .15x = 247.50 
Math
or, you could do it using decimals .... 2 1/5 subtract 1 1/5 = 2.2  1.2 = 1 
Algebra 1
let the part invested at 10% be x let the part invested at 14% be 10000x solve for x .1x + .14(10000x) = 1280 let me know what you get, so I can check it 
Math
Are you solving 3tanA.tanA4?3TanA+3=0 ? What does the . in 3tanA.tanA mean? Is it multiplication? I have no clue what TanA=n,3n.n4?3n+3=0 in the second part of your post means. 
Algebra
You need 2 numbers which have a sum or difference of 3, c will be their product e.g. 1,2 , product = 2 , c = 2  (x+1)(x+2) = x^2 + 3x + 2 5, 2, product = 10 , c = 10  (x+5)(x2) = x^2 + 3x  10 7, 4 , product = 28 , c = 28  (x+7)(x4) = x^2 + 3x  28 1, 4... 
maths
number at the beginning  x Paul took (1/3)x  4 number left after Paul's turn = x  (x/3  4) = 2x/3 + 4 after Sarah ate 6, number left = 2x/3 + 4  6 = 2x/3  2 took 1/4 of that, so remaining = (3/4)(2x/3  2) = x/2  3/2 Kate took 1/3 of that plus 4 = (1/3)(x/2  3/... 
Trigonometry
you can't show graphs in this format 
Math
Just did that 
MATH
max  min = 1  (7) = 8 so a = 4 , could be any of the first 3 from 3? to ? = 2? , so the period is 4? 2?/k = 4? 4?k = 2? k = 1/2 so we should see either sin(x/2) or cos(x/2) so it has to be either a) or b) test a) if x = ? , y = 4cos(?/2)  3 = 4(0)  3 = 3 ? 1 , that is ... 
Trigonometry
If R is the resultant vector, then R = (24cos42,24sin42) + (9cos312,9sin312) = (17.8355, 16.059) + (6.02218, 6.6883) = (23.85766, 9.3707) magnitude = ?(23.85766^2 + (9.3707)^2) = appr 25.63 km/h direction: Ø = tan^1(9.3707/23.85766) = appr 21.44° or make a sketch ... 
math
number of school days  x walking to school = (3/5)x = 3x/5 getting ride = (7/8)(2x/5) = 7x/20 walking plus riding = 3x/5 + 7x/20 = 19x/20 staying home  1 day 3x/5 + 7x/20 + 1 = x 19x/20 + 1 = x times 20 19x + 20 = 20x x = 20 
Math
Recall what I just said in the previous post? This time I will reverse that idea to avoid fractions, start with the largest. Also I noticed that the LCD for 1/3 and 3/4 is 12, so .... let Mary's amount be 12x then Sally has (1/3)(12x) or 4x and Jane has (3/4)(4x) or 3x 12x... 
MATH!!!!
Start with the smallest amount, usually that avoids fractions ... Let Ryan's amount be x then David has 3x , and Henry has 4(3x) or 12x now it is easy: x + 3x + 12x = 128 etc 
precalc
here is one version https://socratic.org/questions/howdoyousolvetheidentitycos3x4cos3x3cosx 
algebra 2
f(x)= (x^22x8)/(x+6) to have a point discontinuity, (x+6) should have been a factor of the numerator and cancelled out. e.g. if g(x) = (x^2  x  12)/(x4) g(x) = (x4)(x+3)/(x4) = x+3, x ? 4 There would have been a discontinuity at the point (4,7) So in your question , we ... 
Math
y = rsinØ, x = rcosØ y^2  8x  16 = 0 r^2 sin^2 Ø  8rcosØ  16 = 0 
Math
Make a sketch of the rightangled triangle with angle 45° and hypotenuse of 4 sin45 = y/4, cos45 = x/4 y = 4(?2/2) , x = 4?2/2 new point = B(2?2 , 2?2) 
geometry
areas ... the areas of similar figures are proportional to the square of their corresponding sides. so 4^2 : 3^2 or 16 : 9 
Math
let the third side be x , where x > 0 then x+15 > 27 > x > 12 and x+27> 15 > x > 12 so far we have x > 12 and 12+27 > x x < 39 so : 12 < x < 39 
Advanced Algebra
Even though you don't say, I will assume the time was 1 year. so look at this way: you started with 8750 and at the end of the year you had 10,000+ 1,000 or 11,000 8750(1+r) = 11000 1+r = 1.25714.. r = .25714 or 25.71% 
GEOMETRY helpppp
arc length = ? r Ø where r is the radius, and Ø is the central angle measured in radians You have all the data. 
Advanced Algebra
I agree 
math
x+y = 30 or y = 30x let S = 2x^2 + 5y^2 = 2x^2 + 5(30x)^2 = 2x^2 + 4500  300x + 5x^2 = 7x^2  300x + 4500 dS/dx = 14x  300 = 0 for a max/min x = 300/14 , sub into y = 30x 
Maths
sin²_cos²/2sin2cosx1/tan² reenter in proper form e.g. sin = 12/13 is meaningless, "sin" is an operator and needs an operand did you mean : sinØ = 12/13 or sinx = 12/13 ?? that is like saying ? = 3 , or log = 1.3 
Geometry
change your 604 ft to inches, then set up the ratio 
Precalculus
Only B is correct in your choices. What are your resources for this major topic if you don't have a textbook ? 
Precalculus
The correct relations are listed in your textbook or in your notes. They are easy to look up Let me know which ones you think do apply. 
Geometry
In a ratio, you need the same units. Change your 5 ft to inches, and set up the ratio. 
Math
total number of outfits = 12 total number of outfits with blue skirt = 3x1x2 = 6 prob of outfit with blue skirt = 6/12 = 12 prob of outfit without blue skirt = 1  1/2 = 1/2 
maths
speed of rocket = (2.99x10^8 m/s)/5 = 5.98 x 10^7 Wow, somebody has been watching Startrek. 
Probability
prob(yellow, then red) = (2/5)(3/4) = 3/10 prob(red, then yellow) = 3/5(2/4) = 3/10 so prob(your event) = 6/10 = 3/5 
Geometry
vector PQ = (2(6), 40) = (8,4) magnitude = ?(64+16) = ?80 = appr 8.9 , ruling out c. angle = tan^1 (4/8) = 26.57° from the xaxis what angle description describes that ? 
math
correct 
Maths
Since they rightbisect each other, you will have 4 congruent rightangled triangles, with legs of 5 and 12. Perhaps you recognize the 51213 rightangled triangle, if not use Pythagoras to find the hypotenuse to be 13 So the perimeter is ...... 
algebra 2
did you mean? 4 ^(3?(3x3)^2)+2=38 or 4^3(?(3x3)^2 + 2 = 38 ?? 
Trigonometry
drift angle is clearly 12° Make a sketch to have a triangle with sides 500 and 580 with 12° as the contained angle. Using cosine law, let the third side be R (the wind speed) R^2 = 500^2 + 580^2  2(500(580)cos12° R = .... then use the Sine Law to find one of the ... 
@ Scott  Math
Thanks, why didn't I see that ? 
Math
I hope you weren't trying to expand all of this. let's look at the last part first, by looking at a some patterns (1+x)^2 = 1 + 2x + x^2 , 3 terms, coefficients run 1,2,1 (1+x+x^2) = 1 + 2x + 3x^2 + 2x^3 + x^4, 5 terms, coefficients run 1,2,3,2,1 (1+x+x^2+x^3)^2 = 1 + ... 
Math
Now: daughter  x mother  2x 2 years ago: daughter = x2 mother = 2x2 x2 + 2x2 = 56 solve for x 
math urgent
I saw this question when you posted it yesterday. I did not answer it since it wasn't quite clearly stated. Is the 30 million split into 25 equal annual payments?? I will assume that. In that case we are simply finding the present value of those payments payment = 30 ... 
Advanced Algebra
I answered your last post for this kind of problem. How about giving me your thoughts on how to start with this question ? It is a straightforward problem. 
Advanced Algebra
Method1 Since the basic formulas for annuity assume payments at the end of a period, a slight adjustment is needed. PV = 9400 +9400(1  1.034^9)/.034 = 81243.05 method 2. look at the geometric series 9400 + 9400(1.034^1) + 9400(1.034^2) + ... + 9400(1.034^9) here a = 9400... 
Math
25a^2+ ? + .25 b^2 You know it must look something like: (5a ± .5b)^2 , expand to see the middle term take your pick 
Math
35 minutes is 35/60 of a ration, so the central angle of the sector covered = (35/60)(2?) radians = 7?/6 radians arc length = radius * angle , where the angle is in radians or circumference = 2?r = 2?(6) = 12? so the hand covered 35/60 of that, so ..... 
Math
polynomials have factors, not factories .... we could write the factors of p(x) as 2*2*3*(x5)*(x+4) any combination of these will also be a factor. How about 2*3*(x5)(x+4) expand it and see what you get 2) correct 3) x^2  x = .24 x^2  x .24 = 0 solve for x using the ... 
Math
the sides would be ?3x and 2x , then (?3x)^2 + (2x)^2 = 10^2 3x^2 + 4x^2 = 100 solve for x and you have the two sides. area = (1/2)(side1)(side2) = .... 
Math
16 men and 12 women A  you want 4 from 28 , so C(28,4) B  3 men, must be 1 woman, so C(16,3)*C(12,1) C  at least 2 men > 2men2women , 3men1woman, 4men , add up the 3 cases D  your turn 
Math
nope, not what I got show me your steps to catch the error 
Math
steph;s wage = x/10 eve;a wage = y/29 but you said: x/10=y/29 10y=29x y = 29x/10 sub that into x+y=60 and solve 2. area of large circle = ?(r+3)^2 area of small circle = ?r^2 ?(r+3)^2  ?r^2 = 21? divide by ?(the r^2 drops out) 3. make a sketch and really think about it Hint: ... 
PreCalc
you have one complex root, but they always come as conjugate pairs The other must be 22?2i You also know that one factor is (x+2) the sum of the complex roots = 2+2?2i + 22?2i = 4 product of the complex roots = (2+2?2i)(22?2i) = 4 + 8 = 12 So the quadratic factor is x^2  ... 
Math
original fraction  n/d new fraction formed = (n+d)/2d you want: (n+d)/2d = 4(n/d) 8nd = nd + d^2 7nd = d^2 7n = d it looks like we can find an infinite number of cases like that. e.g. let n = 1, then d = 7 then the original fraction was 1/7 and the fraction formed by your ... 
algebra
If arithmetic, you know that d=6 and a=6 a+(n1)d = term(n) 6+(n1)(6) = 1536 6 + 6n  6 = 1536 6n = 1536 n = 256 If GP,then a=6, r=2 In the same way, use the definition of term(n) to solve the second part 
Mathematics
Let the radius of the base be r and the height be h (1/3)? r2 h = 5 ?r^2 h = 15 The new cone will be similar to the original cone, the new height i h/3 and the new radius is r/3 volume of top cone = (1/3)?(r^2/9)(h/3) = (1/9)?r^2 h = 15/9 = 5/3 the bottom fulcrum will be 15  ... 
math
yes, you want: k21 = 48 so, k21 = 48 OR k+21 = 48 k = 69 or k = 27 think of a number line and place a dot at 21 now count 48 places to the right > 69 and count 48 places to the left > 27 
Math
Not silver > gold coin you have 123 golds out of a total of 323 prob(not silver) = 123/323 
MATH
I don't have the foggiest idea. my calculator says: (2360448/(2?))² = 1.4113318 x 10^11 , (notice the change in the division by 2?) don't know how the R³/3.98x10^14 fits in 
Math
20 < T < 80 , where T is temperature in Fahrenheit Since C = (5/9)(F  32) , I will let you do the conversion 
Math
correct 
math
number passed  x number failed  36x sum of scores of passers = 78x sum of scores of failures = 60(36x) 78x + 60(36x) = 71(36) solve for x 
math
48/x  x = 2 multiply each term by x to get the quadratic 48  x^2 = 2x x^2 + 2x  48 = 0 (x  6)(x + 8) = 0 x = 6 or x = 8 btw, What she was told to do should have been: (48x)/x if x = 6, (48x)/x = (486)/6 = 7 if x = 8, (48x)/x = (48 + 8)/8 = 7 
math
What she was told to do: (x48)/x what she did: 48/x  x = 2 solve for x, then plug into "what she was told to do" btw, there are two values of x. 
math
My money is definitely on Damon ! Annabelle just tossed some number salad. 
Math
You just told me that Maya was m years old. Why are you asking how old Maya is ? 
Math
3(3/7)^2 + 2/3 = 3(7/3)^2 + 2/3 = 3(49/9) + 2/3 = 49/3 + 2/3 = 51/3 = 17 
Math
By definition: 2? radians <> 360° 
Trig
correct 
Math
The easy part is to find the areas of the 3 rectangles, they are: 2x7, 3x7, and 4x7. The hard part is to find the area of the triangular base. Since it is not rightangled, 2^2 + 3^2 ? 4^2, we need more complex methods. method one: Heron's formula area = ?(s(sa)(sb)(sc... 
Calculus
a = 32 ft/sec^2 v = 32t + c when t = 0 , v = 64 64 = 0 + c , so c = 64, and v = 32t + 64 d = 16t^2 + 64t + k, but when t=0 , d = 0 0 = 0 + 0 + k k = 0 d = 16t^2 + 64t The vertex of this parabola will tell you the maximum height, and the t when that max occurs. I assume ... 
Math
1/12(cos8t3sin8t) = 0 cos8t3sin8t = 0 3sin8t = cos8t sin8t/cos8t = 1/3 tan 8t = 1/3 8t = .32175 or 8t = ?+.32175 t = .0402 or t = .4329 
Alegbra 1
Easiest way: An equation perpendicular to 2x  5y = 3 must have the form 5x + 2y = c plug in our given point on this line: 5(2) + 2(7) = c = 4 5x + 2y = 4 
math
distance straight across = 120 m distance halfway around the circumference = 60? = .. compare them. 
Math
average is 84, so the total is 20(84) or 1680 points points of 6 students at 100 = 600 points of 4 students at 50 = 200 remaining points = 1680  600  200 = 880 average of those 10 students = 880/10 = 88 
math
5 machines 5 minutes to make 5 widgets 100 machines 5 minutes to make 100 widgets  you have 20 times as many machines, so 20 times as many products in the same time of 5 minutes 
MATH HELP ASAP
change all numbers to decimals and it will be easy to tell 
Pre Algebra
(218/245)*360° will be the angle of the larger part. 
Algebra
larger angle  x smaller angle  x/4 x + x/4 = 180 solve for x, and sub in my definitions. or smaller angle  y larger angle  4y y+4y = 180 solve for y, y will be the smaller angle, since I defined it as such 
Algebra
contributions in 2002  contributions in 2003  1.15x contributions in 2004  (1.1)(1.15x) (1.1)(1.15x) = 8855 solve for x 
Maths
take the derivative of the ellipse equation using implicit differentiation. The slope of 3x+2y  5 = 0 is 3/2 so the slope of the perpendicular will be +2/3 set your derivative of the ellipse equal to 2/3 . You will get a linear equation in x and y Solve that with the ... 
Math (Word Problems)
Just set up a simple ratio x/9 = (3/4) / 6 6x = 9(3/4) 6x = 27/4 x = 27/24 = 9/8 or 1 1/8 cups of sugar 
extended mathematics
You can't post diagrams in this forum 
Math
Arora, nicely done, impressive! 
Maths
In these kind of questions, when they state that 30% workers are BTeach holders, we don't assume that it is 30% exclusively. e.g. When I say, that 8% of boys play football, that doesn't mean that they can't play some other sport as well. In a Venn diagram for this ... 
Maths
I disagree .. number(BT or MBA) = 30%+25%  20% = 35% (we can't count the 20% twice ) so 65% are without degrees .65x= 325 x = 500 
geometry
by basic geometry: CP:PD = 30:48 = 5:8 let CP=5x, and PD = 8x let the height between AB and CD = h so area of BCP + area of ADP = 5xh +8xh = 13xh = 78 area of ABC = 13xh = 78 area of whole thing = 78+30+48 = 156 
algebra
Scientific notation consists of a number between 1 and 10, multiplied by a power of 10. I see only one that fits this. 
Maths
I am sure DrBob meant: 600 = r*4 + 2r*3 
Maths
Guessing that the question is to find the sides. x^2 + (3x1)^2 = (3x+1)^2 x^2 + 9x^2  6x + 1 = 9x^2 + 6x + 1 x^2  12x = 0 Use your favourite method to solve this quadratic, remember that x > 0 
Maths
from 4x – 3 = 3x + y y = x  3 ** plug ** into 3x + y = 2y + 5x – 12 3x + x3 = 2(x3) + 5x  12 4x  3 = 2x  6 + 5x  12 4x3 = 7x  18 3x = 15 x = 5 then y = 53 = 2 
Math
I really don't understand what part of my analysis you don't get. Volume is (base area) x (width) So if you consider the sideview as the base, you have rectangle = 44(3) = 132 ft^2 triangle = (1/2)(44)(6) = 132 ft^2 total area of sideview = 264 ft^2 volume = that total... 
Math
The top view is a rectangle It is the side view that illustrates the shape of the pool, it will be the trapezoid. Do you know what a trapezoid looks like ? 
Math
Draw a sideview of the pool to see the trapezoid, the two vertical ends are your parallel sides. draw a horizontal from the short vertical to meet the longer vertical. You now have a rectangle and a rightangled triangle. The rectangle is 44 by 3 and the triangle is 44 by 6 ... 
Pri 5 maths
3s = 2b s = 2b/3 5b + 6s = 108 5b + 6(2b/3) = 108 5b + 4b = 108 b = 12 then s = 8 6 skirts = 48 
pre algebra
amount of pretzels  x lbs amount of cereal  12x lbs 1.5x + 3(12x) = 2(12) continue 
math
You just asked the same question 5 minutes ago! 
math
The volume of a pyramid = (1/3)(area of base)(height) test them, I see two of them 
math
since it is parallel, it will differ only in the constant, so new equation is x  4y + c = 0 plug in the given point to find c. 
Math
No, it can't be W=15, since 15/36 ? 5/18 but 10/36 = 5/18