Monday

March 2, 2015

March 2, 2015

Total # Posts: 29,207

**math**

I can't see your diagram, but the diagonal of the square from (4,1) to (5,8) is also the diameter of the circle length = √(1^2 + 7^2) = √50 = 5√2 so the radius of the circle must be 2.5√2 perimeter of circle = 2πr or dπ = √50π...
*January 4, 2015*

**Math**

mmmh, diagonals in a triangle ? Label your given points A, B, and C in the corresponding order. Clearly AB is a horizontal line, thus AB = 8 AC = √(1^2 + 9^2) = √82 BC = √(7^2 + 9^2) = √130 perimeter = 8 + √82 + √130 = appr 28.5
*January 4, 2015*

**math**

the number is 10y + x 10y + x = 9(x+y) 10y + x =9x + 9y y - 8x = 0 or y = 8x since both x and y must be ≤ 9, the only choice for x = 1 so y = 8 and the number must be 81
*January 4, 2015*

**maths**

100000 = 3000( 1 - 1.0041666...^-n)/.0041666.. .3888.. = 1 - 1.0041666..^- 1.0041666..^-n = .61111.. take log of both sides and use log rules - n = log .61111../log 1.0041666.. -n = - 118.44 n = 118.44 So there are 118 full payments of 3000 plus another partial payment at ...
*January 4, 2015*

**Maths**

done, see the two previous posts of the same question.
*January 4, 2015*

**Maths**

net price = (200)(.9)(.95)(.98)(.95) = 159.20
*January 4, 2015*

**Maths**

Always check back to see if your previous post of the same question has been answered before reposting it. http://www.jiskha.com/display.cgi?id=1420301789 This will prevent unnecessary duplication.
*January 4, 2015*

**ALGEBRA**

i = .03/12 =.0025 n = 12(20) = 240 amount = 200 ( 1.0025^240 - 1)/.0025 = .....
*January 3, 2015*

**Math - Please help**

slope of given line is 4 since the new line is parallel, its slope must also be 4 let y = 4x + b using the point (1,-3) -3 = 4(1) + b -7 = b new equation in slope-intercept form is y = 4x - 7
*January 3, 2015*

**Maths**

You need one more piece of information. The way it stands ar^2 = 7 r^2 = 7/a r = ±√(7/a)
*January 3, 2015*

**ALGEBRA**

You have to know the formulas for the general term and the sum of n terms of an arithmetic sequence term6 = a + 5d = 48 sum6 = (6/2)(2a + 5d) = 300 3(2a + 5d) = 300 2a + 5d = 100 subtract the two two equations: a = 52 back in a+5d = 48 52+5d = 48 5d = -4 d = -4/5 so the first ...
*January 3, 2015*

**math**

yup, there are lots of them let Google be your friend
*January 3, 2015*

**trig**

In other words.... we have to prove that 2sinxcosx + 4cos^2 x - 1 = tan^2 x - 2tanx - 3 I had my doubts about this "identity" so I tried any arbitrary value of x (remember , all we need is ONE exception and the identity is not true) I tried x = 21° LS = 2sin21 ...
*January 3, 2015*

**calculus**

use the product rule .. dy/dx = x^3 (5/5) + 3x^2 ln(5x) = x^2 + 3x^2 ln(5x) or = x^2(1 + 3ln(5x) )
*January 3, 2015*

**^NeEd HeLp^**

What language are you using? The majority of questions posted here are in English.
*January 3, 2015*

**Algebra 1**

Since both equations were in the form y = ... he simply replaced the y value of the first equation with the y value of the second. Some texts call this the "comparison" method e.g. if a = b and c = b , then a = c yes, you could use elimination after some doctoring of...
*January 3, 2015*

**trigonometry**

I see a right-angled triangle with hypotenuse of 60 and a base angle of 52° sin52 = y/60 --> y = 60sin52 = ... cos52 = x/60 ---> x = 60cos52 = ...
*January 3, 2015*

**AP CaLC. AB**

if v(t) = t^2 - 3cos(t) then s(t) = (1/3)t^3 - 3sin(t) + c given : when t = 0 , s(0) = 0 0 = 0 - 3sin0 + c c = 0 so when v = 0 0 = t^2 - 3cos(t) using Wolfram, I got t = 1.13062 where does x enter the picture, your function was defined in terms of t http://www.wolframalpha.com...
*January 3, 2015*

**retype - calculus**

Let me type this again in proper English. (Can I blame it on my keyboard ? ) Clearly the vertex of this parabola is (-2,-4) and it opens downwards. Thus it cannot possible reach the x-axis, thus there are no x-intercepts for the y-intercept, in you let let x = 0 and evaluate ...
*January 3, 2015*

**calculus**

clearly the vertex of this parabola is (-2,-4) and it opens downwards. This is cannot possible reach the x-axis, thus no x-intercepts for the y-intercepts, in you head let x = 0 and evaluated to get y = -4-4 = -8
*January 3, 2015*

**Calculus**

h ' (x) = 3x^2 + b = 0 at a critical point if (2,-4) is a critical point, 3(4) + b = 0 b = -12 but (2,-4) also satisfies h(x) -4 = 8 - 12(2) + c c = 12 thus h(x) = x^3 - 12x + 12
*January 2, 2015*

**Statistic**

for test1 prob correct = 1/4 prob wrong = 3/4 i) could be c or wc or wcc , (c for correct, w for wrong) prof (of that) = 1/4 + (3/4)(1/4) + (3/4)^2 (1/4 = 37/64 ii) less than 4 correct ---> none correct + 1 correct + 2 correct + 3 correct = C(8,0) (1/4)^0 (3/4)^8 + C(8,1)(1...
*January 2, 2015*

**Physics 1**

v = -9.8 t so when t = 10 s v = -9.8(10) = -98 m/s The negative indicates the direction of the stone.
*January 1, 2015*

**algebra 2**

I will assume you meant to type (x^2 + 8x + 15)/(x+5) and you want to simplify it = (x+5)(x+3)/(x+5) = x+3 , x ≠ -5
*January 1, 2015*

**math**

The number of subsets of 6 from 18 is C(18,6) = 18!/(6!12!) = 18564
*January 1, 2015*

**regneing**

Very strange question. 2 x 8084506040 ≠ 8002408082
*December 31, 2014*

**Math**

You would use ADDITION No need for multiplication, division, or fractions in this case. 360+240=600
*December 31, 2014*

**MATH**

If you have two points (a,b) and (c,d) then the distance between them is √( (a-c)^2 + (b-d)^2 ) (notice that since we are squaring the difference, it really would not matter in which direction you are subtracting) e.g. for R(-2,1) and S(-5,1) RS = √( (-2+5)^2 + (1-...
*December 31, 2014*

**Algebra**

Olivia, why did you not evaluate the equation given to you in the first reply ? it gives a time of 2.777... or 2.8 years Bob gave you the calculation using compound interest, the most likely scenario in our 21st Century, and the time for this real-life case would be 2.65 years...
*December 31, 2014*

**Algebra 1**

What is this? Are you expanding 2x(3xy + 4y² + 8y) ? Then it would simply be = 6x^2 y + 8x y^2 + 16xy What you did is pure mathematical gibberish
*December 30, 2014*

**GRANTHAM**

PV = 2000 (1 - 1.06^-14)/.06 = ....
*December 30, 2014*

**Algebra 1**

I agree with Steve, I got x = 6/17 , y = 9/17 , which does not match any of the answers given
*December 30, 2014*

**algebra 2**

divide each term by -3 x^4 - 9x^2 - 400 = 0 (x^2 - 25)(x^2 + 16) = 0 x^2 = 25 OR x^2 = -16 x = ± 5 or x = ± 4i
*December 29, 2014*

**Algebra 2**

The correct statement is Salary = 2000x + 45500 , 0 ≤ x ≤ 10 , x ∈ I so it looks like B is the closest match. James's answer is incorrect, e.g. if x = 1 , the salary based on his formula is 45700 whereas it should be 47500, which is obtained with B
*December 29, 2014*

**Algebra 1**

Lucina's conclusion is correct, but based on an incorrect result. The slope of the first line is -2/3 the slope of the 2nd line is 2/3 so they are neither parallel nor parallel Lucina stated that their slopes were equal, if they had been equal, then the lines would have ...
*December 29, 2014*

**Algebra 1**

We can see that the slope of the given line is -1/4 So the slope of our new line must be 4 thus: y-5 = 4(x+3) Massage this equation to whatever form you need
*December 29, 2014*

**Precalculus**

No you have to expand (800+x)tan33 to get at the x inside the bracket. so ... 800tan33 + xtan33 = xtan35 now get all the x terms to one side 800tan33 = xtan35 - xtan33 x is a common factor: 800tan33 = x(tan35-tan33) divide both sides by tan35-tan33 800tan33/(tan35-tan33) = x ...
*December 29, 2014*

**geometry**

Let a point on the locus be P (x,y) then √(x^2 + y^2) = √((x+2)^2 + (y-5)^2) square both sides: x^2 + y^2 = (x+2)^2 + (y-5)^2 x^2 + y^2 = x^2 + 4x + 4 + y^2 - 10y + 25 4x - 10y = -29 which is the perpendicular bisector of the line joining (0,0) and (-2,5) , as ...
*December 29, 2014*

**CAL-Critical points**

F ' (x) = (x^2(1/x) - lnx(2x) )/x^4 = (x - 2x lnx)/x^4 = 0 for critical values x - 2x lnx = 0 x(1 - 2lnx) = 0 x = 0 , but for lnx to be defined, x > 0 or 1-2lnx = 0 lnx = 1/2 , x = √e x = appr 1.65 y = (1/2) / (1.65)^2 = appr .18 the critical point is appr (1.65...
*December 29, 2014*

**Algebra**

You probably mean, "completing the square", where we take the square root near the end of the process x^2 - 10x + 22 = -2 x^2 - 10x + ..... = -24 + ..... x^2 - 10x + 25 = -24 + 25 (x-5)^2 = 1 take √ of both sides x - 5 = ± √1 = ± 1 x = 5 &...
*December 29, 2014*

**mathematics**

height/15 = tan 30° take over ....
*December 29, 2014*

**Mathematics**

look for common factors first, looking at the 5x^4 and 20x^3 , that would be 5x^3 looking at the (x-7)^(-1/2) and (x-7)^(1/2) , that would be (x-7)^(-1/2) , (take the lower exponent one) also I would take out the fraction of 1/2 = (1/2)(5x^3)(x-7)^(-1/2) [x + (2/1)(4)(x-7...
*December 29, 2014*

**Mathematics**

Use the product rule for the first and the quotient rule for the second. 1. y = (5x^4)(x - 7)^(1/2) dy/dx = (5x^4)(1/2)(x-7)^(-1/2) + 20x^4 (x-7)^(1/2) I found most students find the difficulty not in finding that first derivative line, but rather in simplifying it I don't...
*December 29, 2014*

**Mathematics**

y = |x-3| ----> y = x-3 for x>3 or y = -x + 3 for x<3 for y = x-3, dy/dx = 1 , for x > 3 for y = -x+3, dy/dx = -1 , for x < 3 look at the graph of y = |x-3| http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx-3%7C when x = 3, y = 0 for both parts of the ...
*December 29, 2014*

**maths**

contradiction ! If your tank is half full and it contains 15 L, then the full capacity must be 30 L If the tank only can hold 18 L as you said, then at 15 L it is not "half filled" If you are asking what fraction 15 is of 18 ??? 15/18 = 5/6
*December 29, 2014*

**Math**

No, the point 4,4) ----> (4,-4) after a reflection in the x-a xis but the point (4,4) ---> (-4,4) after a rotation of 90° For a point P(x,y) the slope of PO , where O is the origin is (y-0)/(x-0) = y/x For a point P1(-y,x) , the slope P1O = x/-y, which is the ...
*December 28, 2014*

**AP Calc**

f ' (x) = x(1/x) + lnx + (1-x)(-1/(1-x)) + -1(ln(1-x) = 1 + lnx -1 - ln(1-x) = lnx - ln(1-x) = ln(x/(1-x)) = 0 for a min then e^0 = x/(1-x) 1 = x/(1-x) 1-x = x x = 1/2 Proof: confirmed by Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+x+ln+x%2B%281-x%29ln%281-x%29
*December 20, 2014*

**AP Calc**

I believe this is the same question, and answered by Steve http://www.jiskha.com/display.cgi?id=1419047350
*December 20, 2014*

**Math - Two-Step Inequalities - Please Help**

–3 > –3t + 6 3t > 6+3 3t > 9 t > 3 So for the given numbers, I see that only 4 > 3 so , yes, C is the correct answer.
*December 19, 2014*

**Math**

You have to look for some pattern Did you notice that for every 1 unit increase in the x's there is a 5 unit increase in the y's so you know it starts with y = 5x + b, we still don't know the b plug in one of the points , how about (1,2) 2 = 5(1) + b b = -3 ...
*December 19, 2014*

**math**

"Using 22/7 for pi is just not rational! " good one, they were selling t-shirts with that slogan to the math-nerds at our University of Waterloo a few years back.
*December 19, 2014*

**math**

I think 22/7 is the approximation we used for π in the "olden days" so a + b = π/2 or a and b are complementary angles Construct a right angled triangles with angles a and b along with the right angle since sina = 1/3, the missing side is √8 by ...
*December 19, 2014*

**Algebra**

x • b • y • a = (xy)(ab) = (1/37)(37) = 1
*December 18, 2014*

**math**

Elimination is a poor choice for this question. I would definitely use substitution. sub the 1st into the 2nd 2(5y) - 3y = 7 10y-3y=7 7y=7 y = 1 , then x = 5 compare this with elimination: 5y = x x - 5y = 0 multiply by 2, 2x - 10y = 0 2x - 3y = 7 subtract them -7y = -7 y = 1 ...
*December 18, 2014*

**Algebra math**

In English please.
*December 18, 2014*

**math**

number of people ---- n Company A: CostA = 25n + 50 Company B: CostB = 20n + 130 So for n = 100 CostA = 2500+50 = 2550 CostB = 2000+130 = 2130 When is CostA = CostB ? 25n + 50 = 20n + 130 5n = 80 n = 16 break-even number is 16 people.
*December 18, 2014*

**Math**

Why not just reverse the process and subtract 2 from top and bottom to get 2/3 ?
*December 18, 2014*

**Calculus**

done, look back please
*December 18, 2014*

**math**

first one is correct #2, 6.3% of $77 = .063(77) = $4.85 77+4.85 = 81.85 , so #4
*December 18, 2014*

**Calculus**

First of all you must understand what the intersection is When you intersect two planes you get a straight line, unless the two planes are parallel In this case they are not, since 1:1:-1 ≠ 2:4:-3 multiply the first by 3 3x+3x-3z = -36 subtract 2x+ 4y - 3z = -8...
*December 18, 2014*

**Math**

The inclusive vs exclusive restrictions in rational expressions always leads to debate. I restricted x = -1 and x = -2 since subbing in these values in the original yields 0/0 but subbing those values in my answer (and yours) yields a real number Since I was using the equal ...
*December 18, 2014*

**Math**

I read that as: (x^2 - 2x)/(x+1) * (x^2 - 1)/(x^2 + x - 6) =x(x-2)/(x+1)*(x-1)(x+1)/( (x+3)(x-2) = x(x-1)/(x+3) or (x^2 - x)/(x+3) , x ≠ -1,2
*December 18, 2014*

**math**

Please number your question, how are we to know who is who and what you want done 1. assuming you want to solve 2/3n = 8 multiply each term by 3 2n = 24 n = 12 2. sub the 2nd into the 1st 4x + 3y = 13 4x + 3(-x+4) = 13 4x - 3x + 12 = 13 x = 1 back into the 2nd, y = -1+4 = 3 x=...
*December 18, 2014*

**Algebra**

good job
*December 18, 2014*

**Algebra**

first get rid of nasty fractions by multiplying each term by 3 , LCD 3x^2 - 5x + 2 = 0 which factors quite nicely. Let me know what you got
*December 18, 2014*

**algebra**

speed of boat --- x speed of current -- y x+y = 21 x-y = 5 add the two equations, and continue
*December 18, 2014*

**Algebra**

You typed the equation incorrectly, it should say y = 5 (1/2)^(t/20) so ... 4 = 5(1/2)^(t/20) .8 = (.5)^(t/20) take log of both sides log.8 = log(.5^(t/20)) log.8 = (t/20)log.5 log.8/log.5 = t/20 t = 20(log.8)/log.5) I leave the button-pushing up to you
*December 18, 2014*

**stats**

a) prob = (25/32)(24/31) = .. b) prob = (25/32)(7/31) = ... c) prob (both red) = answer to a) prob(both black) = (7/32)(6/31) = .. prob(different colour) = 1 - a) - both black
*December 18, 2014*

**math algebra**

Let the length along the front be x let the width be y let the height be z x^2+ z^2 = 25^2 = 625 , #1 y^2 + z^2 = 20^2 = 400 , #2 subtract them x^2 - y^2 = 225 , #3 also x^2 + y^2 + z^2 = 28^2 = 784 , #4 add it to #3 2x^2 + z^2 = 1009, but x^2 + z^2 = 625 from #1 so 2x^2 + z^2...
*December 18, 2014*

**math algebra**

recall that if the line is written in the form y = mx + b, then m is the slope so ... 8y = -16 or, how about 8y = 0x - 16 y = (0/8)x - 2 y = 0x - 2 so the slope must be 0 in general if the linear equation can be written in the form y = k, where k is just a constant, you have a...
*December 18, 2014*

**Math**

Zyere is not correct 72/60 = x/40 60x = 40(72) 60x = 2880 x = 48 The ratio of height : shadow must be the same note: 72 : 60 = 6 : 5 , and 48 : 40 = 6 : 5
*December 18, 2014*

**Math**

use a simple ratio and solve for x 72/60 = x/40
*December 18, 2014*

**math algebra**

Use the last two points to find the equation slope = (697-522)/(100-75) = 175/25 = 7 so we have y = 7x + b sub in (75,522) 522 = 7(75) + b b = -3 so we have y = 7x - 3 From your knowledge of y = mx + b, what do you think?
*December 18, 2014*

**math**

Let the capacity of the tank be x L (1/4)x + 90 = (3/4)x times 4 x + 360 = 3x 2x = 360 x = 180
*December 18, 2014*

***repost* - Grade 11 math**

sketch a right-angled triangle. On the horizontal base mark W for Wes. let the fireworks be at P and let Q be the point below P, so that angle Q = 90° let the angle at W be 28° let A for Abby be a point between W and Q so that angle PAQ = 40° , and AW = 20 Look at ...
*December 17, 2014*

**Algebra 1**

http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx+%2B2%7C
*December 17, 2014*

**math**

ar^2 = 25 ar^7 = 25/32 divide the 2nd by the 1st: r^5 = 25/32 ÷ 25 = 25/800 = 1/32 r = 1/2 in ar^2 = 25 (1/4)a = 25 a = 100 where does t come into the picture ?
*December 17, 2014*

**Math (Repost)**

1. u^-3 = 1/125 1/u^3 = 1/125 u^3 = 125 u = 5 2. y-1 = 4y - 2/3 each term times 3 3y - 3 = 12y - 2 -9y = 1 y = -1/9 3. your are right 4. number of miles last week --- x x+40 = 4x + 10 -3x = -30 x = 10 She ran 10 miles last week 5. change it into the form y = mx + b (takes 2 ...
*December 17, 2014*

**Algebra 2**

= 200(1 + .08/12)^12 = 200(1 + .0066666..)^12 = 200(1.006666...)^12 = appr 216.60
*December 17, 2014*

**Algebra 1**

slope of given line = 8/3 so slope of your new line = -3/8 through (-2,3) y = 3 = (-3/8)(x+2) since the original was written in that form, I assume the new one is to be in that same format.
*December 17, 2014*

**Math**

(m + s)/2 = 74 m+s = 148 (m + e )/2 = 83 m+ e = 166 subtract them: e - s = 18
*December 17, 2014*

**Math**

Did you notice that if you multiply the 2nd equation by 4, you get the second? So , you basically only have one equation, thus an infinite number of solutions.
*December 17, 2014*

**Algebra 2**

you know that it must be (x+y)^9 to get a ?x^7y^2 so the term is C(9,7) x^7 y^2 = 36x^7y^2 Observe that the 10th row of Pascal's triangle is 1 9 36 84 126 126 84 36 9 1
*December 17, 2014*

**Algebra**

subtract your equations: 1 Sandwich = 4.75 in the 1st: 4.75 + Salad = 8.7 salad = 3.95
*December 17, 2014*

**MATH PLEASE HELP**

1 e^.012t = 2 take ln of both sides ln e^.01t = ln2 .012t ln e = ln 2 , but ln e = 1 .12t = ln 2 t = ln2/.012 = 57.76 years or 58 years to the nearest year.
*December 17, 2014*

**Math Help**

5^x =125 <----> log5 125 = x I had my students memorize this pattern, 2^3 = 8 <---> log28 = 3
*December 17, 2014*

**Algebra**

total area = 12000 ft^2 still to be mowed = (1/2)(12000) = 8000 ft^2 let the width mowed by Lisa be x ft wide area still to be done = (100-2x)(120-2x) = 12000-200x - 240x + 4x^2 4x^2 - 440x + 12000 = 8000 x^2 - 110x + 1000 = 0 (x-100)(x -10) = 0 x = 100 or x = 10 , but clearly...
*December 17, 2014*

**Calculus**

Steve , you are right, I read the question rather superficially. (notice it was my last post last night, must have been a bit tired)
*December 16, 2014*

**Calculus**

f(x) = e^(4x^2) f(-1/4) = e^(1/4) f(1/4) = e^(1/4) avg value = (e^(1/4) - e^(1/4) )/(1/2) = 0
*December 16, 2014*

**math help!!**

This one is easier than the previous question you posted about GS's Give this one a try, you can do it.
*December 16, 2014*

**math please hellp**

Done, look back
*December 16, 2014*

**algebra 1**

when it hits the water, h = 0 0 = -16t^2 + 20t + 24 4t^2 - 5t - 6 = 0 (t-2)(4t + 3) = 0 t = 2 or t = -3/4, the last answer is inadmissible It will take 2 seconds I have no idea what the last part of your post is. Is that supposed to be a solution ? If so, it makes no sense at ...
*December 16, 2014*

**math help**

a + ar = 12 a(1+r) = 12 , #1 a + ar + ar^2 = 62 a(1 + r + r^2) = 62 , #2 divide #2 by #1 (1+r+ r^2)/(1+r) = 62/12 = 31/6 6r^2 + 6r + 6 = 31 + 31r 6r^2 - 25r - 25 = 0 (r-5)(6r + 5) = 0 r = 5 or r = -5/6 if r = 5 , in #1 6a = 12 a = 2 the first 4 terms are 2 , 10, 50, 250 if r...
*December 16, 2014*

**math**

Draw a right-angled triangle DAC, AC as a base line Let CD be the height of the building. Let B be a point between A and C, so that AB = 230 angle A = 28° angle DBC = 43° Look at triangle ABD, you know angle A = 28, angle ABD = 180-43 = 137 angle ADB = 15° you can ...
*December 16, 2014*

**Math**

Just did this when you posted it as "John"
*December 16, 2014*

**calculus**

Just like taking slope C(101) = 101^2 - 10000 = 201 C(100) = 100^2 - 10000 = 0 average rate of change = (201-0)/(101-100) = 201 instantaneous rate of change = 2x at x = 100 rate = 200
*December 16, 2014*

**Algebra 1**

y+7 = -.54(x-4)
*December 16, 2014*

**math**

double the first: 2x + 4y = 16 subtract from the 2nd x = 4 back into the 1st: 4 + 2y = 8 2y = 4 y = 2 x = 4, y = 2
*December 16, 2014*

**algebra**

prob = (10/24(10/24) = 25/144
*December 16, 2014*

**Math**

1st + last = 100 2nd + 2nd last = 100 ... ... looks like I can form 50 such pairs sum = 50(100) = 5000 use the same concept for the second question.
*December 16, 2014*

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