Friday

August 22, 2014

August 22, 2014

Total # Posts: 26,966

**math**

3. x( 1 - 1.005^-360)/.005 = 543408.48 x = 3258.01 per month
*May 2, 2014*

**math**

1. At a rate of inflation of 2%, the value of today's 300,00 in 30 years is 300,000(1.02)^30 = $ 543,408.48 2. (3000(1.08^5 - 1)/.08) (1.08)^25 + x(1.08^25 - 1)/.08 = 543408.48 I will leave all that button-pushing up to you to solve for x
*May 2, 2014*

**algebra**

easy way to tell, just sub it in Left Side= 21E-7 = 21(.33) - 7 = .07 ≠ 0 so , no, you are wrong 21E - 7 = 0 21E = 7 E = 7/21 = 1/3 as the accurate answer. 1/3 = .3333.... , not .33
*May 2, 2014*

**Calc 2**

tried integration by parts on the 2nd, but it got messy, probably made an error Gave up and used Wolfram with results of log(2(√(x^2-4) + x)) - x/√(x^2-4) + C http://integrals.wolfram.com/index.jsp?expr=%28x%5E2%29%2F%28%28x%5E2+-+4%29%5E%283%2F2%29%29&random=false...
*May 2, 2014*

**Calc 2**

a) (sin^2)(3x) using cos 2A = 1 - 2sin^2 A cos 6x = 1 - 2sin^2 (3x) sin^2 3x = 1/2 - (1/2) cos 6x so integral sin^2 3x = (1/2)x - (1/12)sin(6x) Take it from there, I will let you do the substitution and evaluation
*May 2, 2014*

**math**

width --- w length --- w+3 w(w+3) = 88 which of your choices matches this after simplifying ?
*May 2, 2014*

**Alg**

from the hyperbola: x^2 = y^2 + 4 sub into the ellipse 2(y^2+4) + 3y^2 = 48 5y^2 = 40 y^2 = 8 y = ±√8 or ± 2√2 the x^2 = y^2 + 4 = 8+4 = 12 x = ±√12 or ± 2√3 ---> your 4 points enter as instructed. http://www.wolframalpha....
*May 2, 2014*

**Calculus**

It looks like your profit function is correct as p(x) = (-1/2) e^(-x^2) + c 15000 = (-1/2)(e^-1) + c 15000 = -1/(2e) + c c = 15000.184 so p(x) = (-1/2) e^(-x^2) + 15000.184 strange result. Since the exponential term always has a negative value and approaches zero the profit is...
*May 2, 2014*

**link to Wolfram - math**

http://www.wolframalpha.com/input/?i=solve+9500+%3D+227.5%28+1+-+%281%2Bx%29%5E-60%29%2Fx look at second line output, the negative rates are to be ignored.
*May 2, 2014*

**math**

9500 = 227.5( 1 - (1+r)^-60)/r where r is the monthly rate a very tough equation to solve .... Wolfram says r = .01275 as the monthly rate so annual rate compounded monthly = .153 or 15.3 % equivalent annual rate: 1+i = 1.01275^12 = 1.164 or 16.4%
*May 2, 2014*

**math**

3000 r^6 = 1250 r^6 = .416666... r = .416666...^(1/6) r = .864 so the annual rate of depreciation was 1 - .864 = .136 or 13.6% you did not list your choices.
*May 2, 2014*

**maths**

done, look back at your previous post
*May 2, 2014*

**MATH(markup and markdown )**

I will assume cost price is 40 less 10%,5% so actual cost price = 40(.9)(.95) = 34.20 let list price be x .4x = 34.20(1.25) x = 34.20(1.25)/.4 = 106.875 I interpreted "25% of the cost" as the actual cost, not the stated RM40 less 10%, 5% " check: 60% discount on...
*May 2, 2014*

**maths**

6 red 9 blue total is 15 prob(red) = 6/15 = 2/5 prob(blue) = 9/15 = 3/5 I assume that is a typo and should say "red or blue" prob(red or blue) = 1
*May 2, 2014*

**Math**

Side C --- x side A --- 2x side B ----1.5x side D ---- x+4 x + 2x + 1.5x + x+4 = 81 5.5x = 77 x = 14 plug in 14 into each of my definitions to find the lengths
*May 2, 2014*

**MATH(markup and markdown )**

no, if 1.4x = 30 then 1.4x/1.4 = 30/1.4 x = 30/1.4 = RM 21.43 check: take 40 % of 21.43 and add it to 21.43 or what is 1.4(21.43) ?
*May 2, 2014*

**MATH(markup and markdown )**

so you want 1.4x = 30 x = ....
*May 2, 2014*

**math**

markdown = .2(40) = 8.00 new price = 40-8 = 32.00 or what is .8(40) ?
*May 2, 2014*

**MATH(markup and markdown )**

I respectfully disagree, the answers are not the same If I take a take a 20% markdown on your $300 I get $60, which would leave a new price of $240, not $250
*May 2, 2014*

**MATH(markup and markdown )**

old price --- x .8x = 250 x = 250/.8 = 312.50 check: markdown on 312.50 = .2(312.50) = 62.50 new price = 312.50 - 62.50 = 250
*May 2, 2014*

**algebra**

number of pages ---- n n/4 + 2n/3 + 5 = n times 12 3n + 8n + 60 = 12n n = 60 check 1/4 of 60 = 15 2/3 of 60 = 40 15 + 60 + 5 = 60 , check!
*May 2, 2014*

**Math 2**

what is .4(.20) ?
*May 2, 2014*

**Function Maths 11**

for Ø if Ø is in I , that is your related angle if Ø is in II, related angle = 180-Ø if Ø is in III, related angle = Ø - 180 if Ø is in IV, related angle = 360-Ø so tan 110 = - tan(180-110) = -tan 70° sin 350 = -sin(...
*May 1, 2014*

**math**

4πr^2 = 2058 r^2 = 2058/(4π) r = √ ... = appr 12.8 cm
*May 1, 2014*

**Algebra**

rate of new = 72/2 copies/min rate of old = 72/x copies/min combined rate = 72/2 + 72/x = (72x + 144)/(2x) copies per min 72/(72x+144)/(2x)) = 1.5 72(2x)/(72x+144) = 1.5 144x = 108x + 216 36x = 216 x = 6 rate of old machine = 72/6 or 12 copies/minute
*May 1, 2014*

**last question - math**

if m , m+3, m^2 + 3 are in geometric progression, then (m+3)/m = (m^2 + 3)/(m+3) m^3 + 3m = m^2 + 6m + 9 m^3 - m^2 - 3m - 9 = 0 normally cubics are hard to solve, but I tried factors of 9 and found m = 3 to work so the numbers are 3, 6, 12 so each number is double its previous...
*May 1, 2014*

**math**

For a quadratic function , the turning point would be the vertex of the parabola. since your equation is written in vertex form f(x) = (x+3)^2 - 16 the vertex is (-3,-16) , which would be your turning point. If your quadratic is written in the form f(x) = ax^2 + bx + c there ...
*May 1, 2014*

**math**

difference of squares = (1 + 4(1-y) )(1- 4(1-y)) = (1 + 4 - 4y)(1-4 + 4y) = (5-4y)(4y - 3)
*May 1, 2014*

**Alg**

are we looking at two inequalities: y^2/4 - x^2.25 ≤ 1 y ≥ 2x/3 + 4 ?? What about them? are we graphing their intersection? if so, ... x^2/4 - y^2/25 = 1 is a hyperbola so x^2/4 - y^2/25 ≤ 1 would be the region "inside" the hyperbola see: http://www...
*May 1, 2014*

**math**

dimes --- x nickels ---2x value equation: 10x + 5(2x) = 70 20x=70 x = 3.5 NO WAY!! , can't have 3.5 dimes this question is bogus, no solution. Check your typing, or the problem is silly.
*April 30, 2014*

**College Algebra and Trigonometry**

looking back at your earlier attempts at typing this question I am going to guess you meant x(t)= 2 cos (5πt+π/3) you want this to be 1.5 2cos (5πt + π/3) = 1.5 cos (5πt + π/3) = 1.5/2 = 3/4 I know cos( .722734..) = 3/4 so 5πt + π/3 = ....
*April 30, 2014*

**math**

(-1 , √3) ----> (-1 , -√3) after reflection in the x-axis new point is in III, tanØ = -√3/-1 = 240° in III magnitude = √(1^2 + √3^2) = √4 = 2 point in polar coordinates: (2cos240°, 2sin240°) or (2cos 4π/3, 2sin 4&#...
*April 30, 2014*

**math**

number with 1 Lavender = 1 x C(13,4) = 715 number with 1 yellow = C(5,1) x C(9,4) = 630 exclude yellow and lavender = C(8,5) = 56 number as described = 715+630-56 = 1289
*April 30, 2014*

**Calculus**

I answered the same type of question back in 2009 http://www.jiskha.com/display.cgi?id=1245646756 Just change the numbers.
*April 30, 2014*

**Math**

a) prob winning = 1/C(49,6) = 1/13,983,816 b) 10,000/13,983,816 c) x/13,983,816 = 1/2 , solve for x d) prob not winning = 13,983,815/13,983,816 odds against winning = 13,983,815 : 13,983,816 e) expected value = 1,000,000(prob of a) )
*April 30, 2014*

**math**

100% + 5% salestax = 1 + .05 = 1.05 to increase something by 5% , just multiply it by 1.05
*April 30, 2014*

**math**

.85(1.05)x = 30 x=30/(.85(1.05)) = $33.61
*April 30, 2014*

**Algebra**

same type of question here http://www.jiskha.com/display.cgi?id=1397438547 just change the numbers.
*April 30, 2014*

**Algebra 1/2**

prob(3 or 5) = 2/8 = 1/4 prob(2) = 1/8 prob(3or5 then 2) = (1/4)(1/8) = 1/32
*April 30, 2014*

**Algebra 1/2**

not enough information, what kind of spinner? how many positions are possible ?
*April 30, 2014*

**math**

let the time taken by the eastbound plane until they meet be t hrs let the time taken by the westbound plane until they meet be t-1/2 hrs distance covered by the easbound plane = 700t distance covered by the westbound plane = 750(t - 1/2) 700t + 750(t-1/2) = 3420 700t + 750t...
*April 30, 2014*

**math**

What about it ? Are we integrating ? if so ... ∫sin(πx+1)dx = (-1/π)cos(πx+1) + C
*April 30, 2014*

**Algebra 2**

I answered this as part of the reply to your log question http://www.jiskha.com/display.cgi?id=1398883636 about the third line down ....
*April 30, 2014*

**Probability**

doubles --- 6 of them sumof 8 --- 26,35,44,53 62 total = 10 (we have to count 44 only once) prob = 10/36 = 5/18
*April 30, 2014*

**Math**

number of reds = 26 number of blacks faces = 6 (I think) prob(red card or black face) = 32/52 =8/13 (I believe face cards are defined as Jack, Queen and King, if not change the numbers above to match)
*April 30, 2014*

**Algebra 2**

4x = log5 90 or 5^(4x) = 90 take log of both sides log (5^(4x) = log 90 4x log5 = log90 4x = log90/log5 x = (1/4)(log90/log5) = appr .699
*April 30, 2014*

**Maths**

number of white --- n number of non-white -- 12-n prob of choosing at least 1 white = 1 - prob(choosing both non-white) = 1 - (12-n)/12 * (11-n)/11 = 19/33 (12-n)(11-n)/132 = 1 - 19/33 = 14/33 (132 - 23n + n^2)/12 = 14/3 3n^2 - 69n + 396 = 168 3n^2 - 69n +228 = 0 n^2 - 23n + ...
*April 30, 2014*

**math**

66 2/3 % is equivalent to 2/3 so (2/3)(81) = 54
*April 30, 2014*

**math**

It often helps to see a physical model of the problem Cut out a circular sector with scissors and form it into a cone. You will see that the arc length of the sector becomes the circumference of the circular base of the cone if the cone is to have a radius of 6 cm, then its ...
*April 30, 2014*

**Math**

2H + 1F = 8 ===> F = 8-2H 6H + 6F = 30 or H+F=5 using substitution: H + F = 5 H + 8-2H = 5 -H = -3 H = 3 then F = 8-6 = 2 each hamburger costs $3.00 and each fries costs $2.00
*April 29, 2014*

**Math**

width --- x lengyth -- x+11 x(x+11) = 2040 x^2 + 11x - 2040 = 0 (x-4)(x+51) = 0 x = 40 or x = - 51 , negative width makes no sense, so x = 40 the rectangle is 40 cm by 51 cm
*April 29, 2014*

**math**

I have a feeling you have typos here. Is that supposed to be 24x^2 at the top and 32x^2 ... at the bottom ?
*April 29, 2014*

**calculus**

(9x^3+5x-8) ÷ (3x-2) I assume you are studying long algebraic division, I got 3x^2 + 2x + 3 - 2/(3x-2)
*April 29, 2014*

**math**

number of tickets bought ---- x 2x ≤ 30
*April 29, 2014*

**Algebra**

(89+88+78+95+92+x)/6 = 90 solve for x
*April 29, 2014*

**grade 3 math**

There is no such rectangle. I can make the length some ridiculous length and the width very very small. e.g. length = 5000 width = 39/5000= .0078 check: the area is 5000(.0078) = 39 Perimiter is 2(.0078) + 2(5000) = 1000.0156 ft length = 20,000 width = 39/20000 = .00195 ...
*April 29, 2014*

**Trig**

This is exactly the same type of question as your previous one. Just follow my steps using these numbers.
*April 29, 2014*

**Trig**

if t1 = 7 and t2 = 205 then d = 205-7 = 198 sum(100) = (100/2)(2(7) + 99(198)) = 50(19616) = 980800
*April 29, 2014*

**Trig**

Just use your definition of term(2) and plug in the values.
*April 29, 2014*

**Trig**

a9 = 120 ----> a + 8d = 120 a14 = 195 ---> a + 13d = 195 subtract them 5d = 75 d = 15 then a+8(15) = 120 a = 0 so term(6) = a+5d = 0 + 5(15) = 75
*April 29, 2014*

**maths**

5cosx + 3 = 0 cosx = -3/5, and 180° < x < 306° so that x is in quadrant III did you notice the 3-4-5 right-angled triangle ratios? so sinx = -4/5 tanx = 4/3 3tanx + 25sin^2 x = 3(4/3) + 25(16/25) = 20 ( you can use your calculator to check this result Ø = ...
*April 29, 2014*

**math**

let the distance be d miles for Hannah: let her speed be x mph d = 6.5x for Dylan: let his speed be x+30 mph d = 2.6(x+3) 6.5x = 2.6(x+30) 6.5x = 2.6x + 78 3.9x = 78 x = 20 then d = 6.5(2) or 130 miles (I would have that "caps lock" malfunction looked after on your ...
*April 29, 2014*

**math:mensuration plane shapes**

If radius of cone is 4 cm, and its height is 3 cm, then the "slant" length of the cone is 5 cm (3^2 + 4^2 = 5^2) If cut open , this translates into a "pac-man" game looking sector with arc length equal to the circumference of the base of the cone and its ...
*April 29, 2014*

**math**

2^ = .125 2^x = 1/8 2^x = 1/2^3 = 2^-3 then x = -3
*April 29, 2014*

**Calculus**

go with Steve's I forgot to multiply the .02 by the 3 in front
*April 28, 2014*

**Calculus**

write it as P(t) = 20 (1 + 3e^(-.02t)^-1 P ' (t) = -20(1+3e^-.02t)^-2 (-.02 e^(-.02t) ) now use the product rule to get the 2nd derivatives I suggest cleaning up the first deriv. a bit
*April 28, 2014*

**Math**

I just can't see a pattern even Wolfram, which surprised me with a "pattern" function, could not see anything (I tested to see if Wolfram was able to pick up a pattern. I used n + 2^n to get the terms 3,6,11,20,37 and entered pattern { 3,6,11,20,37} look what it ...
*April 28, 2014*

**Math**

from the 1st ---- y = 8-2x so 8 - 2x = -3(x-3) 8-2x = -3x + 9 x = 1 in y = 8-2x, y = 8-2 = 6 looks like D
*April 28, 2014*

**math (1)**

Just drop in the values and stir. e.g. c) x = 2, y=1 h(2,1) = (4+8)/(2-1) = 12 That's all there is to it.
*April 28, 2014*

**Math**

(3√8 + 4√9)^2 = (3√8 + 12)^2 = 72 + 72√8 + 144 = 216 + 72(2√2) = 216 + 144√2 or appr 419.65
*April 28, 2014*

**math**

2x+8=3x+2 2x - 3x = 2 - 8 -x = -6 x = 6
*April 28, 2014*

**math**

5x-2(x+4)=3(2x+1) 5x - 2x - 8 = 6x + 3 5x - 2x - 6x = 3 + 8 -3x = 12 x = -4
*April 28, 2014*

**Physics waves- check answers please**

agree with all of them
*April 28, 2014*

**Integrated Trig**

if compounded annually 1.03^t = 2 t ln1.03 = ln2 t = ln2/ln1.03 = appr 23.45 years
*April 28, 2014*

**Integrated Trig**

5000 e^(.03t) = 10000 e^(.03t) = 2 take ln of both sides , and use rules of logs .03t = ln 2 t = ln 2/.03 = appr 23.1 years
*April 28, 2014*

**math**

solve for x 2x + 2(3x) = 64
*April 28, 2014*

**Math 1314**

width of pond --- x length of pond --- 3x width of whole thing = x+6 , (3 feet on each end) length = 3x + 6 2(x+6) + 2(3x+6) = 100 2x + 12 + 6x + 12 = 100 8x = 76 x = 9.5 ft the pond is 9.5 ft wide and 28.5 ft long
*April 28, 2014*

**Math 120**

d = -16t^2 , if we have to consider direction or d = 16t^2 if all we care about is distance when t = 17 d = 16(17)^2 = 4624 ft some deep well !!
*April 27, 2014*

**Math HELP HELP**

use Venn diagrams, fill in your data starting with the intersection of all three, then the intersection of two at a time, etc.
*April 27, 2014*

**Maths**

check your previous post for this
*April 27, 2014*

**math/ratio**

let the number of apples, oranges, and pears be 3x, 5x, and x respectively. 5x+x - 3x = 12 3x = 12 x = 4 so 12 apples, 20 oranges and 4 pears check: oranges + pears = 24 apples = 12 is 24 more than 12 by 12 ?? YES
*April 27, 2014*

**Calculus**

area = integral ( e^-x) from 0 to infinitiy = [ - e^-x] from 0 to infinity = [-1/e^x] from 0 to infinity now clearly as x ---> ∞ , 1/e^x --> 0 so we have ( 0 - (-1/1) = 1
*April 27, 2014*

**Math**

Do you want the probability of drawing 2 green balls? = (3/5)(2/4) = 3/10
*April 27, 2014*

**Maths**

the 17 would cancel, leaving you with 93/97
*April 27, 2014*

**Math**

The way you typed it: 5x/6 = 15 5x = 90 x = 18
*April 27, 2014*

**Precalculus**

A = {2,3,5,7,11,13} B = {1,2,3,4,6,9,12} c= {4,8,12,16} Just noticed that in your listing of C you don't have the 16 Does that result in your difficulties? A intersect B = {2,3) (A intersect B)' = {1,4,5,6,7,8,9,10,11,12,13,14,15,16} which in "union" with C...
*April 27, 2014*

**Math**

18 ft / 2 seconds = 9 ft/sec = (9/5280) miles / (1/3600) hours = (9/5280)(3600/1) m/h = (135/22) mph = appr 6.1 mph or 18 ft in 2 seconds = 9 ft in 1 second = 540 ft in 1 minute = 32400 ft in 1 hour = 6.1 mph
*April 27, 2014*

**algebra**

tried: ±1 , ±2 and found x = 2 to be a triple root. successive synthetic divisions shows x^5−8x^4+28x^3−56x^2+64x−32=0 (notice how we show exponents) x=2 to be triple root so x^5−8x^4+28x^3−56x^2+64x−32=0 (x-2)^3 (x^2 - 2x + 4...
*April 27, 2014*

**Math - Trigonomety**

What a silly and unrealistic problem, anyway .... I made a sketch the main working triangle has the height of the tree, its opposite angle as 10°, and the other angles as 105° and 65° The side opposite the 105° is also the hypotenuse of a right-angled triangle ...
*April 27, 2014*

**Geometry**

Ms Sue solved the "same" question. Just change the numbers http://www.jiskha.com/display.cgi?id=1398287442
*April 27, 2014*

**MATHS**

x/2 + 2y/3 = -1 ---> 3x + 4y = -6 x - y/3= 3 --------> 3x - y = 9 elimination: subtract them: 5y = -15 y = -3 sub into the 2nd 3x - (-3) = 9 3x = 6 x = 2 x = 2, y = -3 by substitution: from the 2nd: y = 3x-9 into the 1st: 3x + 4(3x-9) = -6 3x + 12x - 36=-6 15x = 30 x = 2...
*April 27, 2014*

**math**

to me this says: x = 4sin^3 t y = 7cos^3 t dx/dt= 12(sin^2 t)(cost) = 12cost(sint)^2 dy/dt= 21(cos^2 t)(-sint) or -21sint(cost)^2 both dx/dt and dy/dt must be zero for dx/dt =0 , dy/dt=0 12cost(sint)^2 = 0 , -21sint(cost)^2 = 0 in other words, wherever the sine or cosines are ...
*April 27, 2014*

**Pre algebra**

1 km/h = (1/60) km/minute (how many minutes are there in 1 hour? ) You don't post an actual speed (typo?). so suppose you have 80 km/h = (80/60) km/min = (4/3) km/min replace my speed with whatever speed you have, then simplify ??/60 to lowest term fractions.
*April 26, 2014*

**Jim and Mia : - Math (6)**

Jim, they do intersect at one point only, thus creating an open region on the left. By squaring you are introducing a part of the graph which was originally undefined. y = √x is defined only for x ≥ 0 Mia: Both Steve and I gave answers to this earlier http://www....
*April 26, 2014*

**math (4)**

graph of your function http://www.wolframalpha.com/input/?i=y%3D++-xe%5E%28-x%5E2%29++from+0+to+1 notice the region will be below the x-axis, so height = 0 - (-xe^(-x^2)) = xe^(-x^2) area = integral (xe^(-x^2)) dx from 0 to 1 = (-1/2) e^(-x^2) from 0 to 1 = (-1/2) e^-1 - (-1/2...
*April 26, 2014*

**math (2)**

Here is what your curve looks like from x = -1 to +1 http://www.wolframalpha.com/input/?i=y%3D+2x%2F%28x%5E2%2B4%29+from+-1+to+1 So where is the shaded region? Are you finding the area between the curve and the x-axis? (That is the usual case for this question, but let me know...
*April 26, 2014*

**Trig**

Or use the old sum of roots and product of roots property sum of roots = 5+i√2 + 5-i√2 = 10 product of roots = (5+i√2)(5-i√2) =25-2i^2 = 25+2 = 27 x^2 - (sum)x + product = 0 x^2 - 10x + 27 = 0
*April 26, 2014*

**Calculus**

draw a sketch of the situation, at a time of t hours after 9:00 am let A1 be the position of Aida let I1 be the position of Ian Join A1 and I1, to get a right-angled triangle let D be the distance between them D^2 = (6t)^2 + (20-8t)^2 = 36t^2 + 400 - 320t + 64t^2 = 100t^2 - ...
*April 26, 2014*

**Deepa**

let the number of 50 cents increases be n NOW: number of riders = 10000 cost per ride = 20 after increase number of riders = 10000- 200n cost per ride = 20+ .5n Revenue = (10000-200)(20 + .5n) expand this and you will have a quadratic representing a parabola that opens ...
*April 26, 2014*

**For fizz - math**

I answered this for you already http://www.jiskha.com/display.cgi?id=1398482333 I counted about 8 problems dealing with series of discounts, plus numerous questions that have been answered dealing with compound interest. I don't see a single reply by you or even a response...
*April 26, 2014*

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