Tuesday
July 22, 2014

Posts by Reiny


Total # Posts: 26,851

math
from smallest to largest of the 7 consecutive EVENS x, x+2, x+4, x+6, x+8, x+10, x+12 middle is x+6 x+6 = 48 x= 42 smallest is 42

Math
Using Calculus .... x+y = 11 ---> y = 11-x S = 1/x - 1/y = 1/x - 1/(11-x) = x^-1 - (11-x)^-1 dS/dx = -1/x^2 - 1/(11-x)^2 = 0 for a max/min of S -1/(11-x)^2 = 1/x^2 -x^2 = 11-x^2 -2x^2 = 11 x^2 = -11/2 No real solution , there is no maximum see Wolfram http://www.wolframalph...

math
Looking back I see many posts by you involving the quadratic equation and its properties, You have shown no sign that you have attempted any of them, nor did you indicate where your problems lie. The intent of this forum is not to simply do homework or assignments for you. for...

maths
I suspect a typo, since I get 2/(x+p ) = 1/r x+p = 2r ---> linear equation x = 2r-p , which only has one root

maths
For any quadratic, complex roots or irrational roots always come as conjugate pairs so if one root is 2 + i√3, the other must be 2 - i√3 sum of those roots = 4 product of those roots = 4 - 3i^2 = 7 In any quadratic of the form x^2 + px + q = 0 the sum of roots = -p...

math
first reduce the equation to x + 6y - 3 = 0 Since the new line is perpendicular, it must be 6x - y + c = 0 plug in (2,4) 12 - 4 + c = 0 c = -8 new equation: 6x - y - 8 = 0

maths
Since in a square, the diagonals bisect each other, 5x+9 = 5+3x 2x = -4 x = -2

maths
the quadratic must have been (x-tan30)(x-tan15) = 0 x^2 - xtan30 - xtan15 + tan30tan15 = 0 x^2 + x(-tan30 - tan15) + tan30tan15 = 0 comparing this to x^2 + px + q = 0 p = -tan30 - tan15 and q = tan30tan15 then 2 + q - p = 2 + tan30tan15 - (-tan30 - tan15) = 2 + tan30tan15 + ta...

maths
let the roots of the first be s and 4r let the roots of the second be s and 3r 1st: x^2 - 6x + a = 0 sum of roots = 6 product of roots = a s+4r = 6 and 4rs = a 2nd: x^2 - cx + 6 = 0 sum of roots = c product of roots = 6 s+3r =c and 3rs = 6 ---> rs = 2 so in 4rs = a , we hav...

maths
Sachins would have been (x-4)(x-3) = 0 x^2 - 7x + 12 = 0 Rahul's would have been (x-3)(x-2) = 0 x^2 - 5x + 6 = 0 Sachin was wrong with the 12, should have been 6 Rahul was wrong with the -5x , should have been -7x Equation should have been x^2 - 7x + 6 = 0 (x-6)(x-1) = 0 x...

algebra
amount of the 30% solution needed ---- x L amount of the 16% solution needed --- 5-x L .3x + .16(5-x) = .272(5) times 100 30x + 16(5-x) = 136 30x +80 - 16x = 136 14x = 56 x = 4 L 4 L of the 30%, and 1 L of the 16% solution would be needed.

math
For any linear equation in the form Ax + By + C = 0 , the slope is -A/B So for both of your equations, the slope is -1/3 thus they are parallel

Algebra
For a complicated equation such as yours, the most powerful method is probably Newton's Method. let y = 3x^2+4lnx+4 dy/dx = 6x + 4/x newx = x - y/(dy/dx) = x - (3x^2+4lnx+4)/(6x + 4/x) which simplifies to newx = (3x^2 - 4lnx)/(6x + 4/x) now use an iteration process, I star...

algebra
Vikky, what Steve is telling you that complex roots, as well as irrational roots, always come in conjugate pairs. e.g. if one root is 5 - 7i, then there has to be a matching 5 + 7i e.g. if one root is (4 + 3√5)/2 , then there has to be a (4 - 3√5)/2 So, if you know...

math
Using a ruler and compass, draw the base line of 9 inches. Set your compass to 6 inches, from the left end of the base draw an arc above the base line. Set your compass to 4 inches, from the right end of the base, draw an arc above the base line The intersection of the two arc...

Math
To be an arithmetic progression, (2t-1) - t = (2t+4) - (2t-1) solve for t

math
what is 60 + (2/5)(60) ?

algebra math
I don't see any obvious relationship, nor does Wolfram http://www.wolframalpha.com/input/?i=plot+%7B%282%2C3%29%284%2C5%29%286%2C4%29%288%2C6%29%2810%2C5%29%2812%2C12%29%2814%2C16%29%2816%2C22%29%2818%2C26%29%2820%2C32%29%7D

mat/simultaneous equation
I would use elimination here 1st times 3 ---> 6x - 15y = 39 2nd times 5 --> 25x - 15y = -75 subtract them: -19x = 114 x = -6 back into 1st -12 - 5y = 13 -5y = 25 y = -5 x = -6 , y = -5

calculus
Assuming we take the growth to be exponential , ... 5 e^(28r) = 7.5 e^(28r) = 1.5 ln both sides ln (e^(28r)) = ln1.5 28r = ln 1.5 r = .0145 the rate is 1.45% check: 5 e^(28*.0145) = 7.5

maths probability
Answered by MathMate a few days ago under a Physics heading http://www.jiskha.com/display.cgi?id=1403632512

math
In a 32:3 ratio, there are 35 parts 7 m or 700 cm divided by 35 = 20 cm by part So what do you think?

Math
I get 3t-9-20t+15 = 5-42t-7 25t = -8 t = -8/25

Math
I will assume you mean 120a^4b^2/(-24a^9b^-15) if so, then it would be -5 a^-13 b^17 or -5b^17/a^13

Algebra 1
Use this notation to indicate exponents: x^3 - x^2 - 4x + 4 = 0 grouping will work x^2(x - 1) - 4(x - 1) = 0 (x-1)(x^2 - 4) = 0 (x-1)(x+2)(x-2) = 0 so x = 1 , -2 , +2

Algebra
yes

calcus
Isn't that just a straight-forward Pythagorean calculation? Surely somebody who studies Calculus MUST know how to do that. Let me know where your problem lies.

maths
Again, having a hard time trying to establish the order of operation. e.g. #3 I put it into Wolfram the way you typed it , and the webpage interpreted it the same way I did http://www.wolframalpha.com/input/?i=+X%5Elogx%2B5%2F3%3D+10%5E5%2Blog+x What a messy equation that woul...

maths
1. by definition of logs x^2 - 12x + 36 = 10^2 (x-6)^2 = 100 x-6 = ±√100 = ±10 x = 6 ± 10 = 16 or -4 2. you have the product of 3 numbers = 0 so one of them is zero but log4 and log2 are non-zero real numbers, so log2x must be 0 that is, x = 1 3.not ...

maths
11^(1/2) = √11 since 11 is not a perfect square, 11^(1/2) is irrational

maths
1st number --- x 2nd number -- 8-x sum of squares = x^2 + (8-x)^2 = x^2 + 64 - 16x + x^2 = 2x^2 - 16x + 64 d(sum of squares)/dx = 4x - 16 = 0 for max/min 4x=16 x = 4 the two numbers are both 4 check: for the answer, sum of squares = 16+16 = 32 let 1st be 3.99, the other 4.01 s...

math
first you need the monthly payment. i = .11/12= .00916666.. n = 12 Paym (1 - 1.0091666..^-12)/.009166.. = 15000 paym = 1325.72 Here are my titles to the amortization table ( they will not line up niceley) Time - payment - interest - repayment - balance now -- 0.00 -- 0.00 -- 0...

math
prob = C(4,3)*C(4,3)/C(52,6) = 16/20,358,520 4/5089630

math-Ms Sue please help
I am pretty sure that for loans lasting 25 years, compound interest would be used. i = .10/12 = .008333... n = 25(12) = 300 payment( 1 - 1.008333^-300)/.0083333) = 73700 I get payment = $ 669.71

math
All your questions deal with the use of our 4 basic compound interest formulas. What exactly do you not understand about these questions ? They all are very straight forward.

math
i = .08/12 = .006666.. n = 18(12) = 216 amount = 225( 1.00666..^216 - 1)/.00666.. = ... you do the button pushing

math
amount(1.02)^12 = 15000 amount = 11827.40

math
amount after 3 years at 5% pa compounded semiannually = 4494(1.025)^6 = 5211.66 so interest = 5211.66-4494 = 717.66

math
how about y = x^3/(x-1) confirmed: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3%2F%28x-1%29

algebra
√50 = √25√2 = 5√2, which is choice A

MAT 221
-10 < -2 + 8x < 22 add 2 -8 < 8x < 24 divide by +8 , (no change in inequality sign) -1 < x < 3 Can't make out your symbols in the 2nd e.g. use <= for ≤ and >= for ≥

Frequency
assuming that they either supported it or not supported it, P(E) = 80/400 = 1/5

Algebra
yes, I would put your answer in set form, using { } brackets, eg. range = {2,-5}

Trigonometry help
Depends on the interpretation of "makes a 15° angle with the boat". If the rope makes a 15° angle with the water line, (parallel to the bottom of the boat) you would have: depth/24 = cos 75° or depth/24 = sin 15° , both giving you depth = 6.21 If the ...

Math
1 term(n) = ar^(n-1) term(10) = 16(-1/2)^9 = 16(-1/512) = - 1/32 2. ar^9 = 3/512 ar^14 = 3/16384 divide the 2nd by the first r^5 = 1/32 r = 1/2 back into the first a(1/2)^9 = 3/512 a(1/512) = 3/512 a = 3(512)/512 = 3

Math
looks like an arithmetic sequence with d = 17 and term2 = -243 a+d = -243 a = - 260 term(67) = a+66d = -260 + 66(17) = ... you should have at your finger-tips the formulas for the sum of n terms you have the a and the d, so plug in

oops - finite math
that should be .25 + .47 for OR the way I had it would have been for AND

finite math
what is .25(.47) ?

finite math
How many of the 59 homeruns went to left field ?

geometry
Did you carefully read the question ?

geometry
let me rephrase the question ... what is the greatest common factor of 720, 1008, and 672 ? 720 = 8*9*10 = 16*3*3*5 1008 = 8*9*14 = 16*3*3*7 672 = 16*3*2*7 so who is common? looks like 16*3 or 48 check: 720/48 = 15 1008/48 = 21 672/48 = 14 , nothing common in any of those 3 an...

Math
well, let's put z=2 into the 2nd z=y + 2 = 5 y = 3 So now we know that z=2 and y = 3 now into the 1st: x - 6 + 2 = 8 z = 12 So, where was your problem with this ? Looks very very easy.

Math
use term(n) = a + (n-1)d here a = -847 , d = 11 , n = ?? , and term(n) = -11 solve : -11 = -847 + (n-1)(11) which should be pretty straightforward to do.

probability and statistics
Ummmh, if everybody got an 85, wouldn't the average be 85 ??? , so mean = 85 and since nobody "deviated" from that score, wouldn't the standard deviation be zero ????

Math
It must be true that (2x-1) - (3x-2) = (4x-3) - (2x-1) -x + 1 = 2x - 2 -3x = -3 x = 1 check: terms would be 1 , 1, 1 strange sequence but it is arithmetic

Math
so you are adding 64 + 81 + 98 + ... for 17 terms a = 64 d = 17 n = 17 use the formula Sum(17) = (17/2)[128 + 16(17)] = 3400

algebra
so -2x^2 + 8x + 5 = 0 x^2 - 4x = 5/2 complete the square ... x^2 - 4x + 4 = 5/2 + 4 (x-2)^2 = 13/2 = 26/4 x-2 = √26/4 ........ since √26 is close to 5 x = appr 2 ± 5/2 = appr 4.5 or .5

Math
I saw this question and have not been able to get a handle on it we know that ln(x) has an expansion formula http://upload.wikimedia.org/math/6/d/b/6dbf56b2e5f34d298c1e71ddd93b3448.png but it only good for |x-1| < 1 so we could create a series of terms = 1/(x+1) ( (x-1) - (...

geometry
let the mean be x (1/8) / x = x / (8/32) x^2 = (1/8)(8/32) x^2 = 1/32 x = ± 1/√32 or ± 1/(4√2) or ± √2/8

Math
a=2 ,d=4 term(12) = a+11d = 2 + 44 = 46

Math
a = x-y d = 2x+y-3 just use your formula term(101) = a + 100d = x-y + 100(2x+y-3) = x-y + 200x + 100y - 300 = 201x + 99y - 300

Maths
You will need brackets to properly identify the order of operations. you probably mean : 5/(1/2) + 14( 5/(1/2) + 14)(1/4) which is 10 + 14(10+14)/4 = 10 + 60 = 70 As to the relationship between the two number ??? yes, you are right, they are both whole numbers or they are both...

Math
surface area = 2π(2.5)^2 + 2π(2.5)(9) = ---

MATH
Your solution is illustrated by http://www.google.com/search?q=intersection+of+3+planes&tbm=isch&imgil=VKeuvId73BKgcM%253A%253Bhttp%253A%252F%252Ft2.gstatic.com%252Fimages%253Fq%253Dtbn%253AANd9GcTP5OK2B8xVEFseHgCh5S25ao2K4pX-fClEpupY9ltfPRK6cZC8NA%253B332%253B265%253BL5ht1c6d...

MATH
if you divide the 2nd by 2, all your equations start with 2x. That is good, since we could add or subtract them to eliminate the x 2x+y-3z=4 2x+z=10 -2x+3y-13z=-8 subtract 1st from the 2nd -y + 4z = 6 , #4 add the 2nd and 3rd 3y - 12z = 2 , #5 #4 times 3---> -3y + 12z = 18 ...

algebra
Did you mean, are the lines through each pair of points parallel or perpendicular to each other ?

Angles,Lines and Triangles
let the angles be x and y x+y = 116 x-y = 24 add them 2x = 140 x = 70 then y = 46 one angle is 70°, the other is 46° leaving 64° for the third angle

math
use a simple ratio ... miles/7 = 64/80 miles = 7(64/80) = 5.6

Math
since it is parallel to y=x/2 + 4 it will differ only in the y-intercept, so let y=x/2 + b plug in the point(10,12) 12 = 5+b b = 7 y = x/2 + 7

algebra 2
Since you labeled it algebra rather than Calculus, I will use an algebraic solution, completing the square h(t) = -16(t^2 - 9t + 81/4 - 81/4) + 24 = -16( (t - 9/2)^2 - 81/4) + 24 = -16(t - 9/2)^2 + 324 + 24 = -16(t-9/2)^2 + 348 this is a downwards-opening parabola with vertex ...

Math
#1 and #2 are the same type as the ones I just did for you Give them a try #3 a=2 , d=4 a+(n-1)d = term(n) 2 + (n-1)(4) = 106 2 + 4n - 4 = 106 4n = 108 n = 27 term(27) = 106

Math
common difference = 4+p - (6-p) = 4+p - 6 + p = 2p - 2 term(101) = a+100d = 6-p + 100(2p-2) = 6-p + 200p - 200 = 199p - 194

Math
a+32d = -2p a+ 60d = 26p subtract: 28d = 28p d = p a + 32p = -2p a = -34p

Maths
R(t) = e^kt, where R(t) is the percentage remaining after t t years, k is a constant given: when t = 50 , R(50) = .6 .6 = e^(50k) ln both sides ln.6 = 50k lne k = ln.6/50 R(t) = e^( (ln.6/50) t)

Math
volume = h(50-2h)^2

add maths
OP /PA = 1/3 3OP = AP now follow the same method I just showed you in your previous post

add maths
let the point be P(x,y) then PA = 2PB √( (x-1)^2 + y^2) = 2√( (x+2)^2 + y^2) square both sides and expand x^2 - 2x + 1 + y^2 = 4(x^2 + 4x + 4 + y^2) x^2 - 2x + 1 + y^2 = 4x^2 + 16x + 16 + 4y^2 3x^2 + 18x + 3y^2 = -15 x^2 + 6x + y^2 = -5 complete the square: x^2 + 6...

Word Problem
let the length and width be 4x and 3x old area = (4x)(3x) = 12x^2 new length = 4x+4 new width = 3x + 2 new area = (4x+4)(3x+2) = 12x^2 + 20x + 8 12x^2 + 20x + 8 = 2(12x^2) = 24x^2 12x^2 - 20x - 8 = 0 3x^2 - 5x - 2 = 0 (x-2)(3x + 1) = 0 x = 2 or x = -1/3, which is not admissibl...

lehman
number of $30 units ---- x number of $20 units ---- 2x number of $10 units ---- 40000-x-2x = 40000-3x 30x + 20(2x) + 10(40000-3x) = 800000 30x + 40x + 400000 - 30x = 800000 40x = 400000 x = 10,000 so 10,000 of the $30 units 20,000 of the $20 units 10,000 of the $10

lehman
amount invested at 10% --- x amount invested at 8% ---- 3x amount invested at 9% ----- 700,000-x-3x = 700,000-4x .1x + .08(3x) + .09(700000-4x) = 60500 times 100 10x + 8(3x) + 9(700000-4x) = 6050000 34x + 6300000 - 36x = 6050000 -2x = -250,000 x = 125,000 amount borrowed at 10...

math
Here is the "magic" square, where not only are your diagonals equal to a sum of 15, but so are each row and column 8 1 6 3 5 7 4 9 2

UGRENT HELP, math
They used the < sign should have used the ≤ for the ones that are equal

UGRENT HELP, math
number = 80(3)^(8/2) = 6480 C is obviously the biggest, followed by A B and D are the same none of the answers match, after you find the typo, I will let you figure it out

finance
first let the 50,000 and the 100,000 ride for the 12 years. Amount = 50000(1.05)^12 + 100000(1.10)^12 = 403,635.65 PLus our annuity of 30,000 for 12 years at 10% = 30000(1.1^12 - 1)/.1 =641,528.51 for a total of $1,045,164.17 Last part: let the rate be i 1,045,164.17 = 102,000...

maths
All four sides are equal, so each side of the rhombus is 8 cm get angle Ø , opposite the 10 cm diagonal 10^2 = 8^2 + 8^2 - 2(8)(8)cosØ cosØ = 7/32, then sinØ = 5√39/32 area = 8(8)sinØ = ... you take over

MAth
4+√(4+x^2) = x √(4+x^2) = x-4 square both sides 4+x^2 = x^2 - 8x + 16 8x = 12 x = 12/8 = 3/2 since we squared the equation, we MUST verify the answer LS = 4 + √(4 + 9/4) = 4 + √(25/4) = 4 + 5/2 = 13/2 RS = 2/3 LS ≠ RS so actually there is no solut...

Math
prob(blue, then red) = (10/24)(1/23) = 5/276

College Algebra
from vertex, y = a(x+9)^2 + 8 but (9,4) lies on it, so 4 = a(18^2) + 8 324a = -4 a = -4/324 = -1/81 etc you messed up here: 4=a(18)^2+8 4=a(332) , you added 8 to 324a , you can't add unlike terms

College Algebra
from the given vertex, the equation must be y = a(x+2)^2 + 4 but (0,2) lies on it, so 2 = a(0+2)^2 + 4 2 = 4a + 4 4a=-2 a = -1/2 y = (-1/2)(x+2)^2 + 4

Math please help
let y = 3/x + 4(1-x) = 3/x + 4(1-x)^-1 dy/dx = -3/x^2 -4(1-x)^-2 (-1) = -3/x^2 + 4/(1-x)^2 = 0 for a max/min of y 4/(1-x)^2 = 3/x^2 4x^2 = 3(1-x)^2 2x = ± √3(1-x) 2x = √3 - √3x 2x + √3x = √3 x = √3/(2 + √3) = appr .4641 or 2x = ...

algebra
D : B = 27 : 16 = D : 64 D/64 = 27/16 D = 64(27/16) = 108

Math
$1 = 82.8/12 francs so he has 12 + 25 or $37 $37 = 37(82.8/12) francs = appr 255.3 francs Time to update that ancient texbook your school is using. France has been using the Euro since 1999

Math
2nd angle --- x 1st angle ---- 4x 3rd angle ---- x+84 x + 4x + x+84 = 180 6x=96 x = 16 1st angle = 4x = 4(16) = 64°

ALgebra
adults --- x children -- 3x solve: 975x + 525(3x) = 30600

math
In terms of cosx cos 3x = 4 cos^3 x - 3cosx , and cos 2x = 2 cos^2 x - 1 so cos 3x = cos 2x 4 cos^3 x - 3cosx - 2cos^2 x + 1 = 0 let cosx = y so we need 4y^3 - 2y^2 - 3y + 1 = 0 I tried y = 1 and sure enough that was a solution. then by synthetic division ... 4y^3 - 2y^2 - 3y ...

math
i = .08 n = 40 years a) amount = 3000 ( 1.08^40 - 1)/.08 = appr $777,170.00 b) change the exponent from 40 to 30

geometry
second angle --- x first angle ------ 4x third angle ----- x+84 x + 4x + x+84 = 180 you finish it

Math
dimes--- x quarters -- x+2 nickels --- 3(x+2) = 3x + 6 10x + 25(x+2) + 5(3x+6) = 180 10x + 25x + 50 + 15x + 30 = 180 50x =100 x = 2 so 2 dimes and 4 quarters and 12 nickels check: 10(2) + 4(25) + 5(12) = 180 all is good

Introductory Algebra
Ummmh, isn't it about your school updated those old textbooks? France hasn't used the franc for years, they use the Euro.

algebra
cost of pound of copper ---- x cost of pound of tin -------- x+2 3(x + 2) + 7x = 10(3.85) 3x + 6 + 7x = 38.5 10x = 32.5 x = 3.25 copper sells for $3.25 per pound, and tin sells for $5.25 per pound

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