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Posts by Reiny

Total # Posts: 38,372

MATHS
All of the trig ratios shown are based on "standard" angles. We used to have math kits that contained a compass, a protractor and two triangles. One had angles 45-45-90°, the other had 30-60-90° The ratio of sides of the 30-60-90 were 1 : ?3 : 2 and for the ...

Math probability
prob(big winner) = 1/C(68,5) = 1 / 10,424,128 = appr .000,000,1

algebra
first number ---- x second number --- x+9 third number ----- 82 - x - x - 9 = 72 -2x all three numbers are expressed in terms of one variable: x , x+9, and 72-2x

algebra 1
just subtract them: 10y = -10 y = -1 plug that into the first: -4x + 7(-1) = -3 -4x = -3+7 = 4 x = -1 x = -1, and y = -1

Math
There are no "points in the table below"

Math
y+x =10 y - x = 20 add them: 2y = 30 y = 15 15+x = 10 x = -5 x = -5, y = 15

Life Science Math
acceleration --- a then v = at + c at the start, t = 0, and v=0 0 = 0 + c ---> c = 0 so v = at when t = 3 sec = 3/3600 hrs or 1/1200, v = 60 60 = a(1/1200) a = 72000 ------> v = 72000t if s is the distance travelled , s = 36000t^2 + k when t = 0 , s = 0, so k = 0 s = ...

f math
I will assume that by t ta you mean Ø so sin(90 - 5Ø) = cos(180 - Ø) but sin(90 - 5Ø) = cos Ø just like sin(90 - 30) = cos30 so we have cos(5Ø) = cos(180-Ø) take arccos of both sides 5Ø = 180-Ø 6Ø = 180 &...

f math
What is "t ta" ?? Where does "d" enter the picture?

Math
agree with C I did not answer the question that was asked My 4 slices would represent 1/2 of an 8 slice pizza.

Math
If each pizza is cut into 8 slices, then in the 7 pizzas there are 56 slices So each of the 14 student would get 56/14 or 4 slices. You did not post any "answer choices", so I hope 4 is in there.

Math
let one number be x let the other be x+7 x + x+7 = 63 solve for x, and all that is unknown shall be revealed.

Math
Done the way you typed it: |1-15x/5| < 3 1 - 15x/5 < 3 AND -1 + 15x/5 < 3 -3x < 2 AND 3x < 4 x > -2/3 AND x < 4/3 What you probably meant: | (1-15x)/5 | < 3 (1 - 15x)/5 < 3 AND (-1 + 15x)/5 < 3 1 - 15x < 15 AND -1 + 15x < 15 -15x < 14 AND...

Math Quadratic Equations . URGENT!!!!
look back when you posted this earlier

Trig
Did you make a sketch? I followed your labels and let the base of the building be B in triangle DAB, tan30 = DB/30 DB = 30tan30° = ... in triangle CAB, tan 60 = CB/30 CB = 30tan60 = ... CD = CB - DB = ....

Math
correct, ***80 is the only one divisible by 4

Math
A number is divisible by 4 if its last two digits are divisible by 4, or the last two digits are zeros. I see only one such case

Math, Quadratic equations
this was answered when you were Rachel.

Math, Quadratic equaitons
your data does not match the equation , so I don't know which is the correct one I will go with the equation: h = -4t^2 + 8.1t + 3 , (according to your data it would be 8.2t) when h = 6 6 = -4t^2 + 8.1t + 3 4t^2 - 8.1t + 3 = 0 using the formula: t = (8.1 ± ?17.61)/8...

College Math
You are partly on the right track. The C(13,7) is the number of to choose 7 of the 13 marbles. you want the case of 3 reds plus 4 non-reds prob(your stated event) = C(3,3)*C(10,4)/C(13,7) = 1*210/1716 = 35/286

f math
1 - cos^2 x = 0 , for 0 ? x ? 270° cos^2 x = 1 cos x = ± 1 now look at the cosine curve. Where is the y equal to either +1 or -1 within your domain ?

Calculus
y = ln(sint) dy/dt = (1/sint)(cost) = cost/sint for x= cos^2 t = (cost)^2 dx/dt = 2cost(-sint) (dy/dt) / (dx/dt) = (cost/sint) / (-2sintcost) dy/dx = -1/(2 sin^2 t) = (-1/2)(sint)^-2 d(dy/dx) / dx = (-2)(-1/2)(sint)^-3 (cost) = cost / sin^3 t sub in t = ?/4 d(dy/dx) / dx = (?2...

Maths
remember that sinx = cos(90-x) - property of complementary angles, "co-sine" vs sine Your statement is only true if (cos40-sin30)/(sin60-cos50) =tan50 , but not the way you typed it. cos40 = sin50 and sin60 = cos30 so LS = (sin50 - sin30)/(cos30 - cos50) remember ...

Math
let the obtuse angle be A and its opposite diagonal be x. By the cosine law: x^2 = 45^2+28^2-2(48)(28)cosA similarly... y^2 = 45^2+28^2-2(48)(28)cosB but A+B = 180 B=180-A and cosØ = -cos(180-Ø) by the CAST rule e.g. cos 60 = - cos120 then cos B = -cosA x^2+y^2...

math
original fraction: x/y case1 (x+5)/(y+5) = 1/2 2x + 10 = y+5 2x - y = -5 ** case2 (x-1)/(y-1) = 1/5 5x - 5 = y - 1 5x - y = 4 *** subtract ** from *** 3x = 9 x = 3, then from ** 6 - y = -5 , y = 11 the original fraction was 3/11 check: (3+5)/(11+5) = 8/16 = 1/2, check! (3-1)/(...

Math Quadratic Functions
A squaring of the input value is involved. A rather vague question.

math
just like in 5/6 - 3/7 you will need a common denominator. In my example, it would be 42? How did I get 42 ? Next step 35/42 - 18/42 ---> how did I get those fractions = 17/42 Now to your problem 5/(x-2) - 4(x-3) LCD = (x-2)(x-3) ---> same step as above e.g = 5(x-3)/((x-...

Calculus
I will assume you are saying $1 per square foot let the base be x ft by x ft, let the height be y area of top and 4 sides = x^2 + 4xy cost of top and 4 sides = 1(x^2 + 4x) = x^2 + 4xy area of base = x^2 cost for the base = 2x^2 total cost = 3x^2 + 4xy = 114 y = (114 - 3x^2)/4x...

Math (Calculus) (mean value theorem emergency)
your secant equation is correct checking the other parts: f '(x) = 2x - 1 ---> you had that setting that equal to 1, since the slope of our secant is 1 2x-1 = 1 2x = 2 x = 1 so all you have to do is sub that back into the original f(1) = 1 - 1 - 12 = -12 So the point ...

algebra
yes

algebra
no Why do you think it is C or are you just guessing?

algebra
no , B does not have the necessary brackets

algebra
if the point is (a,b) and the slope is m then the equation is y - b = m(x - a) now which one of the given answers follows that pattern?

Math help pls. !!
(2x-3)(5x+2)=0 This is only possible if one or more of the given factors equal zero. But we don't know which one, so 2x-3 = 0 OR 5x+2=0 2x = 3 OR 5x = -2 x = 3/2 or x = -2/5

Math
(1/2)x^2 - 2x = 6 times 2 x^2 - 4x = 12 x^2 - 4x - 12 = 0 it factors: (x - 6)(x + 2) = 0 now follow the steps I showed you here http://www.jiskha.com/display.cgi?id=1479598571

math
number of digits = 3x2x1 = 6 , we could actually list them 137 173 317 371 713 731 Here is a list of primes: http://primos.mat.br/indexen.html you will find that all are prime except 371, 713 and 731 731 =17 x 43 713 = 23 x 31 371 = 7 x 53

math algebra
I did this when you were rita http://www.jiskha.com/display.cgi?id=1479589996

FUNCTIONS HELPPPPP????
After seeing how you responded to Steve when he helped you with this question .... http://www.jiskha.com/display.cgi?id=1479505703

Math
Volume of cylinder = ?(r^2)(h) plug in your values.

math algebra
rate of gandola in still water --- x mph speed of current ---- y mph time to go 2.8 miles with the current = 2.8/(x+y) time to go 2 miles against the current = 2/(x-y) they are the same! 2.8/(x+y) = 2/(x-y) 2.8x - 2.8y = 2x+2y .8x = 4.8y 8x = 48y x = 6y or y = (1/6)x All we ...

math algebra
Gray's rate = 1/15 Anna' rate = 1/20 Job done by Gray = 6(1/15) = 2/5 leaving 3/5 of the job left to be done by Anna time for Anna to complete = (3/5) / (1/20) = 12 It will take her 12 days to finish the roof

Math
6 1/7 - 1 5/21 = 43/7 - 26/21 = 129/7 - 26/21 = 103/21

math algebra
assuming that you meant: f(x) = (x+1)/(x^2-9) and g(x) = x/(x-3) The domain for both f(x) and g(x) are all values of x except those that make the denominator zero domain of f(x): all x's except x = ±3 domain of g(x): all x/s except x = 3 (f+g)(x) = (x+1)/(x^2 - 9...

math - business
Steve is probably off line now, so I will answer. For any quadratic function of the form y = ax^2 + bx + c the x of the vertex is -b/(2a), once you have the x you just sub that back into the equation to get the y of the vertex. In your case: P = -.005x^2 + 4x - 200 a = -.005 b...

GEOMETRY
You have similar triangles. Since XA = AY AY : XY = 1 : 2 triangle XYZ is similar to triangle AYB XZ/XY = AB/AY 8.4/2 = AB/1 AB = 8.4/2 = 4.2

Algebra
3n^2+5n-100=? If this is a quadratic equation, the your ? is 0 If you are dealing with the corresponding quadratic function you would normally find it as y = 3n^2 + 5n - 100 , where y is the dependent variable, and n is the independent variable What about it ?

Pre-calculus
Watch those brackets, you must have meant: (sin(x+y)+sin(x-y))/(cos(x+y)+cos(x-y))=tanx LS = (sinxcosy + cosxsiny + sinxcosy - sinxcosy)/(cosxcosy - sinxsiny + cosxcosy + sinxsiny) = 2sinxcosy/(2cosxcosy) = (sinx/cosx)(cosy/cosy) = tanx = RS

Pre-calculus
I checked with my calculator and actually found the angles. It works !!!

Pre-calculus
If siny = -2/?13 , and coty ?0, then y is in quad III so cosy = -3/?13 then sin 2y = 2sinycosy = 2(-2/?13)(-3/?13) = 12/13 cos 2y = cos^2 y - sin^2 y = 9/13 - 4/13 = 5/13 so sin 2y = 12/13 and cos 2y = 5/13 if sin 2x = 7/25 remember cos^2 (2x) = 1 - sin^2 (2x) = 1 - 49/625 = ...

Probability Help
at least one boy ----> exclude the case of all 5 girls, which is (1/2)^5 = 1/32 prob(at least one boy in 5) = 1 - 1/32 = 31/32

Math
A:B:C = 5:5:7 or 5x : 5x : 7x Cindy ate 30 Skittles less than Ann and Ben together -----> 7x = 5x + 5x - 30 -3x = -30 x = 10 5x = 50 7x = 70 They ate 50+50+70 = 170 of them

Calculus
g(x) = sinxcosx g ' (x) = sinx(-sinx) + cosxcosx = cos^2 x - sin^2 x = cos 2x at x = ?/3 g '(x) = cos (2?/3) = -.5 equation: y - ?3/4 = (-1/2)(x - ?/3) So I agree with your answer. for a max/min of g(x) , g '(x) = 0 cos 2x = 0 2x = ?/2 or 2x = 3?/2 x = ?/4 or x = 3...

Calculus
with the information given, you should be able to form the equation h = -16t^2 + 68t + 6 dh/dt = -32t + 68 = 0 for a max of h 32t = 68 t = 2.125 evaluate h when t = 2.125

argghh - Calc
forgot to change the units from km/h to m/s go with Damon's answers

Calc
if we have acceleration of a, then v = at + c case1: when t=0, v=25 25 = 0+c ---> v = at + 25 so when t = 13, v = 90 90 = 13a + 25 a = 65/13 = 5 m/s^2 -----> v = 5t + 25 distance = (5/2)t^2 + 25t + k when t=0 , distance = 0 , so k = 0 distance = (5/2)t^2 + 25t when t = ...

Math
I agree with all of them

Math
amount taken out as loan = 25 - .2(25) = 20 or just take .8(25) = 20 amount owing after 8 years = 20(1.025)^8 = 24.368 gh cedis

Math
1 7/10 = 17/10 "as many" suggests multiplication e.g. bill eats 3 times as many donuts as Bob if Bob eats 4 donuts, then Bill would eat 3*4 or 12 donuts so Elizabeth has (17/10) as many as Rosalie. let Rosalie's number of plants be x then: (17/10)x = 51 ----> ...

Math
time for first trip = d/x time for return = d/y total time = (d/x + d/y) = (dy + dx)/(xy) = d(x+y)/(xy) total distance = 2d average speed = 2d/( d(x+y)/(xy) ) = 2xy/(x+y) = 50 xy/(x+y) = 25 xy = 25x + 25y 25y - xy = 25x y(25 - x) = -25x y = 25x/(x-25) e.g. let x = 50, then y...

math
horizontal path = 15(2.5) = 37.5 units^2 vertical path = 9(2.5) = 22.5 units^2 total = 60 units^2 BUT, we counted the intersection of the paths twice, so we have to subtract 2.5(2.5) or 6.25 units^2 leaving us with 63.75 units^2

Geometry
So what is (3/2)(4.8) ? Just add up your 4 sides, remember they come in equal pairs.

Order MATH!
I suggest you change them all to decimals, and then it is easy to see.

Pre-calculus
correction for #1, should say: (1+cosx)/(1-cosx) = (secx + 1)/(secx - 1) RS = (1/cosx + 1)/(1/cosx - 1) = (1/cosx + 1)/(1/cosx - 1) * cosx/cox = (1+ cosx)/(1 - cosx) = LS Well, that was easy. #2, hint: change everything to sines and cosines expand and simplify the LS #3, use ...

Maths
So in 60 minutes he can type 3200 words. How many words can he type in 1 minute? Then how many in 15 minutes ?

additional maths (maths)
so you just want the max of d(t) find the derivative, set it equal to zero, and solve that for t Once you have the value of t which gives you the maximum, plug it back into d(t) to actually find that distance. Very straight-forward.

Maths
The missing angle ? = 45° by the sine law: a/sin35 = 40/sin100 a = 40sin35/sin100 = appr 23.3 c/sin45 = 40/sin100 c = 40sin45/sin100 = appr 28.7 area = (1/2)(ab)sin45 = appr 329.5 units^2

maths
so he gave away 60%, leaving him with 40% .4x = 9600 solve for x

Math (Differentials)
our f(x) = x^(1/3) , and f ' (x) = (1/3)x^(-2/3) = 1/(3(x)^(2/3) ) I will go with your x = 27 , dx = -2 f(x + dx) is appr = f(x) + f ' (x) (dx) f(25) = f(27) + (1/3)(27)^(-2/3) = 3 + (1/27)(-2) = 3 - .0741 = 2.926 you simply added the part at the end instead of ...

algebra 2
Your calculations are correct (sum of roots = 2+3i + 2-3i = 4 product of roots = (2+3i)(2-3i) = 4-(-9) = 13 ) It said to write the quadratic equation, which is x^2 - 4x + 13 = 0 you had y = x^2 - 4x + 13 , which is the quadratic function.

Math
I will place the parabola as opening to the right, with its vertex at (0,0) so the equation is y^2 = 4px, where (p,0) is the focus but (6,16) lies on it 16^2 = 4p(6) p = 256/24 = 32/3 So it should be placed at (32/3 , 0)

Geometry
original area = base x height = bh new area = .7b x 1.2h = .84bh so there is a 16% decrease in the area

Calculus: Centers of Mass
A quick calculation shows that the line intersects the parabola at (2,2) in the first quadrant lots of work ahead of us: first you must find the area of the region, it has to be done in two parts: from x=0 to x=2 under the curve, then from x=2 to x=4 under the straight line ...

correction - Difficult Math
I misread "Thirty of the cards from his cousin are National League players" as one third of the cards from his cousin are NL players

Difficult Math
total collection ---- x from dad --- x/4 from uncle --- x/5 ---> (.2)x = (2/10)x = x/5 from brother --- x/2 leaving : x -x/4 - x/5 - x/2 = x/20 so from cousin = x/20 so (1/3)(x/20) = 30 x = 1800 Steve has 1800 cards check: from dad = 1800/4 = 450 from uncle = .2(1800) = 360...

Math
999,999,999,999 = appr 1,000,000,000,000 = 10^12 ( you would be off by $1 on 1 Trillion dollars) 100,000,000,000,000 = 10^14 so 100,000,000,000,000 times 999,999,999,999 = 10^12 * 10^14 = 10^26 that would be 100 septillion.

Math
In arithmetic "of" means multiplication, so 1/10 of 2(10)+4(1)+6(1/10)+7(1/100)+8(1/1000) = (1/10)(20) + 4 + .6 + .07 + .008 = 2+4+.6+.07+.008 = 6.678 http://www.wolframalpha.com/input/?i=evaluate+1%2F10+*+2(10)%2B4(1)%2B6(1%2F10)%2B7(1%2F100)%2B8(1%2F1000) if you ...

Algebra
Help with what? You have given us two different circles. What do you want to do? They do intersect. Here is a picture of your problem http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%2B6y%2B5%3D0+,+x%5E2%2By%5E2-2x-8%3D0

Maths
no XYYYY , where X is the vowel, Y can be anything else number of ways = (2)(4!) = 48 e.g. E(BGIN) - one of the 24 ways to arrange BGIN I(GBEN) - one of the 24 ways to arrange GBEN

Maths
That result is like adding 3/10 + 14/20 + 24/30 = 41/60 Wow, just adding the numerators and the denominators ! Unfortunately Math doesn't work like that 3/10 + 14/20 + 24/30 = 18/60 + 42/60 + 48/60 = 108/60 for 3 tests so average = (108÷3)/60 = 36/60 = 60% By simply...

calc
no, for the 2xy term you have to use the product rule 2y dy/dx + (2x)(dy/dx) + 2y(1) - 3x^2 = 0 keep all the dy/dx terms on the left, everybody else goes to the right 2y dy/dx + 2x dy/dx = 3x^2 - 2y factor out the dy/dx dy/dx (2y + 2x) = (3x^2 - 2y) divide dy/dx = (3x^2 - 2y...

math
The best way to do this is to actually sketch it. I am sure it will make perfect sense to you after you draw it. Remember that y =-2 is a horizontal line 2 units below the x-axis

math
profit = revenue - cost = 12x - .01x^2 - 8^x - 7 d(profit)/dx = 12 - .02x - (8^x)(ln8) = 0 for a max of profit 12 - .02x = ln8 (8^x) if x = 0, LS = 12 , RS = ln8 or appr 2.08 if x = 1, LS = 11.98 , RS = appr 16 so there is a solution between 0 and 1 This question does not make...

Math
Strange wording. "What fraction" of what should the shorter side be increased? Since the sides are stated in a ratio, they could be 4 cm by 5 cm, 40 miles by 50 miles, 8 ft by 10 ft, etc In each case the shorter side would be increased by 1/4 of its original length. ...

math
you are simply solving the quadratic 187 = -16t^2 + 45t + 364 16t^2 - 45t - 177 = 0 solve by using the formula, one of the answers will probably be negative. Reject it.

Maths
I will assume the 2nd direction is 125° The angle between the two directions is 90° so AC = ?(120^2 + 200^2) = 233.238 km or Suppose we did not see that 90° ,we could simply use vectors AC = (120cos35,120sin35) + (200cos125,200sin125) = (98.298.., 68.829..) + (-114...

Maths
As an illustration of your problem, place 3 identical coins, e.g. 3 quarters in such a way that they are tangent to each other. Sketching a triangle around them results in an equilateral triangle, we want the perimeter of that triangle. Let's concentrate on one of these ...

Algebra
place the vertex at (0,0) and the focus at (8,0) The directrix will be x = -8 let P(x,y) be any point By definition: ?( (x-8)^2 + y^2) = x+8 square both sides x^2 - 16x + 64 + y^2 = x^2 + 16x + 64 y^2 = 32x so at the point where the dish is 10 ft wide, y = 5 25 = 32x x = 25/32

Math
10,000(1.04)^n = 15000 1.04^n = 1.5 take logs of both sides log 1.04^n = log 1.5 n log 1.04 = log 1.5 n = log 1.5/log1.04 = 10.338.. 10 years will not be enough , so she makes 15,000 or more in the 11 th year for the second question you have an arithmetic sequence with a = ...

6 grade math
no need for guessing, just reverse the steps: the first thing we did was multiply by 2, then subtract 27 to get 407 So everything done in reverse: ( 407+27) divide by 2 = 434 ÷ 2 = 217

Algebra
x e^.06t = 70000 x = 70000/e^(.06(19)) = 22,387.33

Statistics
prob(exactly one boy) = C(7,1)xC(5,4)/C(12,5) = 7(5)/792 = 35/792 prob(exactly 2 boys) = C(7,2)xC(5,3)/792 = 21(10)/792 = 35/132 at least one boy = 1 - prob(all girls) = 1 - 1/792 =791/792

Math
you second equation is x-2055 = .25y , what's with the G ? but y = x x-2055 = .25x .75x = 2055 x = 2740

Math
Did you mean, find cos t ? if so, cos t = 5/?29

mathematics
Did you mean x+y=1 x-y=3 ?? if so, add them to get 2x=4 x=2 now subtract them 2y = -2 y = -1

math
Just translate from English to Math larger number --- x smaller number --- y x-y = 15---> x = y + 15 3x = 8y 3(y+15) = 8y 3y + 45 = 8y 45 = 5y y = 9 , then x = 9+15 = 24 state your conclusion

math
speed of train ---- t km/h speed of car ----- c km/h 120/t + 480/c = 8 15/t + 60/c = 1 times tc tc = 15c + 60t 200/t + 400/c = 25/3 times tc (25/3)tc = 200c + 400t tc = (3/25)(200c + 400t) = 24c + 48t 24c + 48 = 15c + 60t 9c = 12t c = 4t/3 sub into 15/t + 60/c = 1 15/t + 60/(...

math
boys rate = 1/b men's rate = 1/m job done by 2 men and 5 boys in 4 days = 4(2/b + 5/m) = 8/b + 20/m job done by 4 men and 4 boys in 3 days = 3(4/m + 4/b) = 12/m + 12/b 8/b + 20/m = 12/m + 12/b 8/m = 4/b 8b = 4m m = 2b or b = m/2 The man's rate is twice the boy's ...

TRIANGLE MATH HELP!!!
Obviously.

TRIANGLE MATH HELP!!!
clearly 47:29:104 ? 46:30:104, but close and 4 : 6 : 8 ? 5.6 : 8 : 11 because: 5.6/4 = 1.4 8/6 = 1.333... 1.375 which answer matches my conclusion

Math Help!!!
6/202.5 = x/52.5 202.5x = 6(52.5) 202.5x = 315 x = 315/202.5 = 3150/2025 = 14/9 or 1 5/9 or 1.5555.... take your pick 1.555... rounded to one decimal is 1.6

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