Thursday
July 30, 2015

Posts by Reiny


Total # Posts: 30,497

Differential Calculus
let the radius of circle be r let the side of the square be x 4x + 2πr = 10 2x + πr = 5 x = (5 - πr)/2 total area = πr^2 + x^2 replace the x with (5 - πr)/2 careful with the squaring. a) Differentiate, set that equal to zero and solve for r sub back ...
March 29, 2015

Algebra
first of all let's simplify the example -3 < x+5 < 8 subtract 5 from each part -8 < x < 3 In this notation, a < x < b, a is usually less than b and x is any value "between" them. As a matter of fact, I recall one text actually calling this the &...
March 29, 2015

Math
d^2 = t^2 + (5t)^2 = 26t^2 d = t√26 is correct
March 28, 2015

Math
I am almost sure you meant: 6/(√3 + 2) then ... = 6/(√3 + 2) * (√3-2)/(√3-2) = (6√3 - 12)/(3-4) = 12 - 6√3 , you are correct btw, those brackets I put in are essential, or else you would have two terms
March 28, 2015

math
If g(x) = √x then (f/g) (x) = (x^2 + 3)/√x domain: all real values of x, x ≠ 0
March 28, 2015

Math
the answer I should get is 18.2955 let x = 3^√7 then x^(1/√7) = 3 x^(1/√7) - 3 = 0 let y = x^(1/√7) - 3 = x^.3779645 - 3 dy/dx = (1/√7)^(1/√7 - 1) = .3779645 x^-.62204 iteration expression: x - (x^.3779645 - 3)/(.3779645x^-.62204) x = 2...
March 28, 2015

geometry
Triangle PQS has all 3 sides given, so using the cosine law, we can find angle P The use the cosine law again in triangle PRT to find RT
March 28, 2015

Math questions
#1, does he pay off the remaining 110320 with a single payment after 30 years, or does he make monthly payments? the fact you are using the word "mortgage" appears to suggest there are monthly payments involved. Confirm before I answer #1 #5. I confirm the $144 ...
March 28, 2015

math
total time from 1:00 to 6:00 is 5 hours or 300 minutes each half hour is 30 minutes, so number of students needed = 300/30 = 10
March 28, 2015

math
You have listed playing football and basketball playing twice, with different numbers. I will conclude that the second football and basketball should be football and volleyball. Made a Venn diagram filled in the data as given, and got this equation. 2x + 2x + 2x + x + 20+15+26...
March 28, 2015

Math
a = 124 a/(1-r) = 64 124/(1-r) = 64 124 = 64 - 64r r = -60/64 = -15/16
March 28, 2015

Math
c must be 225/4 or 56.25 take 1/2 of 15, then square it check: (x + 15/2)^ = x^2 + 15x + 225/4
March 27, 2015

Algebra
(x^15 y^18)/a^15
March 27, 2015

dps
log 10^25 + 10log 10^4 = 25log10 + 10(4)log10 , recall log10 = 1 = 25 + 40 = 65
March 27, 2015

Pre-Calculus
You are correct, but write it as x = (-5 ± √37)/6 I use a Mac and to get √7 I press "option v"
March 26, 2015

math
done, check to earlier post of this
March 26, 2015

Math Check
#1 should be A, look at your last sum (1/2)[ ..0 + 9 ] = [ ....9/2] #2 you have a 1 by 3 matrix multiply by a 3 by 1 which will give you [(6+6+0)] = [12]
March 26, 2015

Math
your discriminant is correct so for 2 points: 100-4k^2 > 0 -4k^2 > -100 k^2 < 25 -5 ≤ k ≤ +5 for 1 point k = ± 5 for 0 points, 100 - 4k^2 < 0 k < -5 OR k > 5
March 26, 2015

math
At the ends it could be Jeff, Dariya or Dariya, Jeff So for the first row: 2x3x2x1 or 12 ways, leaving 15! for the other positions. but there are 4 rows, prob(of your event) = 4x12(15!)/20! = .000025799
March 26, 2015

Math
clearly false All you need is one exception to the rule and the rule becomes bogus since 6+7 = 13 and 13 is NOT a composite number the statement is false.
March 26, 2015

math
It would work if you had used the correct number 1 1/6 weeks is NOT 1.16 it is 7/6 , so secondly, this is not a direct proportion, but rather an inverse proportion. That is, the more workers you have, the less time it takes. the correct proportion is 5/x = (7/6) / 3.5 then (7/...
March 26, 2015

math
think of it in terms of "workweeks" Number of total workweeks needed is 5(3.5) or 17.5 that is workweeks = number of workers x number of weeks so number of workers = workweeks/number of weeks = 17.5/(7/6) = 17.5(6/7) = 15
March 26, 2015

Algebra
in your first equation the coefficient of y is 1, so that becomes your obvious choice. y = 5x - 3 sub that into the 2nd 3x - 8(5x-3) = 24 3x - 40x + 24 = 24 -37x = 0 x = 0 back into y = 5x-3 y = 0 - 3 = -3 x = 0 , y = -3
March 26, 2015

Math
Wolfram shows 2 solutions, which verify when substituted. http://www.wolframalpha.com/input/?i=+solve++ln%28x%2B3%29+%3D+-3%2Be%5Ex+ btw, I assume that your f ' (x) is not the derivative of the given f(x) .
March 26, 2015

Calculus
This is the same type of question as your previous one dealing with rent increases. Follow my steps, by defining the number of $16 rebates as n for c) recall that profit = revenue - cost so just subtract the cost expression from your expression from a) and repeat the steps.
March 25, 2015

Calculus
let the number of $10 increases be n new rent = 460+10n number rented= 80-n Revenue = (80-n)(460+10n) = 36800 + 340n - 10n^2 d(Rev)/dn = 340 - 20n = 0 for a max/min 20n=340 n = 17 So there should be an increase of 17(10) or 170 and the new rent should be 630 and 63 units would...
March 25, 2015

math
cannot be determined as the data is written. e.g. are the data values exlusive, that is, how do we know that some students like the program but still think it is unnecessary. How are the 220 who are running for government distributed among the 190 who like the program, and ...
March 25, 2015

Math
sigh !
March 25, 2015

calculus
f ' (x) = (x^2+1) -(x)(2x) all over (x^2+1)^2 = (x^2 + 1 - 2x^2)/(x^2+1)^2 = (1 - x^2)/(x^2 + 1)^2 You can be sure that the denominator will always be positive, so let' just look at the top. recall that a function is increasing when its derivative is positive, and it ...
March 25, 2015

algebra
I looked at how Steve answered your question and he did it correctly. (Trust Steve's answers !!) The way you just typed it now, it would be √18/√18 - 3 which would simply be 1 - 3 or -2
March 25, 2015

Payment calculation
i = .045/12 = .00375 n = 10(12) = 120 paym( 1 - 1.00375^-120)/.00375 = 100000 you do the button pushing, you should get $1036.38
March 25, 2015

math
If I read this correctly as an = (1/5) an-1 , where 1 = 20 then 1 = 20 2 = 4 3 = 4/5 etc then this not an arithmetic but rather a geometric sequence with a = 20 , r = 1/5 t6 = ar^5 = 20(1/5)^5 = 20/3125 = 4/625
March 25, 2015

Math payment calculation
i= .12/12 = .01 n = 12(30) = 360 Paym( 1 - 1.01^-360)/.01 = 100000 paym(97.218331..) = 100000 payment = $1028.61
March 25, 2015

geometry
r = 17/2 = 8.5 V = (4/3)π r^3 = (4/3)π(8.5)^3 = appr 2575.44 inches^3 mass = 2575.44(.033) = 84.89 pounds seems very unreasonable. A hailstone with a diameter of 17 inches ? ABsurd
March 24, 2015

Business mathematics
What is 650(1.04)^5 - 650 ?
March 24, 2015

algebra--1 question
SA = 4πr^2 = 4π(4x+1)^2 = 4π(16x^2 + 8x + 1) = 64πr^2 + 32πx + 4π None of the choices match this
March 24, 2015

mathhhhhhhhhhhhhhhhhhh
All I did was to sub in your choice into each of the equations. #7 is correct, the other two are not #5 since both say y = ... we can substitute: x-2 = 6-x 2x = 8 x = 4 back in the first: y = 6-4 = 2 , so (4,2) #6 , same way ... 2x-1 = x+3 x = 4 then y = 8-1 = 7 solution: (4,7)
March 24, 2015

Probablity
sum of six: 1,5 2,4 3,3 4,2 5,1 ---> 5 ways top faces the same: 1,1 2,2 3,3 4,4 5,5 6,6 ---> 6 ways number of ways of our event = 5+6-1 (can't count the 3,3 twice) = 10 prob(of our event) = 10/36 = 5/18
March 24, 2015

Needs help in math
x/4 + (3/5)(3x/4) + 3600 = x x/4 + 9x/20 + 3600 = x times 20 5x + 9x + 72000 = 20x 72000 = 6x x = 12000 metres -- the total distance check: swims 1/4 of 12000 or 3000 , leaving 9000 paint left over = 5 quarts 1 square foot takes 1/8 of quart, so number of square ft = 5/(1/8...
March 24, 2015

maths
at least 2 the same ---> 1 - prob(all different) = 1 - 6*5*4/216 = 1 - 120/216 = 96/216 = 4/9
March 24, 2015

math
prob(score) = 6/8 = 3/4 prob(not score) = 1/4 odds in favour of scoring = (3/4) : 1/4) = 3 : 1 you are right.
March 24, 2015

geometry
V= (1/3)π r^2 h 600π = (1/3)πr^2h 1800 = r^2 h h = 1800/r^2 pick any r value you feel like, then evaluate h e.g. r = 9 h = 1800/81 = 200/9 or 22.22.. find as many as you want
March 23, 2015

math
new square: (x+2)(x+2) (x+2)^2 - 4 = 21 x^2 + 4x +4 - 4 - 21 = 0 x^2 + 4x - 21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3, x = -7 making no sense new square = 2+3 or 5 units long check: old square = 2x2 = 4 new square = 5x5 = 25 increase is 25-4 = 21 , as given All is good
March 23, 2015

Algebra 1
1. Rule: a^x * a^y = a^(x+y) b^(1/6)^3 * b^(1/6) = b^(1/2) * b^(1/6) = b^(1/2 + 1/6) = b^(2/3) 2. (2x^-3)^2 (0.2x)^2 = 4x^-6 * .04x^2 = .01 x^-4 3. (3^7)^2 (3^-4)^3 = 3^14 * 3^-12 = 3^2 = 9
March 23, 2015

Math
looks like we are increasing the previous number by 4, so ..... let me know what you think.
March 23, 2015

Calculus
Did you make a sketch? I called her distance from the pole x ft, and the length of her shadow y ft So by similar triangles, 6/y = 15/(x+y) 15y = 6x + 6y 9y = 6x 3y = 2x 3dy/dt = 2dx/dt we know that dx/dt = 5 3dy/dt = 10 dy/dt = 10/3 ft/sec So her shadow is increasing at 10/3 ...
March 23, 2015

math
amount = 2500(1.06)^15 = 5991.40 so the interest for that time is $3491.40
March 23, 2015

Calculus
let the height of the water level be h m let the radius of the water level be r m we are told r/h = 1.75/13 = 7/52 52r = 7h r = 7h/52 let the rate at which water is pumped be x m^3/min V = (1/3)π r^2 h = (1/3)π(49h^2/2704)h = (49π/8112) h^3 dV/dt = (49π/...
March 23, 2015

Absolute value inequalities
1 - 3|7-x| ≤ -11 -3|7-x| ≤ -12 |7-x| ≥ 4 7-x ≥ 4 or -7+x ≥ 4 -x ≥ -3 or x ≥ 11 x ≤ 3 OR x ≥ 11 I think that matches your answer.
March 23, 2015

Calculus
V = (4/3)π r^3 dV/dt = 4π r^2 dr/dt when r = .6 , dV/dt = 3.2 3.2 = 4π(.6)^2 dr/dt dr/dt = 3.2/(1.44π) = appr .707 so d(diameter)/dt = 1.415 ft/min
March 23, 2015

Math help check
8t^5 x 8t^5 = (8)(8)(t^5)(t^5) = 64t^10
March 23, 2015

Algebra
.76 = 1 (1/2)^(t/5730) log both sides: log .76 = (t/5730) log .5 t/5730 = log .76/log .5 = .39592... t = 2268.67 years or t = appr 2300 years, correct to the nearest 100 yrs.
March 23, 2015

algebra 2
1. I will assume you mean 4(fifthroot(3x+1) - 8 = 0 4(3x+1)^(1/5) = 8 (3x+1)^(1/5) = 2 raise both sides to the 5th power 3x+1 = 2^5 3x+1 = 32 3x = 31 x = 31/3 #2, same way (5m+6)^(1/3) = -13 cube both sides 5m+6 = -2197 5m= -2203 m = -2203/5 or -440.6
March 23, 2015

Math
#1 For which choice has the y value been increased by 3 ? #2. mmmh, which choice has the 3 subtracted from the x, and 2 added to the y ? #3, wow, let's see now, starting with (4,3) we added 2 to the x and subtracted 5 from the y to get ..... ?
March 23, 2015

math
50% larger than a right angle would be (90+45)° or 135° That leaves 45° for the two equal angles, making each one 22.5°
March 23, 2015

math
8/7 = 56/x 8x = 392 x = 49 You are correct
March 23, 2015

calc
I assume you made a diagram. I let the angle of elevation be Ø, and the horizontal distance of the plane as x km In mine, tanØ = x/5 xtanØ = 5 dx/dt tanØ + x sec^2 Ø dØ/dt = 0 when Ø = π/3 , (I recognize the 30-60-90° ...
March 23, 2015

Trig
let the base be 2x Construct an altiude to the base, resulting in a right-angled triangle with hypotenuse 4, angle 15° and opposite side x sin15 = x/4 x = 4sin15 so the base is 2x, or 8sin15° you do the button pushing.
March 23, 2015

math
looks like Damon is still cleaning seagull poop .... prob(busy) = 1/10 prob(not busy) = 9/10 prob(at least 3 of 6 are busy) = C(6,3)(1/10)^3 (9/10^3) + C(6,4) (1/10)^4 (9/10)^2 + ... + C(6,6) (1/10)^6 I will let you do the button-pushing
March 23, 2015

arithmetic
a+d = 8 a+3d = 14 subtract them: 2d = 6 d = 3 I will let you finish it
March 23, 2015

Calculus
since you are dealing with "half-life" , we can use the formula amount = c (1/2)^(t/40) amount = 700 (1/2)^(t/40) when t = 40, amount = 350 so when t = 30 amount = 700 (1/2)^(30/40) = 700 (1/2)^.75 = 416.22.. mg reading your question again, I gather you want to use ...
March 23, 2015

Algebra
I am not happy to learn that I went through the effort of solving the question to relieve your boredom.
March 23, 2015

Algebra
carefully expand to get x^4+12x^3+47x^2+72x+36 - 3x^2 = x^4 + 12x^3 + 44x^2 + 72x + 36 I assume it will factor, (or else why have the question?) I tried all possible factors of 36, and none made the expression zero, so there are no binary factors with rational numbers. I then ...
March 23, 2015

Calculus
I strongly suggest you listen to the two videos by Khan In the first he establishes the formula: T(t) = c e^(-kt) + Ta , where Ta is the ambiant temperature. your given data will be: Ta = 34 T(0) = 70 T(30) = 52 your t will be in minutes The first video results in the basic ...
March 23, 2015

Urgent geometry help
Still makes no sense. If the bottom angle is 45° and it is isosceles, then you have a right-angled triangle.
March 22, 2015

Urgent geometry help
You seem to have conflicting data. Where is the 45° angle ? if the base is 12 and the two equal sides are 32 each, then there can't be a 45° angle. If the base is 32 and the two equal sides are 12, you will not be able to draw the triangle, since that is not possible.
March 22, 2015

Math
with semi-annual compounding: amount = 4000(1.07)^16 = ...... with quarterly compounding: amount = 4000(1.035)^32 = ....
March 22, 2015

Math
What was your quadratic equation ? Make sure that all your points satisfy it, if even one of them does not work, your equation is wrong. If they do, and a is negative, then it opens downwards. If your a is positive then it opens up
March 22, 2015

trig
Several ways to do this. This might be the easiest to understand ... Make a sketch of a right-angled triangle in quad II since cosA = x/r = -6/7 x = -6 and r = 7 (remember r is always positive) by Pythagoras: x^2 + y^2 = r^2 36 + y^2 = 49 y^2 = 13 y = ±√13 , but ...
March 22, 2015

Pre algebra
1. amount of 5.0% stuff --- x ml amount of 50% stuff ---- 20-x .05x + .5(20-x) = .075(20) .05x + 10 - .5x = 1.5 -.45x = -8.5 x = -8.5/-.45 = 18.888... or appr 18.9 ml 2. don't understand the problem, no idea what AWP is
March 22, 2015

Math
When the 2nd overtakes the first, they will have travelled the same distance: let the time of the first plane since 1:00 pm be t hrs distance covered by first plane = 400t miles let the time of the 2nd plane be t-2 hrs distance covered by 2nd plane = 600(t-2) 400t = 600(t-2) ...
March 22, 2015

Math
according to the order of operations, 5 squared + 8 divided by 2 =25 + 8/2 =25+4 = 29
March 22, 2015

math
of the 26 letters, how many are vowels ? so prob = ?/26
March 22, 2015

math
since they are parallel, k/6 = 3/2 2k = 18 k = 9
March 22, 2015

Math
1. I will assume you want simple interest rather than compound interest, judging by the level of the other questions. amount paid = 6(516.5) = 3099 interest paid = 99 I = PRT R = I/(PT) = 99/((3000)(.5)) = .066 or 6.6% How did you get .33% ???? 2. This question makes little ...
March 22, 2015

maths
since A+B = 90 B = 90-A and sinB = sin(90-A) = cosA similarly cosB = sinA sinAsinB = sinAcosA = (1/2)sin 2A thus y = (1/2)sin 2A has an amplitude of 1/2 so the range is -1/2 ≤ y ≤ 1/2
March 22, 2015

related rates calculus 1
from 15 = π/9 (100)dh/dt I multiplied both sides by 9/(100π) which left me with dh/dt on the one side and 15(9/(100π) ) or 135/(100π) on the other side
March 22, 2015

related rates calculus 1
height ------- h base radius --- h/3 V = (1/3)π r^2 h = (1/3)π (h^2/9)(h) = (π/27) h^3 dV/dt = (π/9) h^2 dh/dt for the given data: 15 = π/9 (100)dh/dt dh/dt = 135/(100π) ft/hr
March 22, 2015

Algebra
let the border be x cm wide picture is (30-2x) by (36-2x) (30-2x)(36-2x) = 480 1080 - 132x + 4x^2 - 480 = 0 4x^2 - 132x + 600 = 0 x^2 - 33x + 150 = 0 solve using the quadratic equation,
March 22, 2015

Advanced Algebra
It would simply be 10 x 9 x 8 x 7 or 5040 ways This is the same as P(10,4) = 10!/(10-4)! = 10!/8! = 5040
March 22, 2015

Math
Set them equal or R(x) - C(x) = 0 2x + 10 = -5x^2 + 21x 5x^2 - 19x + 10 = 0 x = .6311 thousand or appr 631 or x = 3.169 thousand or appr 3169 check: if x = .6311 , R(.6311) - C(.6311) = .00053.. , not bad if x = 3.169 , ...... = .001805 both answers are valid
March 21, 2015

Pre-Calculus
It is considered "better form" to have your quadratics start with a positive x^2 term So for #2, I would write: 6x^2 - 25x + 24 = 0 , (just switch all the signs, like multiplying by -1) Each of your roots satisfy your equations, but each of your quads should have a ...
March 21, 2015

algebra
Is y = -3x^2 - 4x + 3 supposed to be your answer ? Can't be right, since (0,-4) clearly does not satisfy your equation. Method1: let the equation be ax^2 + bx+c = y for (0,-4), 0+0+c=-4 , c = -4 for (-2,-20), 4a-2b - 4 = -20 4a - 2b = -16 2a - b = -8 for (4,-20), 16a + 4b...
March 21, 2015

Calculus
V = (4/3)π r^3 dV/dt = 4π r^2 dr/dt so when r = .5, dr/dt = .01 just plug it in... dV/dt = 4π(.25)(.01) = ..... cm^3/day
March 21, 2015

maths
fourth term is 11 ---> a+3d = 11 sixth term is 17 ----> a+5d = 17 subtract them 2d = 6 d = 3 back in a+3d = 11 a + 9 = 11 a = 2 tenth term = a+9d = 2+9(3) = 29
March 21, 2015

math
sub in y = x+k x^2 + y^2 = 25 x^2 + (x+k)^2 = 25 x^2 + x^2 + 2kx + k^2 - 25 = 0 2x^2 + 2kx + (k^2-25) = 0 a = 2, b = 2k, c = k^2-25 discriminant = b^2 - 4ac = 4k^2 - 4(2)(k^2-25) = 4k^2 - 8k^2 + 100 = 100 - 4k^2 now proceed the same way as in the previous post to "Eloise&...
March 21, 2015

MATH
I will assume your "equation" is equal to zero, that is, kx - 10 - 5x^2 = 0 or 5x^2 - kx + 10 =0 your discriminant is b^2 - 4ax, or k^2 - 4(5)(10) = k^2 - 200 to have one real root: k^2 - 200 = 0 k^2 = 200 k = ±√200 or ±10√2 for 2 distinct ...
March 21, 2015

math
so you want the vertex of the parabola the x of the vertex is -b/(2a) = -50/-3.724 = 13.426.. subbing that back int gives a height of 2+50(13.426..) - 1.862(13.426..)^2 = appr 337.66 m above "ground" --> h(t) > 0 , for t ≥ 0 solve 2+50t-1.862t^2 = 0 to ...
March 21, 2015

Math
3x + 2y < 6 2y < -3x + 6 y < -(3/2)x + 3 so the slope is -3/2 and the y-intercept is 3 so start with the y-intercept of 3 , or the point (0,3) slope is rise/run = -3/2 so from (0,3) , drop down 3 , then 2 units to the right. This should bring you to the point (-3,5) ...
March 21, 2015

math
oranges --- x apples ---- x + 32 overripe oranges = (3/5)x overripe apples = (1/3)(x+32) but they are the same .... (1/3)(x+32) = (3/5)x multiply by 15 , the LCD 5(x+32) = 9x 5x + 160 = 9x 160 = 4x x = 40 overripe fruit = (1/3)(x+32) + (3/5)x = (1/3)(72) + (3/5)(40) = 48 check...
March 21, 2015

Algebra
boat's speed in still water --- x mph against the current ----- x-3 mph with the current -------- x + 3 mph time against current = 12/(x-3) time with the current = 12/(x+3) 12/(x+3) + 12/(x-3) = 3 times (x-3)(x+3) or x^2 - 9 12(x-3) + 12(x+3) = 3(x^2 - 9) 12x-36 + 12x + 36...
February 23, 2015

algebra
Let the shorter wire be x m long and let that wire be y m from the base of the pole so x^2= 576 + y^2 ----> x^2 - y^2 = 576 let the longer be x+5 and we have (x+5)^2 = 24^2 + (y+11)^2 x^2 + 10x + 25 = 576 + y^2 + 22y + 121 x^2 - y^2 = 22y - 10x + 672 22y - 10x + 672 = 576 ...
February 23, 2015

Algebra
I agree with all you answers
February 23, 2015

Vectors Math
Anwered here: http://www.jiskha.com/display.cgi?id=1424665237 take a vector (a,b,c) now do (a,b,c) x (a,b,c) to get (0,0,0) by whatever means you have learned. The steps will become your explanation.
February 23, 2015

Math
Maria, as I told you yesterday, you don't have enough information http://www.jiskha.com/display.cgi?id=1424650591
February 23, 2015

Math
amount = 3000(1.02)^8 = ... subtract $3000 from that answer and you got your interest earned.
February 23, 2015

Math
Circumference of the wheel = 1.05π number of turns = 3300/1.05π Btw, on your calculator, key in 3300 ÷ (1.05 x π) = to make sure the order of operations is correct
February 23, 2015

Maths
numbers which when divided by 5 leave a remainder of 1: 6 11 16 21 26 31 36 41 46 .. numbers which when divided by 8 leave a remainder of 1: 9 17 25 33 41 49 ... looks like 41 is the smallest common to both
February 23, 2015

Vectors Math
http://www.jiskha.com/display.cgi?id=1424665199
February 22, 2015

Vectors Math
If using whichever method you have to find the cross-product, if you take (a,b,c) x (a,b,c) you will get (0,0,0)
February 22, 2015

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