Posts by Reiny

Total # Posts: 38,876

math
A regular hexagon can be divided into 6 equal equilateral triangles. So each one has an area of 64?3 let's look at one of those. Area of a triangle = (1/2)absinØ, where a and b are sides with Ø as their contained angle. If each side is x, then (1/2)x^2 sin60&...

math
Of the 40 marbles you have, 30 of them are blue, so Prob(blue) = 30/40 = 3/4 or .75

Math fp1
clearly the roots of the given equation must be complex numbers, thus they must be conjugates of each other let w = a+bi then w* is a - bi sum of roots = a+bi + a-bi = 2a product or roots = (a+bi)(a-bi) = a^2 + b^2 but from the given equation: sum of roots = -4-i-qi product of...

math
time for first leg = 24/18 hrs resting = 1/2 hour last leg = 6/20 hrs add up the three times

Physics
h = -16t^2 + 32t + 300 , from your data v = dh/dt = -32t + 32 so when t = 1 v = -32 + 32 = 0

math
L = km/h when L = 40, m=175, h = 286 , (skipping the units) 40 = k(175)/286 k = 286(40)/175 = 2288/35 L = (2288/35)m/h , plug in h=50 and m=250

Precalculus
check for intersection x^2 - 5x + 3 = -x^2 + 5x - 5 2x^2 - 10x + 8 = 0 x^2 - 5x + 4 = 0 (x-1)(x-4) = 0 x = 1 or x = 4 but we need the area for 0 ? x ? 4 , so we have two sections, because there is a cross-over at x = 1 Area = ?(x^2 ? 5x + 3 + x^2 - 5x + 5)dx from 0 to 1 + ?(-x...

Math
let the numerator be x then the denominator is x+7 3 is added to the numerator, so the new numerator is ...... 1 is subtracted from x+7 , so the new denominator is ...... the new fraction is ???/???? ???/???? = 4/5 solve for x show me your steps, so I can check it

Precalculus -- Systems of Equations
or, the distance from (0,0) to x-2y - 8 = 0 is |0 - 0 - 8|/?(2^2 + 1^2) = 8/?5 so yes, r = 8/?5

Math
missing information: number of purple marbles

Geometry
You should of course know that the sum of the 3 angles is 180° how about angle Y = x then angle X = (5/8)x and angle Z = (1/4)x so 5x/8 + x/4 + x = 180 I suggest you multiply each term by 8, the LCD and it is a piece of cake after that.

math
originally there were 25 odds and 25 evens, the 5 numbers already drawn are all odd, so there remains: 25 evens and only 20 odds so for the next draw: prob(odd) = 20/45 prob(even) = 25/45 so what do you think?

math
1. So, don't you just need two equal widths for your rectangle ??? x + x + 9 = 25 Can't get any easier. 4. I can't follow your description. My rectangle has two width of 12 ft, and some length x x + 12 + 12 = 44 x = 20 , so it overlaps the existing 12 ft fence.

Math
#1, I would include the spinner part as well. Since the spinner has no memory , whatever happened on the first spin, has no effect on the second #2 correct

co-ordinate geometry need help steve reiny
There are several ways to do this: 1. There is an actual formula to do this, Google "distance from a point to a line" and study it 2. rigorous method. There is a great video form the KhanAcademy webpage that explains in great detail . Your line is y = 2x , (easier ...

co-ordinate geometry need help steve reiny
Your wording is incorrect. Did you mean : find the distance from the point to the given line?

Math
Looks like they want you to cut the circle into "many" equal isosceles triangles, finding the base of one of them , then multiplying by the number of such triangles e.g. in your case , visualize 360 isosceles triangles each with equal sides of 5 and a vertex angle of...

algebra
length ---- x width = 2x/3 x - 2x/3 = 7 once you have the width and length, perimeter = 2widths + 2lengths

Math
Depends what information you are given. I would prefer if you didn't concentrate on a "formula" but rather analyze the problem. Here is a nice short video where they find the slant height as part of another problem. https://www.youtube.com/watch?v=r5EQCSW_rLQ

Math
Of course being a day late with your joke makes it fall flat. Yesterday, 26 April 2017 could have been written as "today"

Math
let Dad start with x belt: x/2 + 50 amount left = x - (x/2 + 50) = x/2 - 50 sandals: (1/2)(x/2 - 50) + 30 = x/4 + 5 amount left = x/2 - 50 - (x/4 + 5) = x/4 - 55 T-shirt: (1/5)(x/4 - 55) + 20 = x/20 + 9 x/4 - 55 - (x/20 + 9) = 15 x/4 - 55 - x/20 - 9 = 15 x/5 = 79 x = 395 pesos

Math
How is it compounded? monthly? , quarterly? daily?, continuously ? ????

math
cotØ = 11/12 tanØ = 12/11 r^2 = 11^2 + 12^2 = 265 r = ?265 since tanØ is positive, Ø would be in I or III in I, tanØ = 12/11 , sinØ = 12/?265 in III tanØ = 12/11, sinØ = -12/?265

Math-Please Help
nope, show your steps so I can see where you went wrong.

Mathematics
I always taught that 0/0 was indeterminate and did not fall into the "undefined" category. Such as in limits that result in 0/0 situations, e.g. lim (x^2 - 4)/(x-2) , as x ---> 2 you would get 0/0 = lim (x-2)(x+2)/(x-2) as x ---> 2 = limi x+2 , as x --->2 = ...

Mathematics
here is another explanation: if multiplication is repeated addition, e.g. 3x4 = 3+3+3+3 = 12 and division is repeated subtraction: e.g. 20 ÷ 4 20-4 = 16 16-4 = 12 12-4 = 8 8-4 = 4 4-4 = 0 I subtracted the 4 five times to get to zero so 20÷4 = 5 so how about 20 &...

Mathematics
Look at these cases: 12/3 = 4 because 3x4 = 12 20/10 = 2 because 2x10 = 20 5/0 = ?? because ?? x 0 = 5 , but that is a contradiction, since anything times zero is zero. or 5/.1 = 50 5/.01 = 500 5/.001 = 5000 5/.000000000001 = 5000000000000 notice I am dividing by a smaller and...

science
let the distance be x km time for first bus = x/54 time for 2nd bus = x/36 total time = x/54 + x/36 = 5x/108 total distance = 2x avg speed = total distance / total time = 2x / (5x/108) km/h = 108/5 km/h = 21.6 km/h

Maths
number of fivers --- x number of twos ---- 3x 5x + 2(3x) = 77 solve for x and state conclusion

Math
let the total be x students so x/3 + x/4 + x/6 + 18 = x multiply by 12 4x + 3x + 2x + 216 = 12x finish it up

maths
I would use substitution. from x-2y = 0 ---> x = 2y sub that into the 2nd: 3(2y)+ 4y = 20 continue to find y, then replace in x = 2y

Math
The algorithm I use sets it up this way: D = -3(3-0) - 2(0 - (-3)) - 3(0 - (-3)) = -9 -6 - 9 = -24 KhanAcademy shows 2 basic methods https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-determinants-and-inverses-of-large-matrices/v/finding-the-determinant-of-a-3x3-...

math
(5/8) ÷ (y/9) = 9/8 5/8 = (9/8)(y/9) 5/8 = y/8 y = 5

math
yes

math
vertical asymptotes have slopes which are undefined. An answer of "undefined" is caused by division of zero. So what is your conclusion?

Final Maths
For half-life questions, it is usual to use a base of 1/2 or .5 amount = 12 (1/2)^(t/5700) , where t is the number of years if the amount = 10 10 = 12 (.5)^(t/5700) .8333... = .5^(t/5700) take logs of both sides and use log rules log .8333... = (t/5700) log .5 t/5700 = log ....

Math - probability
out of the 224, the expected number of A+ i = .357(224) = 79.968 or 80 cases out of the 224, the expected number of AB- = .006(224) = .... carry on

Math
2. multiply the probability you found in 1. by 60

Calculus - Fundamental thm of Calc
To fully understand what Steve did, watch these two KhanAcademy clips https://www.khanacademy.org/math/ap-calculus-ab/fundamental-theorem-of-calculus-ab/fundamental-theorem-of-calculus-tut-ab/v/fundamental-theorem-of-calculus and https://www.khanacademy.org/math/ap-calculus-ab...

Math
let the angles in the interior of the triangle be x, y, and z Extend the base at the z angle let the exterior angle be k we know x+y+z = 180° we know that the z + k = 180 , (angles forming a straight line) so x+y+z = z + k x + y = k state your conclusion

fgh
Not being familiar with the game of cricket, I find this sentence confusing: "A team of 11 players must have at least 5 batmen, 4 bowlers and 1 wicket-keeper" Assuming that you would want 11 players, that could mean: 6 batmen, 4 bowlers, 1 wicket-keeper; 5 batmen, 5 ...

math
Really? How can you claim that it is negative, after having it shown that it is positive. Look at the calculation.

math
first one: slope = (5-1)/(6-3) = 4/3 how did you get it to be negative? 2nd: slope = (-5-(-6))/(-3-(-3)) = 1/0 can't divide by zero, so "undefined"

Algebra
t(1) = 3 = 1x3 t(2) = 8 = 2x4 t(3) = 15 = 3x5 t(4) = 24 = 4x6 t(5) = 35 = 5x7 .. looks like t(n) = n x (n+2) so t(11) = 11x13 = 143

Pre calculus
term(1) = 1^2 -2 = -1 term(2) = 2^2 - 2 = 2 term(3) = 3^2 - 2 = 7 term(4) = 4^2 - 2 = 14 ... term(n) = n^2 - 2 62 = 8^2 - 2 , so we have 8 terms sigma (n^2 - 2) for 1 to n = n(n+1)(2n+1)/6 - 2n recalling that sum n^2 = n(n+1)(2n+1)/6 checking for sum(5) = 5(6)(11)/6 - 10 = 55-...

Probability
odds are defined slightly different from probability. odds in favour of some event = prob(of that event) : prob (not that event) so odds in favour of rain on Sept 21 = .358 : .642 = 358 : 642 reduce to lowest term ratio

Math (ugh)
Don't know what the hangup is between mixed fractions and "improper" fractions mixed fractions may be nice to look at, but they are basically useless for arithmetic calculations and must be changed to improper fractions so, 3 3/4 x 2 4/5 = (15/4)(14/5) = (3/2)(7/...

Math 1
80x^4 - 60x^3 - 60x^2 - 45x This one looks more promising. = 5x(16x^3 - 12x^2 - 12x - 9) let f(x) = 16x^3 - 12x^2 - 12x - 9 f(±1) ? 0 f(±3) ? 0 tried ±3/2, ±3/4, ±3/8, ±3/16 found f(3/2) = 16(27/8) - 12(9/4) - 12(3/2) - 9 = 54 - 27 - ...

Math1
Well, let's look at everything again. clearly x^2 is a common factor. Look at the numbers, start with the 24 24 = 3*8 = 3*2*2*2 so the 195 is only divisible by 3 but not 28, so the HCF is x^2 195x^5 + 168x^4 - 28x^3 - 24x^2 = x^2(195x^3 + 168x^2 - 28x - 24)

Math
review your rules of exponents as it applies to division of powers. This one is a straightforward application of one of those rules. If this is for a test, you MUST know this. btw, x^9/x^2 is the same as x^9 ÷ x^2

algebra
did you mean log(2x-6)^256=4 ?? according to the numbers, I will assume so. You must know your rules of logs by definition 256 log (2x-6) = 4 log (2x-6) = 1/64 2x-6 = 10^(1/64) 2x-6 = 1.0366329.. 2x = 7.0366... x = 3.518316... round to whatever accuracy you want. that answer ...

Statistics
I only answered part b) since a) is very simple a) would be .51^7 = .0089741 I have no idea how yo got 8.9741, the digits are the same, but no probability can be greater than 1. for b) the answer correct to 4 decimals is .0494, your is correct only to 3 decimals

Statistics
prob(b) = .51 prob(x) = .49 , where x is "not blue eyes" one such case could be xxbxxxx , which would be (.51)(.49^6) but there are 7 such cases, so prob(your event) = 7(.51)(.49^6) = .... in stats notation: C(7,1)(.51)(.49)^6

maths
R = k/r^2 when R = .24, r = .05 .24 = k/.0025 k = .006 when r = .04 R = .006(1/.0016) = .375

calculus
done, look back

clculus
dy/dx = 2x at (-2,4), slope = -4 equation of tangent: y-4 = -4(x+2) y = -4x -4 let x = t y = -4t - 4

Maths
Assuming you mean: 4x^2 - 5x - 1 = 0 x = (5 ± ?41)/8 so alpha = (5+?41)/8 and beta = (5-?41)/8 a^2b = (5+?41)/8 * (5+?41)/8 * (5-?41)/8 = (5+?41)/8 * (25 - 41)/64 = (5+?41)/8 * (-16/64) = (-5-?41)/32 GAURAV concluded that a = 1, b = 1/4 but those are not the zeros of ...

Math
What is 6x15 ?

MAth
Of course the bisector of angle C is 45° let the bisector hit AB at P in triangle BCP tan 45 = BP/15 BP = 15tan45 = 15 continue

alg II
yes, and yes

Calculus
yes

geometry please help!!!!
I made a rough sketch. For the total surface area I see two equal trapezoids, and 4 rectangles. the rectangles are: 14 by 10 , 8 by 10 and 2 of 5 by 10 the area of the trapezoid = (1/2)(8+14)/2 finish the arithmetic and use the correct units

math help please check my answer
tan Ø = 60/25 = 2.4 Ø = tan^-1 (2.4) = 67.38..° = 67° to the nearest degree

math
I disagree, Odds and probability are defined slightly different. The odds of some event happening = prob( event) : prob(not the event) so if prob(a 21 ) = 1/38 then the prob(not a 21 ) = 1 - 1/38 = 37/38 odds in favour of a 21 = (1/38) / (37/38) = (1/38)(38/37) = 1 : 37

Pre calc
Or for the 2nd Cos 2x cosx -sin 2xsinx = 0 Cos(2x + x) = 0 cos 3x = 0 3x = pi/2 or 3x = 3pi/2 x = pi/6 or x = pi/2 The period of cos 3x = 2pi/3 So add multiples of that together Steve's other answers

math
the sixth term of an arithmetic progression is 37 ---> a+5d = 37 5d = 37-a sum of the first six term is 147 ---> (6/2)(2a + 5d) = 147 3(2a + 37-a) = 147 a +37 = 49 a = 12 d = 5 If you had a question, take it from there

Math
Juan's present age --- x Ben's present age ---- x+4 in two years: Juan ----- x+2 Ben -------x=4+2 = x+6 x+2 + x+6 = 50 continue

MAth
2l + 2w = 240 l + w = 120 l = 120-w new length = 1.1l new width = .8w 2(1.1l) + 2(.8w) = 240 1.1l + .8w= 120 1.1(120-w) + .8w = 120 11(120-w) + 8w = 1200 1320 - 11w + 8w = 1200 -3w = -120 w = 40 then l = 120-40 =80 state a proper conclusion

Mathmatics
slope of line Q = (-8+2)/(-8+10) = -6/2 = -3 slope of line R = (a-2)/(10-1) = (a-2)/9 but they are perpendicular, so (a-2)/9 = -1/3 continue

Mathmatics
let B be (x,y) for the x: (x-3)/(12-x) = 2/1 x - 3 = 24 - 2x 3x = 27 x = 9 find the y in the same way

Mathmatics
slope AB = m = (1+7)/(-8+12) = 8/4 = 2 using (2,5) y-5 = 2(x-2)

Maths
sub in the two points to set up two equations for (0,3) 3 = a b^0, but b^0 = 1 so a = 3 for (2,12) 12 = 3 b^2 4 = b^2 b = ± 2, but we need b> 0 a = 3 , b = 2 ---> y = 3 (2)^x

math
dc/dq=0.08q^2-1.8q+2.5 c = (.08/3) q^3 - .9 q^2 + 2.5q + 5000 plug in 1000 for q

math
I would expand it first, y = 4x^-2 + x^-5 now it is elementary.

Mathematics
Surface area of original = 2(11)(6) + 2(11)(4) + 2(6)(4) cm^2 = 268 cm^2 volume of original = (11)(6)(4) cm^3 = 264 cm^3 For a cube to hold 264 cm^3, each side must be 264^(1/3) or 6.415... cm long surface area of the cube = 6(6.415...)^2 = appr 246.92 cm^2 (I only rounded ...

QMI
amount = 2000(1.1^35 - 1)/.1 = ....

precalculus
p = 32 e^(kt) , where k is a constant when t = 3, p = 200 32 e^(3k) = 200 e^(3k) = 6.25 3k = ln 6.25 k = appr .61086 p = 32 e^(.61086 t)

Trig
Fish at a depth of 45 km in Lake Ontario ???? I live about 45 minutes from Lake Ontario, and let me guarantee you that lake is not that deep, lol. Anyway ..... I will assume you meant 45 m. let the line be l m long cos 45 = 46/l ----- ( 1 m above the water + 45 l = 46 m) l = ...

precalculus
If I read it correctly you want 230000(.95)^t = 150000(1.11)^t 23(.95^t) = 15(1.11)^t take logs of both sides and use log rules log 23 + t log .95 = log 15 + t log 1.11 log 23 - log 15 = t(log 1.11 - log .95) carry on

math
What are you trying to do ?? is it 6 = e^(5r) or the way you typed it?

math
correct, but remember that q will be half-years so you will have to divide q by 2 to get the number of years

College Algebra
good grief! I just did this for you a few minutes ago!!!!

Help College Algebra
At what will the ball be ... ????? Time ?? set -16t^(2)+128t = 213 and solve 16t^2 - 128t + 213 = 0 you will get two answers, one positive and one negative. Reject the negative answer.

College Algebra
Besides that , it was already answered.

College Algebra
V = (1/3)? r^2 , solve for r 3V/? = r^2 r = ±?(3V/r)

algebra
a) x = 5y ? 3 5y = x+3 y = (1/5)x + 3/5 b) the slope is 1/5, they are the same equation c) they are the same equation

Algebra
d=kt^2 kt^2 = d t^2 = d/k t = ± ?(d/k)

Algebra
part one, height = 32 -16t^2 + 32t = 32 t^2 - t +1 = 0 by the formula: t = (1 ± ?-3)/2 , not real so it will never reach a height of 32 ft we can see that by noting that the x-intercepts are 0 and 2 so the vertex is at t = 1 max height is h(1) = -16+32 = 16 I also ...

metric unit
behold the beauty of the metric system 48567 kg = 48.567 tons

Math
clearly B

Math
No, this is an example of Binomial Distribution. You are planting 7 plants, and you want the prob that exactly 1 does not grow. Suppose it is the 3rd plant which did not grow. GGNGGGG, where G stands for grow, N for not grow. That specific probability is (.7)(.7)(.3)(.7)(.7)(....

Math
same question here: http://www.jiskha.com/display.cgi?id=1445605410

francis
the 8th term of an A.P is twice the 5th term ----> a + 7d = 2(a+4d) a+7d = 2a + 8d a = -d 12th term = a + 11d = -d + 11d = 10d e.g. let d = 4, then a = -4 term(8) = -4 + 7(4) = 24 term(5) = -4 + 4(4) = 12 so term 8 is twice term 5 term 12 = -4+11(4) = 40 which is 10d or 10(...

Math
I would just use a simple ratio. 29/35 : 6/35 = 29 : 6 since 3 5/12 = 41/12 so x/(41/12) = 6/29 29x = 6(41/12) = 41/2 x = 41/58 quarts needed to finish the job

Maths
surface area = 2 circles + 1 rectangle = 2?r^2 + (2?r)(h) = 2?(5^2) + 2?(5)(15) = 50? + 150? = 200? cm^2 1 m^2 = 10000 cm^2 so our surface area = 200?/10000 m^2 cost = 4500(200?/10000) naira = 90? naira = ..... I will let you do the arithmetic

Maths
rest of distance = 1 - (3/8 + 3/5) = 1 - 39/40 = 1/40 (1/40)x = 2 x = 80 km so he went (3/5)(80) km by bus = .....

Maths
volume = length x width x height = (85)(62)(36) cm^3 = .. continue

maths
done here http://www.jiskha.com/display.cgi?id=1492480948

arithmatic series
quotient of the larger number and the smaller number is just a list of the terms e.g. a,b,c,d,.. the series is the sum of those arithmetic terms a+b+c+d+..

math
larger --- L smaller --- 74-L "quotient of the larger number and the smaller number" ---> L/(74 - L)

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