Monday

March 30, 2015

March 30, 2015

Total # Posts: 29,332

**algebra2**

so the hypotenuse of your right-angled triangle is 102 (ignoring the slack in the line) let the height be h sin 54.9° = h/102 h = 102sin54.9° = ...
*December 10, 2014*

**calculus**

limit ( √(x^2 + 7) - 4)/( √(x^2 - 8) - 1) , as x --> 3 my first step always is to actually sub in the approach value, sure enough, I get 0/0 That means the "eventually" my expression should factor. multiply top and bottom by (√(x^2 - 8) + 1) I ...
*December 10, 2014*

**Math**

let the length of the large rectangle be y let each of the parallel divider sides be x so we have 4x + 2y = 940 2x + y =470 y = 470 - 2x Area of whole field = xy = x(470-2x) = 470x - 2x^2 d(Area)/dx = 470 - 4x = 0 for a max of Area 4x = 470 x = 117.5 then y = 235 and the ...
*December 10, 2014*

**Ap calc**

let the distance run by the running player be x from the line of scrimmage. Let the distance between them be d In my diagram, I have a right-angles triangle with fixed side of 30, the other side (x+2.5) and the hypotenuse d, so that d^2 = (x+2.5)^2 + 30^2 2d dd/dt = 2(x+2.5) ...
*December 10, 2014*

**math**

first part is simply 40 choose 5 = C(40,5) = 658008 b) The leader can be picked in 8 ways, and then we have to choose 4 more from 39 = 8 C(39,4) = 658008 Are you surprised that the answers are the same ?
*December 10, 2014*

**math**

225+75+200-50+125 + x = 895
*December 10, 2014*

**D J HIGH SCHOOL SOST GOJAL PAKISTANmaths trignometry**

Did you make a diagram ? On mine I labeled the top of the observation point A and its bottom as B The farter boat as P and the closer boat as Q So we have two right-angled triangles with the angle at P as 30° and the angle at Q as 45° in triangle AQB , tan 45° = ...
*December 10, 2014*

**Calculus**

amount at the beginning = 5000 amount after 20 years = 5000 e^(.04(20)) = 11127.70 evaluated the "average value" as defined in your text book or notes. I don't know how it was defined for your course.
*December 10, 2014*

**Math**

Question is not clear. How is the interest rate compounded? When are payments made? What is that payment?
*December 9, 2014*

**Math**

f ' (x) = 3x^2 + 12 which is clearly positive for any value of x you give me. So, yes, you are correct
*December 9, 2014*

**CAL**

Why do you keep switching names ? As you can see from the previous replies there is a max at x = 1 form 0 to 3 for x = 1 y = 3 - 25 + 60 + 1 = 39 so the max is (1,39) the graph I gave you confirms this
*December 9, 2014*

**Derivative Test**

I did most of this in the previous post Here is a picture of your graph http://www.wolframalpha.com/input/?i=plot+y+%3D+3x%5E5+%E2%80%93+25x%5E3+%2B+60x+%2B+1
*December 9, 2014*

**Math**

no, points consist of ordered pairs of two numbers. ±1 and ±2 are the x's of the points. I told you what to do with those x's above, please read it.
*December 9, 2014*

**Math**

I am sure you meant: y = 3x^5 - 25x^3 + 60x + 1 dy/dx = 15x^4 - 75x^2 + 60 = 0 for your critical values 3x^4 - 15x^2 + 12 = 0 x^4 - 5x^2 + 4 = 0 (x^2 - 1)(x^2 - 4) = 0 x^2 = 1 or x^2 = 4 x = ± 1 OR x = ± 2 sub in those values of x in the original to get the ...
*December 9, 2014*

**7th grade math**

why are you repeating the questions? btw , the very last one is correct
*December 9, 2014*

**7th grade math**

#1 - correct , all you had to do is multipy 1 1/4 by 3 , sinc 9 helpings = 3 x 3servings #2 5 cm <----> 1500 ft 1 cm < ----> 500 ft, that is a scale #3, no need to convert, if you use the same units in each fraction 2.5/4.25 = 50/x 2.5x = 212.5 x = 212.5/2.5 = 85 ...
*December 9, 2014*

**Trigonometry**

Does this help ? http://www.wolframalpha.com/input/?i=plot+y%3D3cos%282x%29+%2C+y%3D-4sin%284x%29
*December 9, 2014*

**math**

by proper subsets I assume we would exclude the empty set So with the empty set there were 256 subsets for n elements, the number of subsets is 2^n 2^n = 256 but 256 = 2^8 so n = 8 and there were 8 elements in the set
*December 9, 2014*

**MATH HELP ASAP!**

Time = Interest/(principal x rate) = 550/(1000(.05) = 550/50 = 11 yup, its 11
*December 9, 2014*

**Pre-Algebra can you please help?!**

interest from simple interest = 400(.045)(3) = 54 interest fromt he compound account = 450(1.032)^3 - 450 = 44.60 total interest = 54 + 44.60 = 98.60 , which is D
*December 9, 2014*

**Math**

i = .05004/12 = .00417 n = 25(12) = 300 let the monthly payment be p p(1 - 1.00417^-300 )/.00417 = 292649 the monthly payment is $ 1711.48
*December 9, 2014*

**math**

I entered your date into this wonderful website http://davidmlane.com/hyperstat/z_table.html and got 21.19 %
*December 9, 2014*

**Math**

you are given 2 ordered pairs (5 , 1050) and (9,900) slope = (900 - 1050)/(9-5) = - 150/4 = - 75/2 N = (-75/2)C + b using (5,1050) 1050 = (-75/2)(5) + b 1050 + 375/2 = b b = 2475/2 N = (-75/2)C + 2475/2 or N = -37.5C + 1237.5 where N is the number sold and C is the price of ...
*December 9, 2014*

**math**

Don't know if they teach you algebra where you are. Think of the points being split into 9 parts, where Alan would get 2 parts, Gil would get 3 parts and Debbie 4 parts So for her 2 parts deb got 114400/4 = 28600 per part so the total number of points = 9(28600) = 257400 ...
*December 9, 2014*

**Math**

so treat your data as two ordered pairs (0,97000) and (6,109000) Just like in a normal x-y equation, slope = (109000-97000)/(6-0) = 12000/6 = 2000 using (0, 97000) , which would be the y-intercept y = 2000x + 97000
*December 9, 2014*

**Math**

g(x) = 15x + 9 - 9-12 = 3(5x+3) - 21 = 3 f(x) - 21 or g(x) = 15x + 15 - 15 - 12 = 5(3x +3) - 15 - 12 = 5 f(x) - 27
*December 9, 2014*

**Algebra**

I don't blame you for being lost, since the question is poorly worded. Since they started off my talking about linear equations, I had assumed that all the given points lie on the same straight line. But they do not. anyway... suppose we take the first two points (5,1) and...
*December 9, 2014*

**Euler's method help in Calculus?????**

This is tedious work I found an excellent youtube for you where they solve a problem very similar to yours. I assume your text or your notes contain the basic original formula for Euler's Method I suggest you pause the video at critical points and make the necessary ...
*December 9, 2014*

**math**

Let Sam's age 7 years ago be s let Tom's age 7 years ago be t So s+7 + t+7 = 27 s+t = 13 ---> t = 13-s "seven years ago, tomas was three years more than one-fourth as old as sam" --- t = (1/4)s + 3 13-s = (1/4)s + 3 times 4 52 - 4s = s + 12 -5s = -40 s = 8...
*December 9, 2014*

**Math**

how about 130 and 121 ? I would not count those starting with 0 e.g. 031 is a 2 digit number
*December 8, 2014*

**Math**

Larry , you are right and observant to catch my error. So just make the necessary changes here is a neat trick to make an inverse answer is correct (which I did not do) pick any "nice" x value and find y e.g. x = 0 y = (9-0)/(0-9) = -1 now put that into the inverse ...
*December 8, 2014*

**Math**

let y = (9-8x) / (10x-9) for the inverse, interchange the x and y variables ---> x = (9-8y)/(10y-9) 10xy - 9x = 9 - 8y 10xy - 8y = 9+9x y(10x - 8) = 9+9x y = (9+9x)/(10x - 8) f^-1 (x) = (9x+9)/(10x-8)
*December 8, 2014*

**General Calculus Question**

No, notice the highest powers are NOT the same, so my explanation is not valid. as x --> inf √(x^2 - 2x) ---> x e.g. pick x = 1000000 and use your calculator to see so the numerator ---> 3x^2 the denominator ----> x so the limit is inf.
*December 8, 2014*

**General Calculus Question**

did you mean something like lim (4x^2 -2√x)/(3x^2 + 5√2x) of course it could only approach + inf , or else the root terms would be undefined. Other than that, the same rule applies the limit would be 4/3
*December 8, 2014*

**General Calculus Question**

as x ---> inf and the top and bottom have the same highest power, then those terms will determine the limit See my answer to a similar question by James at 11:06
*December 8, 2014*

**Math**

divide top and bottom by x^2 to get lim (7/x + 6)/(7 + 6/x) as x ---> inf both 7/x and 6/x ---> 0 so we are left with (0 + 6)/(7 + 6) = 6/7
*December 8, 2014*

**Math**

use your rules of logs logx + logx + logx = 3 log (x)(x)(x) = 3 log x^3 = 3 3logx = 3 logx = 1 or x = 10^1 = 10 check: What is log1010 ? isn't it 1 ?
*December 8, 2014*

**math**

you want your ball to be #7 AND black There is only one such ball prob (black and #7 ) = 1/10
*December 8, 2014*

**APCalculus**

lets look at your graph first of all http://www.wolframalpha.com/input/?i=plot+y%3D2sin%28x%29-cos%5E2%28x%29 clearly no vertical or horizontal asymptotes you had that, your y-intercept is correct symmetry: about each vertical line passing through a max or a min I disagree ...
*December 8, 2014*

**Math (Simplifying Fraction)**

= ( 1/x + 4/x^2) / (1 - 16/x^2) multiply top and bottom by x^2 = ( 1/x + 4/x^2) / (1 - 16/x^2) * (x^2/x^2) Since I am multiplying by 1, I am not changing the value of my fraction , simply its appearance = (x+4)/(x^2 - 16) = (x+4)/( (x+4)(x-4) ) = 1/(x-4) , x ≠ -4 (or ...
*December 8, 2014*

**APCalculus**

taking your typing at face value the way you typed it your domain is correct as a matter of fact: "I got some: domain: (-infinity, infinity) y-intercept: y=4 Vertical asymptotes: none Horizontal asymptotes: none Symmetry: y-axis F'(x): 2/3x^3-4x Critical numbers: x=0...
*December 8, 2014*

**Math**

you were right to factor it, but your second part is totally bogus I also think you placed brackets in the wrong place, probably should have been: 6/(x^2+5x+6) + 9/(x+3) = 6/( (x+2)(x+3) ) + 9/(x+3) we now need a common denominator which is (x+2)(x+3) = 6/((x+2)(x+3)) + 9(x+2...
*December 8, 2014*

**math**

ones digit --- x tens digit ---- 2x thousands --- 4x hundreds -----y x+2x + 4x + y = 19 y = 19-7x but x and y must be single digit positive integers. let x = 1, then y = 12 , not possible let x = 2, then y = 5 The number is 8542 let x = 3, then y = 19-21 = negative, no good ...
*December 8, 2014*

**Math**

(x-(1/x))/(1-(1/x)) = ( (x^2 - 1)/x) / ( (x-1)/x) = ( (x-1)(x+1)/x ) * (x/(x-1)) = (x-1)(x+1)/(x-1) = x+1 , x ≠0,1
*December 8, 2014*

**math**

I assume you mean: 25 = (748/7)^x take log of both sides log25 = log(748/7)^x = x log(748/7) = x(log748 - log7) x = log25/(log748-log7) get out your calculator and push some buttons I got appr .689
*December 8, 2014*

**Math**

1. cos^-1(sin(π/2) we know sin π/2 = 1 so cos^-1 (sin π/2) = cos^-1 (1) = 0 (because cos 0 = 1 ) 2. this one is easy, since arccos is the same as cos^-1 the answer is obviously 7π/2 However, they might just want a reduced answer since cos 7π/2 = cos 3...
*December 8, 2014*

**math**

Let the cost of John's 4 pencils and 3 erasers be x then the cost of Smith's 8 pencils and 6 erasers is 2x , notice twice as many cost of Smiths 3 pens --- y cost of John's 6 pens ---- 2y , notice twice as many pens Johns cost = 2y + x Smith's cost = y + 2x y...
*December 8, 2014*

**Calculus**

First we have to find their intersection to establish the boundaries. x^2 - 6 = 12 - x^2 2x^2 = 18 x^2 = 9 x = ± 3 so we have a closed region from -3 to +3 the height of the region for that domain = 12-x^2 - (x^2 - 6) = 18 - 2x^2 area = [integral] (18-2x^2)dx from -3 to...
*December 7, 2014*

**math**

So the distance between the two trains is changing at a rate of 100 km/h, (the sum of their speeds) so it will take them 100/100 or 1 hour to collide. In the meantime, the fly is merrily flying back and forth at 75 km/h, so in the 1 hour it would have simply traveled 75 km. ...
*December 7, 2014*

**Math**

1(1 + .024/12)^(12t) = 2 , any starting sum will do, I started with $1 and want to end up with $2 1.002^(12t) = 2 take log of both sides log(1.002^(12t) ) = log2 rules of logs .... 12t log 1.002 = log 2 12t = log2/log1.002 = 346.92.. t = 346.92/12 = 28.91
*December 7, 2014*

**math**

amount left = a (.5)^(t/14.9) , where a is the initial amount, and t is the time in hours a) sub in t = 48 amount left = a(.5)(48/14.9) = .1072a = appr 10.72% of what you started with b) can't be answered since you did not say what they started with. set 1 = a(.5)^(t/14.9...
*December 7, 2014*

**MATH**

good grief ! I think you posted the same question about 6 times tonight. Please look back before posting the same question again http://www.jiskha.com/display.cgi?id=1417998282
*December 7, 2014*

**Calc I**

your derivative will be the slope and since (π/6,1) lies on the curve, slope of tangent = 8cosπ/6 sinπ/6 = 8(√3/2)(1/2) = 2√3 ( you might recall that sin 2x = 2sinxcosx so 8sinxcosx = 4(2sinxcosx) = 4 sin2x then slope = 4sin(π/3) = 4√3/2...
*December 7, 2014*

**Algebra 1**

so your two points are (0,2) and (2,8) where (0,2) is the y-intercept slope = (8-2)/(2-0) = 3 without further ado y = 3x + 2
*December 7, 2014*

**Pre-Cal**

done , check back
*December 7, 2014*

**Pre Cal**

done, check back
*December 7, 2014*

**Pre-Calc**

I assume we are solving this equation ? by rules of logs .... log( (x-6)(x+3) ) = 1 10^1 = (x-6)(x+3) x^2 - 3x - 18 = 10 x^2 - 3x - 28 = 0 (x-7)(x+4) = 0 x = 7 or x = -4 , but to be defined in log(x-6), x > 6 so x = 7
*December 7, 2014*

**Calculas**

Did you notice that in the "Related Questions" below I answered a similar question back in 2008. All you have to do is change the numbers http://www.jiskha.com/display.cgi?id=1204511609
*December 7, 2014*

**Calculas**

have not seen that variation of the popular "make a box" question before. Made a diagram showing the net of the box with a lid. let the sides of the square to be cut out be x cm the the width of the box is 72 - 2x let the length of the box be y cm According to my ...
*December 7, 2014*

**Calculas**

Let the size of the cut-out square be x inches so the base of the box is (19-2x) by (19-2x) and the height is x V = x(19-2x)^2 = x(361 - 76x + 4x^2) = 4x^3 - 76x^2 + 361x dV/dx = 12x^2 - 152x + 361 = 0 for a max of V x = (152 ± √5776)/24 = (152 ± 76)/24 = ...
*December 7, 2014*

**Math - Differentiate**

No sure what you are "solving" From your subject title, should we conclude you want to differentiate ?? if so, then f ' (x) = 3x^2/(x^3 + 5) + 6
*December 7, 2014*

**Math**

the vertex of your parabolic path is (7,21) so y = a(x-7)^2 + 21 but (0,0) lies on it, so 0 = a(0-7)^2 + 21 0 = 49a + 21 49a = -21 a = -21/49 = -3/7 so y = (-3/7)(x - 7)^2 + 21
*December 7, 2014*

**Calc I**

I haven't got a clue how you came up with that first derivative. f(x) = (4t+1)^(1/2) f ' (x) = (1/2)(4t+1)^(-1/2) (4) = 2(4t+1)^(-1/2) f '' (x) = -1(4t+1)^(-3/2) (4) = -4(4t+1)^(-3/2) or = -4/(√(4t+1)^3 ) f '' (2) = -4/√9^3 = -4/27
*December 7, 2014*

**Factoring**

If you expand your answer, you don't get back what you started with. So you knew you were wrong. the common factor is 7, you had that correct answer: = 7(2z^2 - 7z + 35)
*December 7, 2014*

**Calc I**

your answer of 4(x^2+x^3)^3 * (2x+3x^2) is not incorrect, you just didn't go far enough 4(x^2+x^3)^3 * (2x+3x^2) =4(x^2 + x^3)(x^2 + x^3)(x^2 + x^3)(2x + 3x^2) = 4(x^2)(1+x)(x^2)(1+x)(x^2(1+x)(x)(2+3x) = 4x^7 (1+x)^3 (2+3x) Your "correct" answer is NOT correct
*December 7, 2014*

**solve**

snow storm speed --- x mph rain storm speed ---- 2x mph 168/x - 168/2x = 3 times 2x 336 - 168 = 6x x = 168/6 = 28 So he went 28 mph in the snow storm and 56 mph in the rain check: snow: 168/28 = 6 rain: 168/56 = 3 , so 3 hours less than in the snow
*December 7, 2014*

**Math word problem**

how about 18 nickels and 1 dime or 9 dimes and 10 penny or .. suppose we restrict ourselves to p pennies, n nickels, d dimes, q quarter then we need integer solutions to pennies + nickels = 100 p + 5(19-p) = 100 p + 95 -5p = 100 -4p = 5 --->no integer solution pennies + ...
*December 7, 2014*

**problem solving**

The question is much too vague. I assume that p is the perimeter (p is not defined) Are the sides to be integer value? Are the triangles scalene ? , isosceles ? The largest triangle of course would be an equilateral triangle with sides 100/3 each and an area of (1/2)(100/3)^2 ...
*December 7, 2014*

**problem solving**

Wow rectangles? squares? triangles? hexagons? .... star-shaped things convex septagons ? ...
*December 7, 2014*

**problem solving**

number of blocks --- x cost per block --- y 1.05xy = 315 xy = 300 without sales tax the cost would have been (x+6)y = 315 so divide the two equations: ( (x+6)y)/(xy) = 315/300 (x+6)/x = 21/20 21x = 20x + 120 x = 120 , then y = 2.5 He bought 120 blocks at $2.50 each check: 120(...
*December 7, 2014*

**calculus**

V = lwh dV/dt = lw dh/dt + lh dw/dt + wh dl/dt you are given all the values, just plug in and evaluate
*December 6, 2014*

**Math help**

Since the angle of incidence is equal to the angle of reflection in the mirror you have tow similar right-angled triangles. Thus we can use our good ol' fashioned ratios x/7.5 = 5.5/3 3x = 41.25 x = 13.75 or 13.8 ft to the nearest tenth of a foot
*December 6, 2014*

**Algebra**

I don't think you are using the concept of the "inverse of a function" in the proper way, you are just solving the equation for c d = .15c - 1.5 .15c = d + 1.5 c = (d+1.5)/.15 now plug in d = 18 c = (18+1.5)/.15 = 130 We could have just plugged in d = 18 in the ...
*December 6, 2014*

**calculus**

you had ∫ e^(8x) (e^(8x) + e^(-8x) )/2 dx which is = ∫ ( e^(16x) + e^0 )/2 dx = (1/2)(1/16)e^(16x) + (1/2)x | from 0 to 1/16 = (1/2)(1/16) e^1 + 1/32 - (1/2)(1/16)e^0 - 0 = (1/32)e or = e/32
*December 6, 2014*

**capacity problems**

ummmh, what is 2 x 80 ??
*December 6, 2014*

**7th grade math**

#4 There are only 6 students, so just take (5/6)(120) = 100 so 100 prefer pepperoni #6. Taylor/Kate = 3/2 Taylor/120 = 3/2 2 Taylor = 360 Taylor = 180 #9 d) (-2/5) / (-1/5) = (-2/5)(-5/1) = 10/5 = 2 The others are correct
*December 6, 2014*

**algebra**

let the speed of the plane in still air be x mph let the speed of the wind be y mph then 570/(x+y) = 3 --->3x + 3y = 570 x + y = 190 570/(x-y) = 5 ---> 5x - 5y = 570 x - y = 114 add them 2x = 304 x = 152 back in the first: 152 + y = 190 y = 38
*December 6, 2014*

**algebra**

If you are taking Calculus .... E ' (v) = -.032v + 1.408 = 0 for max of E .032v = 1.408 v = 44 E(44) = ....just sub in
*December 6, 2014*

**maths**

Please proof-read your post before sending it route = root squre = square i/3 = 1/3 ?? So if 1/3 of the diagonal is 3√2, then the diagonal is 9√2 let the side of the square be x x^2 + x^2 = (9√2)^2 2x^2 = 162 x^2 = 81 x = √81 = 9
*December 6, 2014*

**Algebra**

notice you can take out r^2 as a common factor r^2(15.64 + 4.16) = 235.619 19.8 r^2 = 235.619 r^2 = 11.899945... r = appr 3.45 to the nearest hundredth
*December 6, 2014*

**Math Trig**

sec Ø = -13/5 in quad II so cosØ = -5/13 x = -5, r = 13 and y = +12 sinØ = 12/13 cotØ = -5/12
*December 5, 2014*

**math**

let the number of days be x let the rate per mile be $ y 4x + 450y = 244.5 3x + 200y = 149 1st times 3 ---> 12x + 1350y = 733.5 2nd times 4 --> 12x + 800y = 596 subtract them: 550y = 137.5 y = .25 sub back into 2nd 3x+200(.25) = 149 3x + 50=149 3x = 99 x = 33 The daily ...
*December 5, 2014*

**math help**

just replace you x with -7 and evaluate. you appear to have a typo
*December 5, 2014*

**Calculous Finding K, using zeros**

since as x ---> ± infinity, y --> + infinitey, the function must be of even exponent, so one of the roots must be a double root, as you have f(x) = k(x-3)(x+3)(x-5) but we are also told that the y-intercept is 17, so we have the point (0,17) on our polynomial. 17...
*December 5, 2014*

**Math Calculous**

so we have x-intercepts of 0 and 3 thus f(x) = kx(x-3) but (5,30) also lies on f(x), so ... 30 = k(5)(2) 10k = 30 k = 3 f(x) = 3x(x-3) or f(x) = 3x^2 - 9x
*December 5, 2014*

**Calculous (Finding Zeros!)**

Oh no, don't expand, then we would be in a real mess y = (x^2 + 2x - 5) (x^3 + 3x^2 - 40x) the first factor does not factor any more, so we use the quadratic equation to find two roots from there. x^2 + 2x - 5 = 0 x = (-2 ± √24)/2 = (-2 ± 2√6)/2...
*December 5, 2014*

**Pre-Calc/Trig...**

A poorly worded question, we would not use logs to expand this perhaps you meant: if y = [(x+3)^4(x-5)^7] then log y = log (x+3)^4 + log (x-5)^7 = 4log(x+3) + 7log(x-5) btw, here are the 12 simplified terms of the expansion. http://www.wolframalpha.com/input/?i=expand+%28x%2B3...
*December 5, 2014*

**intermediate algebra**

√(40x^3) = √4*√10*√x^2*√x = 2x√(10x)
*December 5, 2014*

**math**

36 cm : 9 dm = 36 cm : 90 cm = 36 : 90 = 2 : 5
*December 5, 2014*

**Precalc/Trig**

looks like a direct case of the cosine law d^2 = 434^2 + 525^2 - 2(434)(525)cos 60° = 188356 + 275625 - 227850 = 236131 d =√236131 = 485.933
*December 4, 2014*

**Algebra**

after subbing .... -5(16) / 8^-1 = -80 (8) = -640 8^-1 = 1/8^1 so 1/8^-1 = 8^1 = 8
*December 4, 2014*

**Algebra**

5/√20 - 2√45 = 5/(2√5) - 6√5 = 5/(2√5) *√5/√5 - 6√5 = 5√5/10 - 6√5 = √5/2 - 12√5/2 = -(11√5)/2 I have a strong feeling you meant 3/(y+2) + 2/y = (5y-4)/(y^2-4) do you know why we would multiply by y(...
*December 4, 2014*

**algebra 1**

Just noticed a typo in my conclusion statement, should have read: The chemist will need 80 L of the 30%, and 120 L of the 50% solution. notice I did use 120L in my check
*December 4, 2014*

**algebra 1**

amount of 30% solution needed ---- x L amount of 50% solution needed ---- 200-x L .3x + .5(200-x) = .42(200) .3x + 100 - .5x = 84 -.2x = -16 x = -16/-.2 = 80 The chemist will need 80 L of the 30%, and 20 L of the 50% solution. check: .3(80) + .5(120) = 84 or , using the 2 ...
*December 4, 2014*

**calculus**

sec x = -3 then cos x = -1/3, and x is in the 2nd quadrant the triangle with angle x is in quad II and has a hypotenuse of 3 and an adjacent of 1, so the opposite is √(9-1) = √8 or 2√2 cot x = adjacent/opposite = -1/√8 or -√8/8 = -2√2/8...
*December 4, 2014*

**Help math**

let the two pieces be 3x and 7x , then 3x + 7x = v+4 10x = v+4 x = (v+4)/10 The longer piece was 7x or 7(v+4)/10
*December 4, 2014*

**Math**

|x-4| ≤ 10 - |x+4| x-4 ≤ 10-|x+4| AND -x+4 ≤ 10 - |x+4) |x+4 ≤ 14-x AND |x+4| ≤ 6 + x x+4≤14-x AND -x-4 ≤ 14-x AND x+4 ≤ 6+x AND -x-4 ≤ 6+x 2x ≤ 10 AND -4 ≤ 14 AND 4 ≤ 6 AND -2x ≤ 10 x ≤ 5 AND ...
*December 4, 2014*

**Math**

cube both sides 4 - x^(2/3) = -8 -x^(2/3) = -12 (x^2)^(1/3) = 12 x^2 = 1728 x = ± √1728 = ±24√3 so the difference between the two roots is 48√3
*December 4, 2014*

**math**

didn't Steve do this for you on Tuesday ? http://www.jiskha.com/display.cgi?id=1417568391 Always check back before posting the same question again.
*December 4, 2014*

**Math: Reiny**

In that case we need the intersection of y = x and y = -x+3 x = -x+3 2x = 3 x = 1.5 so area = ∫(upper y - lowery) dx from 0 to 1.5 = ∫(-x+3 - x)dx from 0 to 1.5 = ∫ 3 dx from 0 to 1.5 = 3x | 0 to 1.5 = 3(1.5) - 3(0) = 4.5
*December 3, 2014*

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