Saturday
February 13, 2016

Posts by Reiny

Total # Posts: 32,979

Algebra
number of hrs at job A -- x number of hrs at job B -- y x+y ≤ 15 4x + 8u ≥ 80 or x + 2y ≥ 20
January 1, 2016

Math
a) The way you typed it .... 125x = 65 x = 65/125 = 13/25 if you meant: 5^(3x) = 65 take log of both sides, then use log rules 3x log5 = log65 x = log65/(3log5) = appr .865 b) again, the way you typed it... 4x + 3 = 80 4x = 77 x = 77/4 did you mean 2^(2x + 3) = 80 or did you ...
January 1, 2016

Maths
let that constant value be k according to your wording , we should get a value of k no matter what x we choose. let x = 0 then 0A + 0B + 0C + (-2)(3) = k k = -6 let x = 2, 0 + 0 + 10C + 0 = -6 C = -3/5 let x = -3 , 0 + 15B + 0 + 0 = -6 B = -2/5 let x = -1 , 6A + 3B - 2C -6 = -...
January 1, 2016

MATHS
You are welcome, Happy New Years
December 31, 2015

MATHS
Let their times to do the job alone be A, B, and C days respectively A and B can do a piece of work in 10 days --> 1/A + 1/B = 1/10 A + B = AB/10 10A + 10B = AB B and C in 15 days: 1/B + 1/C = 1/15 B+C = BC/15 15B + 15C = BC A and C in 12 days 12A + 12C = AC Not the nicest ...
December 31, 2015

physics
you have two ordered pairs of the form (t,v) namely (0,0) and (6,30) average acceleration = change in velocity / change in time = (30-0)/(6-0) (m/s) / s = 5 m/s^2 I suspect a typo in your book
December 31, 2015

math
speed of train = x km/h speed of car = y km/h total distance is D km 60/x + (D-60)/y = 4 60y + (D-60)x = 4xy 100/x + (D-100)/y = 4 1/6 = 25/6 100y + (D-100)x = 25/6 xy you seem to have some missing information, because we have 3 variables, but only 2 equations. well, let's...
December 30, 2015

math
given the circumference, we can find the radius r Once you have that, use the formula Area = πr^2
December 30, 2015

Math
let the three numbers be a , ar, and ar^2 after 4 is subtracted from the third, we have a , ar , and ar^2 - 4 they are now in an AP, that is ar - a = ar^2 - 4 - ar 2ar - a - ar^2 = -4 a(2r - 1 - r^2) = -4 a = 4/(r^2 - 2r + 1) = 4/(r-1)^2 now we subtract 1 from the 2nd and 3rd...
December 30, 2015

ravehs school
Make two diagrams, one showing the sector in the original circle, and the second showing the cone It should be clear to you that the arc of the sector becomes the circumference of the base of the cone. arc/circumference = 108/360 arc/20π = 3/10 arc = 60π/10 = 6π...
December 30, 2015

math 10
for #2, I suggest taking logs x = 2^100 logx = 100log2 = 30.102.. y = 3^60 logy = 60log3 = 28.627.. z = 10^30 logz = 30log10 = 30 thus logy < logz < logx then y < z < x ----> y is the smallest
December 30, 2015

math 10
#1 sum(1) = 1/2 sum(2) = 1/2 + 2/3! = 1/2 + 1/3 = 5/6 sum(3) = 5/6 + 3/4! = ( (3+1)! - )/(3+1)! = 5/6 + 1/8 = 23/24 sum(4) = 23/24 + 4/5! = 23/24 + 1/30 = 119/120 = ((4+1)! - 1)/(4+1)! it looks like sum(n) = ( (n+1)! - 1)/(n+1)! so sum(11) = (12! - 1)/12! = 479001599/479001600...
December 30, 2015

geometry
let the equation have the form y = ax^2 + bx + c for (1,1) --> 1 = a + b + c for (2,2) --> 2 = 4a + 2b + c for (-1,5) --? 5 = a - b + c subtract #1 - #3: 2b = -4 , b = -2 subtract #2 - #1: 3a + b = 1 sub in b = -2 3a - 2 = 1 3a = 3 a = 1 sub into the first: 1 - 2 + c = 1...
December 30, 2015

Math
Have you tried with a Venn diagram Draw 2 circles, C and M for Computer and Math, which do NOT intersect. Draw a third circle P for Physics, which intersects the two others. You should have two intersections, C with P and M with P. Enter 150 into M AND P You will now have to ...
December 30, 2015

maths
I did this for you on Sunday http://www.jiskha.com/display.cgi?id=1451271437 and I assume that 1÷3 meant 1/3
December 29, 2015

Math
You should know the ratio of sides of your triangle to be: 1 : √3 : 2 or x : √3x : 2x, where x is a constant so in the next one: a : 2x : c then c/2x = 2x/√3x √3 cx = 4x^2 c = 4x/√3 a/x = 2x/√3x a = 2x/√3 general triangle: (2x/√3...
December 29, 2015

maths
Log3^x+logx^3=2.5 xlog3 + 3logx = 2.5 nasty equation to solve let's try this very primitive method: let x = 1.5 , LS = 1.5log3 + 3log1.5 = 1.243, too small let x = 1.8, LS = 1.62 , still too small let x = 2.5, LS = 2.3866 , getting there let x = 3, LS = 2.86 , too high let...
December 29, 2015

Math
I assume point A is on line l Place B and C anywhere on line m draw the perpendicular bisector of BC, and extend the line Notice that no matter where you draw B and C, this right bisector will cut line l only once. label that point A. properties of this right bisector: AB = AC
December 29, 2015

Math
pears eaten by Pete --- 2x Tweet -- 3x Honk ---5x Honk - Pete = 12 5x - 2x = 12 x = 4 so Pete ate 8 Tweet ate 12 and Honk ate 20
December 29, 2015

maths (bedmas)
15-[8³+3²-{8²-(42+2³)-5³}-2²] keep nibbling away at it from the inside = 15-[8³+3²-{8²-(50)-5³}-2²] = 15-[8³+3²-{-111}-2² = 15-[8³+3²+111-2²] = 15-[512 + 9 + 111 - 4] = 15 - 628 = -613
December 29, 2015

math
Steve answered this for you at 5:45. Why are you posting the same question again ?
December 29, 2015

MATH
straight-forward product rule f(x)=(5x-7x^3)(2+sqrt(x)) f(x)=(5x-7x^3)(2+(x)^(1/2)) f ' (x) = (5x - 7x^3)(1/2)x^(-1/2) + (2 + x^(1/2))(5 - 21x^2) clean it up as needed
December 29, 2015

mats
done, see your previous post on this
December 27, 2015

maths
This one you should be able to do. (as well as the others I did for you) Do you know how to find areas of triangles and parallelograms ?
December 27, 2015

Maths
lots of 2:1 ratios, triangle DCE = 1/4 triangle ABC = (1/4)(144) = 36 m^2
December 27, 2015

Maths
the triangle and the ||gram have the same height and base so the ||gm = 2(75.2) = 150.4 m^2
December 27, 2015

mats
btw, do you realize that G is the centroid of the triangle ?
December 27, 2015

mats
label all your stuff since BD = CD, area BDG = area DGC = x since DG : GA = 1 : 2 area of BDG : BGA = 1 : 2 = x : 2x label area of triangle BGA as 2x same for triangle AGC so triangle BGC = 2x triangle AGC = 2x triangle ABC = 6x so triangle AGC = 2x/6x = 1/3
December 27, 2015

accounting and finance
let the semi-annual rate be i 2000(1+i)^18 = 5000 (1+i)^18 = 2.5 take the 18th root of both sides 1+i = 2.5^(1/18) = 1.05222 i = .05222 the rate is .10445 or appr 10.445% per annum compounded semi-annually
December 27, 2015

Math
correct, I attempted to find angle A sinA/10 = sin100°/5 sinA = 10sin100/5 = appr 1.97 not possible , so no such triangle can exist Trust you math ability
December 27, 2015

Math - not komenco
How did they define "exponential sequence" in your course ?
December 27, 2015

math
no, you have a product rule y = (x^2)(e^(x^2)) y' = (x^2)(2x)(e^(x^2)) + (e^(x^2)) (2x) now factor this y' = (2x)(e^(x^2)) (x^2 + 1) now you have triple product, so y'' = (2x)(e^(x^2)) (2x) + (2x)(x^2 + 1)(2x(e^(x^2)) + 2(e^(x^2)) (x^2 + 1) = 2 e^(x^2) (2x^2 + ...
December 27, 2015

math
let me see what you got for the first derivative, so I can see if you are on the right track.
December 27, 2015

math
The way you typed it, sinπ would just be a constant, and h ' (x) = -sinπ/x^2 I will guess that you meant h(x) = sin (π/x), which would be a totally different function h '(x) = cos(π/x) ( -π/x^2) so h ' (4) = (-π/16)cos(π/4) I will...
December 27, 2015

math
√k^2/3 =(k^(2/3) )^(1/2) = k^(1/3) b) is it √ab^2 , the way you typed it, or √(ab^2) ? first way would be a^(1/2) b^2 2nd way would be a^(1/2) b c) and d) same problem with interpretation. is it: 4√81x^8y^12 or 4√(81x^8y^12) etc
December 26, 2015

Math
so it takes 6 working hours to clean split that amongst 4 people takes 6/4 hrs or 1.5 hours
December 26, 2015

algebra
I assume that is: (x^2 - 4xy) ÷ x = x(x - 4y)/x = x - 4y , x ≠ 0
December 26, 2015

JNU
Your choices are quite limited. Since the digits have to be whole numbers, and 8 = 1x8 or 2x4 only 4 choices for the first condition are: 18, 81, 24, or 42 Which of these also matches the second condition of your problem?
December 26, 2015

math
time taken by larger diameter tap --- x hrs time taken by smaller diameter tap ---x + 10 hrs combined rate = 1/x + 1/(x+1) = (2x+10)/(x(x+10)) (2x+10)/(x(x+10)) = 1/(75/8) = 8/75 8x^2 + 80x = 150x + 750 8x^2 - 70x - 750 = 0 (x-15)(8x + 50) = 0 x = 15 or x = some negative, ...
December 26, 2015

math
Your lack of punctuation and poor sentence structure makes this question ambiguous. e.g. Did you mean: "K is 9 years older than L. After 7 years the total of their age is 93." or "K is 9 years older than L after 7 years. The total of their age is 93." We ...
December 26, 2015

Math
treat the given data as two ordered pairs (0,180000), (10,10000) , where the first element is the time, and the 2nd is the value slope = (10000 - 180000)/(10-0) = -17000 , interpret that as depreciating $17000 each year equation: V = -17000t + 180000 (0,180000) would be like ...
December 24, 2015

stats
From the several back and forth replies, your post is not very clear. looking at your chart, there are a total of 60 chicken, of which 10 are French hens so prob(selecting 3 French hens from the 60 chicken) = C(10,3)/C(60,3) = 120/34220 = 6/1711 you also make mention of ...
December 23, 2015

physics
h = -4.9t^2 + 100 A. to reach the ground h = 0 0 = -4.9t^2 + 100 4.9t^2 = 100 t^2 = 100/4.9 t = √(100/4.9) = appr 4.5 seconds B. v = -9.8t sub in t = 4.5 C. original equation is h = -4.9t^2 + 12t + 100 set equal to zero again, and solve using the quadratic equation. Take...
December 23, 2015

Math
Paul, if you had looked back, you would have seen that variations of your question have been answered several times I even did it for you both ways, with 300 books and with 3000 books. ignore Oscar's reply, I have shown it to be wrong http://www.jiskha.com/display.cgi?id=...
December 23, 2015

Nicholas
it is generally agreed that the Formula 1 cars of today will go from 0 to 100 km/h in less than 2 seconds. My guess that it will reach 10 m/s within a few metres.
December 23, 2015

Math
ok, y = tanx/x dy/dx = (x(sec^2 x) - tanx (1) )/x^2 which could be split up into sec^2 x/x - tanx/x^2 Did you forget the last term of -tanx/x^2 ? there really is not much point in further simplifying my first line answer of (x sec^2 x - tanx )/x^2
December 23, 2015

Math
y = tanx/x dy/dx = (x sec^2 x - tanx)/x^2 when x = π/4 , which is 45° dy/dx = ( (π/4)(2) - 1)/(π^2/16) =(8π-16)/π^2 so the slope of the normal is π^2/(16-8π) also when x = π/4, y = 1/(π/4)= 4/π equation of normal: y - 4/&#...
December 23, 2015

Math
y = sinx + 3 dy/dx = cosx when x=π, dy/dx = cosπ = -1 so the slope = -1 also when x = π, y = sinπ + 3 = 3 so the point of contact is (π,3) equation of tangent: y-3 = -1(x-π) y = -x + π+3
December 23, 2015

math
triple the first: 9x + 6y = 57 double the 2nd: 4x - 6y = -12 add them: 13x = 45 x = 45/13 sub into first: 3(45/13) + 2y = 19 2y = 19 - 135/13 = 112/13 y = 56/13 I checked the answers, they are correct
December 22, 2015

Math
I don't understand the question the 5 3/5 has no units. Are you saying that it fill with 5 3/5 gallons every 7/5 hrs? At that rate a 50,000 gallon swimming pool would take over 265 days to fill, ooops the swimming season is over. Check your question and repost it
December 22, 2015

Calculus
from 2y-3x=5 , we know that the slope of the tangent must be 3/2 f(x) = a + b√x = a +b(x)^(1/2) f ' (x) = (1/2)b x^(-1/2) or b/2√x so b/2√x = 3/2 2b = 6√x b = 3√x also (1,4) lies on f(x) = a + bx 4 = a + b since b = 3√x = 3√1 = 3 ...
December 22, 2015

Math
Seith = 160 + 8w , where w is the number of weeks Keira = 270 - 3w so we want 160 + 8w = 270 - 3w solve for w, Your solution becomes the explanation
December 22, 2015

MATH HELP
First of all, I would have reduced the equation to x + 2y = 400 , so now you can mentally find the x and y intercepts as (400,0) and (0,200) See how easy it is now to sketch the line ? so you clearly want all the stuff below that line in the first quadrant your answer has to ...
December 22, 2015

Stats
number of Jacks = 4 number of red cards = 26 , of which 2 are Jacks so Jacks or red cards = 26 + 4-2 = 28 prob(Jack or red) = 28/52 = 7/13
December 22, 2015

correction - PrimaryMatheMatics 4A textbook
OOPS, I read that as 300, should have been 3000 easy to fix x+2x+2x+10 = 3000 5x = 2990 x = 598
December 22, 2015

PrimaryMatheMatics 4A textbook
I would start with defining the number of books in the third pile is x then the number of books in the 2nd pile is 2x and the first pile is then 2x+10 (I just translated the English to Math) their sum is 300 x + 2x + 2x+10 = 300 5x = 290 x = 58 Third pile has 58 books (2nd has...
December 22, 2015

Math
the range is from -11 to 27 or 38° so in our trig function we have T = 19sin(.....) + 8 as a start the period is 365 days, so 2π/k = 365 and k = 2π/365 so we have T = 19 sin (2π/365)d + 8 where d is the number of the day in our year (there are charts ...
December 22, 2015

Trignometric Functions
see your post above this one
December 22, 2015

maths, physics,
Please define "heading of 70° Are you pointing clockwise from North?
December 22, 2015

math
Nothing to solve. To "solve" we need an equation, you have given me no equation.
December 22, 2015

math
We don't need the principal nor the time to find the effective annual rate All we are looking for it the annual rate i, which is equivalent to a rate of .0387/12 per month that is, (1+i)^1 = (1+.0387/12)^12 1+i = 1.0393939 i = .03939 or appr 3.939% (note, the decimals only...
December 21, 2015

math
I side with Ms Sue. Doesn't matter what Google said. We solve equations. You did not give us an equation. So "no can do"
December 21, 2015

maths
the smallest 2 digit number is 10, the largest is 99 How many is that ? ---> sum1 multiples of 5 are all those that end in zero or end in 5 e.g. 10, 20 , ... 90 15, 25, 35 ... 95 how many is that --> sum2 prob = sum2/sum1
December 20, 2015

math
2x + 3y = 7 now double the 2nd: 2x - 4y = 8 subtract them: 7y = -1 y = -1/7 sub into the 1st: 2x + 3(-1/7) = 7 2x = 52/7 x = 26/7
December 20, 2015

math
adult tickets sold --- x student tickets sold --- 540-x solve: 10x + 7(540-x) = 4765 or x+y = 540 10x + 7y = 4765
December 20, 2015

Math
number of push-ups for Doug = 8x number of push-ups for Adam = 3x solve: 8x - 3x = 15 take over
December 20, 2015

trigonometry
I will let you play around with http://www.wolframalpha.com/input/?i=y%3D+sin%282%28x%2B1%29%29 remember x is in radians, also notice the extra set of brackets I put in. What happens when we enter it as you typed it ? try y = cos(5(x - 3)) + 2 ignore the fancy math at the ...
December 20, 2015

Danville
According to your data, the height would be given by h =-4.9t^2 + 20t + 5 totally absurd numbers, as you will see when we "solve" this problem we have a downwards parabola and the t of the vertex is -20/-9.8 = appr 2.04 seconds his maximum height is -4.9(2.04)^2 + 20...
December 20, 2015

Maths tangent help me damon or steve help
2x + x dy/dx + y = 0 dy/dx = (-2x - y)/x from the tangent line we can see that the slope is 3 so, (-2x - y)/x = 3 -2x - y = 3x y = -5x sub back into the original equation: x^2 + x(-5x) + 16 = 0 x^2 - 5x^2 = -16 -4x^2 = -16 x^2 = 4 x = ± 2 when x = 2, 4 + 2y + 16 = 0 y...
December 20, 2015

math
picking it up from Damon's first = 4 third = 4+2d 7th = 4+6d but these also form a GP (4+2d)/4 = (4+6d)/(4+2d) 16 + 16d + 4d^2 = 16 + 12d^2 8d^2 -16d = 0 8d(d - 2) = 0 d = 0 , or d = 2 for a=4, and d=2, the sum of the first three AP terms are 4 + 6 + 8 = 18 check: term1 = ...
December 20, 2015

Math
#1, A and D is correct #2 .0112 = 112/10000 = 7/625 they should have reduce the answer of C
December 19, 2015

MATH HELP
I think Oscar meant f(t) = 3(2)^t so f(6) = 3(2^6) = 192 at least that way one of the answers will fit.
December 19, 2015

Maths
to have your expanded cubic start with x^2 you must have cubed a binomial of the form (x + m)^3 if we expand (x+m)^3 we get x^3 + 3x^2 m + 3x m^2 + m^3 compare that with your given x^3 + 3ax^2 + bx + c we can say: 3a = 3 ---> a = 1 3xm^2 = bx ---> b = 3m^2 and c = m^3 so...
December 19, 2015

Maths
I answered this for you when you typed it out correctly, (in its present form, where do the p and q enter the picture ??) http://www.jiskha.com/display.cgi?id=1450523328 What part of my solution did you not like, I even verified my answer.
December 19, 2015

Math
Jocelynn, looking at your answer, I can see that you just multiplied the whole number parts and then the fraction parts of your mixed fractions which is not the way fractions are multiplied Mixed fractions are sort of cute to look at but they serve no purpose, (sort of like ...
December 19, 2015

math
let the weight of the container be x kg let the weight of the water when full be y kg x + y = 2.25 kg x + .2y = .77 subtract them .8y = 1.48 kg y = 1.85 kg then x+1.85 = 2.25 x = .4 kg so x + .4y = .4 + .74 kg = 1.14 kg
December 19, 2015

Maths
Your solution for x = 3 is correct, now all you have to do is sub x = 3 into your 3 terms to get 4, 8, 16 you already knew r = 2 from r = 2(3) - 4 = 2 and a = 4 from a = x+1 = 4
December 19, 2015

Math
let the roots be m and n where n = m^2 we know sum of roots = m+n = p and the product of the roots is mn = q LS = p^3 - q(3p+1) - q^2 = (m+n)^3 - mn(3m+3n+1) - m^2n^2 = m^3 + 3m^2n + 3mn^2 + n^3 - 3m^2 n - 3m n^2 - mn - m^2 n^2 = m^3 + n^3 - mn - m^2n^2 but n = m^2, so ... = m...
December 19, 2015

Maths
we must have squared an expression such as (x^2 + bx + c) let's see what we get: (x^2 + bx + c)^2 = (x^2 + bx + c)(x^2 + bx + c) = x^4 + bx^3 + cx^2 + bx^3 + b^2x^2 + bcx +cx^2 + 2bcx + c^2 = x^4 + 2bx^3 + x^2(c+b^2+c) + 2bcx + c^2 comparing this with x^4+6x^3+13x^2+mx+n...
December 19, 2015

Math
the roots would be (-b +√(b^2 - 4ac)/2a and (-b - √(b^2 -4ac)/2a we are told that the difference between them is 1 so, (-b+√(b^2-4a))/2a - (-b - √(b^2-4ac)/2a = 1 2√(b^2-4ac)/2a = 1 √(b^2 - 4ac) = a square both sides b^2 - 4ac = a^2 b^2 - a^...
December 19, 2015

Math
after you simplify , you get: 6x = 2 x = 2/6 = 1/3 In general, the equation of a line describes the relationship that the x and the y have for each ordered pair on the line. e.g. if we had y = 2x + 1, that would mean that for every x value that you choose, the y will be one ...
December 19, 2015

calc
I will assume you meant s = 1/(t^2 + 1) , (use ^ to show exponentiation) = (t^2 + 1)^-1 v = ds/dt = -1(t^2 + 1)^-2 (2t) = -2t/(t^2 + 1)^2 so at t = 2 v = -4/(5)^2 = -4/25 ft/s the negative tells me the object is slowing down
December 18, 2015

calculus
(1/2)^(t/5730) = .29 (.5)^(t/573) = .29 take logs of both sides and follow rules of logs to get (t/5730)log.5 = log.29 t/5730 = log.29/log.5 t = appr 10,233 years
December 18, 2015

Maths
we would be solving: 50000(1+i)^5 = 100000 (1+i)^4 = 2 take the 4th root 1+i = 1.189207.. i = .18920.. or 18.92 % as the effective rate to 2 decimals
December 18, 2015

Maths trigonomentry
Go with Damon's , he used an easier method (but I thought mine was quite elegant)
December 18, 2015

Maths trigonomentry
let's change 3cosx+4sinx into a single sine curve of the form y = a sin (x+k) we know asin(x+k) = asinxcosk + acosxsink comparing our terms asinxcosk = 4sinx acosk = 4 a = 4/cosk acosxsink = 3cosx a sink = 3 a = 3/sink then 3/sink = 4/cosk 4sink = 3cosk sink/cosk = 3/4 ...
December 18, 2015

math
The sum of the exterior angles of any polygon is 360° the interior sum is 180(n-2), where n is the number of sides so 180(n-2) = 360 n-2 = 2 n = 4 so it is true for any quadrilateral
December 18, 2015

3rd grader
I just memorized them
December 17, 2015

math
prob(white) = 12/20 = 3/5 prob(not white) = 2/5 you want prob that 3 are white or 4 are white or 5 are white = C(12,3) (3/5)^3 (2/5)^9 + C(12,4) (3/5)^4 (2/5)^8 + C(12,5) (3/5)^5 (2/5)^7 I will do the first term, you do the rest = .012457 +....
December 17, 2015

MATH HELP
yes
December 17, 2015

Algerbra
for addition: the sum of 2 odds is even e.g. 3+5 = 8 the sum of 2 evens is even the sum of an even and an odd is odd e.g. 3 + 4 = 7 for multiplication: odd x odd = odd, e.g. 3x5=15 even x even = even , e.g. 6x8 = 48 even x odd = even , 4 x 5 = 20 assuming x is also an integer ...
December 17, 2015

Algerbra
the ^ symbol is used to show exponents (-2x-6)^2 = ( (-2)(x+3) )^2 = (-2^2( (x+3)^2 = 4y btw, where does the f in f y come in? I assumed it meant question f) let me know otherwise Just noticed my assumption was right from the first of the Related Questions below from 2013
December 17, 2015

Math
scalar product or dot product: a∙b = |a| |b|cosØ, where Ø is the angle between then 1(16)cosØ = 90 cosØ= 90/16 = 5.625 , which is not possible, since cos(anything) falls between -1 and +1
December 17, 2015

Math
Recall that perpendicular lines have slopes that are negative reciprocals of each other. so the slope of the given line is 3/5 then the slope of the new line is -5/3 new equation: y = (-5/3)x + b but (-1,3) lies on it, so 3 = (-5/3)(-1) + b b = 3 - 5/3 = 4/3 new line: y = (-5/...
December 17, 2015

math
speed = distance / time = 49/(4/3) = 49(3/4) = 147/4 or 36.75 mph
December 17, 2015

math
If 1/4 inch represents 1 mile, then 1 inch represents 4 miles , and 1 3/4 inches or 7/4 inches will represent (7/4)(4) miles = 7 miles or just use a ratio: (7/4)/(1/4) = x/1 (1/4)x = 7/4 x = 4(7/4) = 7
December 17, 2015

Math
so you need the derivative of this thing. y = 1 + (cscx + cotx)^1/2 dy/dx = (1/2)(cscx + cotx)^(-1/2) ( -cscx cotx - csc^2 x) I was going to simplify this, but then realized that you were missing some information. e.g. what point does the tangent pass through ? I am also ...
December 16, 2015

Math
notice the result is 7.47 x 10^-38 which I would consider close to zero.
December 16, 2015

Math
prob(right ) = 1/5 prob(wrong) = 4/5 let the number that are right be x C(100,80) (1/5)^80 (4/5)^20 I am stymied for a method to evaluate this, my calculator cannot handle it Wolfram says: http://www.wolframalpha.com/input/?i=evaluate+C%28100%2C80%29+%281%2F5%29%5E80+%284%2F5%...
December 16, 2015

Math
You are wrong. Think of it this way: Each of the 12 teams can play against the other 11 teams, that would would be 12x11 = 132 But each of these has a double, e.g team A plays team B is the same game as team B vs team A so we have to divide our 132 by 2 to get 66. Trust me, 66...
December 16, 2015

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