Tuesday
October 21, 2014

Posts by Reiny


Total # Posts: 27,486

MAth
cos 31° = PQ/20
April 15, 2014

Math
the way you typed it, the entire bracket is divided by 2. 5(2x - 10)/2 + 14 = 19 5(x - 5) + 14 = 19 5x - 25 = 19-14 5x = 5 + 25 5x = 30 x = 6
April 15, 2014

Trig
ARggghhhh!!!!
April 15, 2014

Trig
we need cos 225° and sin225° 225 = 180+45 , it is in quadrant III and has the same numerical trig values as 45°, but in III both the sine and cosine are negative sin 225 = - sin 45° = -1/√2 cos 225 = - cos 45° = -1/√2 so 7(cos255degrees + ...
April 15, 2014

MATH
sin 10.5° = PR/120 PR = 120 sin 10.5° = ....
April 15, 2014

Math
P(x) = 1.3x-.01x^2-30 = -.01x^2 + 1.3x - 30 in more standard notation you will need the vertex. The x of the vertex is -b/(2a) = -1.3/(-.02) = 65 then P(65) = -.01(65)^2 + 1.3(65) - 30 = 12.25 when x = 65
April 15, 2014

geometry
surface area of box = 2(2.5)(7) + 2(2.5)(12) + 2(7)(12) = 263 inches^2 surface area of cylinder = 2πr^2 +2πrh = 2π(3^2) + 2π(3)(7.5) = 18π + 45π = 63π or appr 197.9 inches^2 so what do you think?
April 15, 2014

Math
I recommend getting rid of brackets first to get nice straightforward terms, then simplify, and then "move" terms from side to side. -5 - x = 2x - 4x - 6 -5 - x = -2x - 6 2x - x = -6 + 5 x = -1 (your -x on the right side should have been +x )
April 15, 2014

mathematics for management
I will assume they are the same x recall that loga b = log b/log a so logxy = logy/logx and logyx = logx/logy so your equation can be written as: logy/logx + logx/logy = 5/2 let logx/logy = a then we have 1/a + a = 5/2 times 2a 2 + 2a^2 = 5a 2a^2 - 5a + 2 = 0 (a - 2)(2a - 1...
April 15, 2014

mathematics for management
I saw this one pass by me before. Are you distinguishing between "x" and "X"? If so, you have 4 variables with only 2 equations.
April 15, 2014

math
first bounce --- 3 ft 2nd bounce = 2(1/4)(3) = 6(1/4) 3rd bounce = 2(1/4)(3)(1/4) = (6)(1/4)^2 4th bounce = ... = (6)(1/4)^3 .... so we have 3 + 6(1/4) + 6(1/4)^2 + 6(1/4)^3 + ... to infinity = 3 + 6(1/4) (1 + 1/4 + (1/4)^2 + ...) from the 2nd term on, we have a geometric ...
April 15, 2014

Math
short leg --- x longer leg --- 2x-1 x^2 + (2x-1)^2 = 17^2 x^2 + 4x^2 - 4x + 1 = 289 5x^2 - 4x - 288 = 0 (x-8)(5x + 36) = 0 x = 8 or x is an inadmissable negative number short leg = 8 ft long leg = 15 ft area = (1/2)(8)(15) = 60 ft^2
April 15, 2014

Algebra 1 Explanation (Anyone, please!)
If you know very little about the topic, a good way would be to simply make a table of values for x and y pick reasonable small values for x and evaluate to get the y e.g. x y 0 -3 1 -4 2 -3 ------> 2^2 - 2(2) - 3 = 4-4-3 = -3 3 0 4 5 ----> 4^2-2(4)-3 = 16-8-3 = 5 5 12 -...
April 15, 2014

Algebra
first rate ---- x mph return rate --- x+11 sum of times = 22.5 550/x + 550/(x+11) = 22.5 times x(x+11) 550x + 6050 + 550x = 22.5x(x+11) 1100x + 6050 = 22.5x^2 + 247.5x 22.5x^2 - 852.5x - 6050 = 0 using the formula x = 44 or a negative he went at 44 mph going there, and 55 mph ...
April 15, 2014

statistics
same webpage ... click on "between" and enter -3 and 3 to get .9973 choose you matching answer.
April 15, 2014

statistics
Use either your tables available to your or use http://davidmlane.com/hyperstat/z_table.html to get .9772 or .98 from your choices
April 15, 2014

MATHS - AREA
2L + 2W = perimeter 2(80) + 2w = 410 2W = 410 - 160 2W = 250 W = 125 area = LW = 80(125) = 10,000 m^2
April 15, 2014

Stats
RANDOM can be arranged in 6! or 720 ways. prob of getting it in that form = 1/720
April 15, 2014

Math
plug your data into this ... http://davidmlane.com/hyperstat/z_table.html click on "above" and enter 6 to get .3694 (that's very high SD )
April 15, 2014

mathematics for management
logv[ 2x/(x+2b) [ = 1 2x/(x+2b) = b^1 2x =bx + 2b^2 2x - bx = 2b^2 x(2 - b) = 2b^2 x = 2b^2/(2 - b)
April 15, 2014

math
3 important rules of logs 1. log (AB) = log A + log B 2. log(A/B) = log A - log B 3. log A^n = nlogA so 2log15 + log(5-x) - log 4x = 2 log 15^2 + log(5-x) - log 4x = 2 log (225(5-x)/(4x) ) = 2 225(5-x)/(4x) = 10^2 = 100 400x = 1125 - 225x 625x = 1125 x = 1125/625 = 9/5 or 1.8
April 15, 2014

college Algebra
let each of the two end fences be x ft long let the side parallel to the river be y ft long so we have: cost = 12y + 8(2x) = 12y + 16x but 12y + 16x = 3600 3y + 4x = 90 y = (90-4x)/3 area = xy = x(90-4x)/3 = 30x - (4/3)x^2 d(area)/dx = 30 - (8/3)x = 0 for a max of area (8/3)x...
April 15, 2014

Precalculus
1. a) and b) are correct c) the normal is perpendicular to the tangent So if the slope of the tangent at (3,9) is 6 then the slope of the normal is -1/6 y = (-1/6)x + b, plug in the point (3,9) 9 = (-1/6)(3) + b b = 19/2 y = (-1/6)x + 19/2 or y = (-1/6)x + 9.5 2. a) good! g) ...
April 14, 2014

Math
did this yesterday http://www.jiskha.com/display.cgi?id=1397441682
April 14, 2014

Math
profit = 6n - 2n - 400 - 100 = 4n + 600 , where n is the number of people 4n - 500 = 400 4n = 900 n = 225 need 225 people to make $400
April 14, 2014

Math
Did this for Lynda back in December http://www.jiskha.com/display.cgi?id=1386034705
April 14, 2014

Trigonometric Function
6 rotations take 1 minutes 1 rotation takes 1/6 minutes 2π/k = 1/6 k = 12π let's start using only amplitude and frequency to get height = 10 sin ( 12πt) We want to move the curve up 12 units height = 10 sin (12πt) + 12 so now we have to have a ...
April 14, 2014

Math
This little YouTube fits your problem quite nicely http://www.youtube.com/watch?v=62Lj-g5owgo
April 14, 2014

statistics
z-score for chemistry = (82-75)/6.25 = 1.12 z-score for physics = (63-59)/3.57 = 1.12044 I would consider the difference insignificant, so the two scores would be equivalent.
April 14, 2014

math
Jerry-height = 50 + (1/24)m Adam-height = 47 + (1/8)m they have the same height when ... 50 + m/24 = 47 + m/8 3 = m/8 - m/24 m/12 = 3 m = 36 or, from 50 + m/24 = 47 + m/8 multiply each term by 24 to get rid of fractions 1200 + m = 1128 = 3m 72 = 2m m = 36
April 14, 2014

Math
let the speed of the river current be x mph speed going upstream = 9 -x mph speed going downstream = 9 + x mph 10/(9-x) = 20/(9+x) 90 + 10x = 180 - 20x 30x = 90 x = 3 the speed of the river is 3 mph
April 14, 2014

math
The side parallel to the highway be x ft let each of the other two sides by y 2x + y = 640 y = 640 - 2x area = xy = x(640-2x) = -2x^2 + 640x I assume you know how to find the vertex of this downwards parabola, and that vertex is (160 , 51200) if x = 160 y = 640 - 2(160) = 320 ...
April 14, 2014

math
z is defined in two ways ? what's with the 1 2 ?
April 14, 2014

Math help asap
I interpreted your question this way: e^(x/2.9099) =ln (7.8x10^10) take ln of both sides , so we taking ln (ln(...)) on the right side x/2.9099 = ln (ln (7.8 x 10^10) ) x/2.9099 = 3.22207 x = 9.3759...
April 14, 2014

HELP! 5th grade math
There is more than one way to do this What Alison gave you is one of those. I would use the two containers measuring only Litres to hold the whole numbers e.g. 4 L + 4 L that leaves .53 L or 530 ml now you can split the 530 into any two parts using the two containers that ...
April 13, 2014

Calculus Help Please Urgent!!!
lim -> 0 (cot(x)-(1/x)) , x---> 0 = sec^2 x + 1/x^2 by L'Hospital's Rule but that is just as bad try experimentally ... using a Calculator let x = .0001 I get -.0000333 let x = .000001 my calculator says 0 http://www.wolframalpha.com/input/?i=limit+cot%28x%29+-+1...
April 13, 2014

Math
did you notice that the derivative of the denominator is 9 e^(9x) which just happens to be sitting in the numerator as a multiple thereof. Which is the ln derivative pattern. So without any great fanfare..... ∫(e^(9x))/(2 + e^(9x)) dx = (1/9) ln (2 + e^(9x) + c
April 13, 2014

Math
How about giving this one a try ?
April 13, 2014

math
Are you saying f(x) = 17/(x^2 + 4x - 12) ? (I will assume that) = 17/((x+6)(x-2) ) remember we can't divide by zero, which happens if x = 2 or x = -6 We can use any other value of x so domain: = { x ∈ R | x ≠ -6,2 }
April 13, 2014

oops - Math
didn't see the "monthly" part rate = .05/12 = .0041666... amount = 125000(1.00416666...)^6 = $128,157.73
April 13, 2014

Math
125,000 invested for 6 months = 125000(1.025 = $128,125 So what do you think?
April 13, 2014

Math
Wilder: amount = 85000(1.05)^2 = $93,712.50 after 1st year Cheapskate: amount = 85000(1.0081666..)^12 = $93,714.53 after 1st year b) you try it, (you only have to change the exponents)
April 13, 2014

Math
Tom: Paym(1.08)^3 = 15000 Paym = 15000/1.08^3 = $11,907.48 Lana: monthly rate = .07875/12 = .0065625 Paym(1.0065625)^36 = 15000 Paym = 15000/1.0065625^36 = $11,852.89 etc
April 13, 2014

Math
a) ridiculous question ! , makes no sense the "arithmetic" would be 8200(1.0988) = .... b) weekly rate = .0988/52 = .0019 number of weeks in 18 years = 936 amount = 8200(1.0019)^936 = $48,465.24
April 13, 2014

Calculus
let the length of the side using bricks be x ft let the other two sides each be y ft given: xy = 900 --> y = 900/x cost = 5(x + 2y) + 10x = 15x + 10y = 15x + 10(900/x) d(cost)/dx = 15 - 9000/x^2 = 0 for min of cost 15 = 9000/x^2 15x^2 = 9000 x^2 = 600 x = √600 = 10&#...
April 13, 2014

Algebra
amount invested at 11% --- x amount invested at 8% ---- 6300-x solve for x ..... .11x + .08(6300-x) = 597
April 13, 2014

Math
∫5(1+1/u + 1/u^2) du from 5 to 7 = 5[u + ln u -1/u] from 5 yo 7 = 5( 7 + ln7 - 1/7 - (5 + ln5 - 1/5) = 5(2 + ln7 - ln5 -1/7 + 1/5) = 10 +2/7 + 5ln 7 - 5ln5 = appr 11.97
April 13, 2014

Math 10
sure, all you have to do is to find the vertex of this "downwards" parabola. I will assume that you do not know Calculus , so (easiest way): the x of the vertex for y = ax^2 + bx + c is -b/(2a) so for your equation, the t of the vertex is -10/-10 = 1 sub into the ...
April 13, 2014

Algebra
amount of 20% juice used ...... x L amount of 5% juice used ....... 15 - x L .20x + .05(15-x) = .16(15) times 100 to get rid of those decimals 20x + 5(15-x) = 16(15) 20x + 75 - 5x = 240 15x = 165 x = 11 Answer as needed.
April 13, 2014

Math
All four choices fit the description. As to your "most specific term", it probably refers to its main property. Since a parallelogram is most often defined in terms of its parallel sides, that would be choice.
April 13, 2014

math
I am used to expressing complex numbers in the form a + bi, instead of your a + bj if z = 1 + 2i r = √(1^2+2^2) = √5 and if Ø is our angle, tan Ø = 2/1 , Ø is in I of your complex plane Ø = appr 1.107 radians then z = √5(cos 1.107...
April 13, 2014

maths
let the tens digit be x let the unit digit be y x+y = 12 x-y = 4 add them 2x = 16 x = 8 y = 4 the number is 84 Since the choices were quite limited, (x = 5,6,7,8,or9 ) it would have been just as fast to "guess" at the solution
April 13, 2014

math
Kelly's original number of bonus point --- x Julia's original number of bonus points -- x-150 let the number used by both be y each. now Kelly has x - y Julia has x-150 - y for Kelly: (x-y)/x = 3/4 4x - 4y = 3x x - 4y = 0 or x = 4y for Julia: (x-150-y)/(x-150) = 1/2 2x...
April 13, 2014

math
the surface area of similar solids is proportional to the square of their corresponding sides Area / 90 = 10^2/5^2 = 100/25 = 4 Area = 90(4) = 360 inches^2
April 12, 2014

math
downpayment = 629.95(.25) = $157.49 amount to be financed = 472.46 The rest of the question sounds like something from the last century. A very silly way of doing the financing and it misleads the uninformed. I will assume they will now take 472.46 , add on $60 to get $532.46 ...
April 12, 2014

maths
Kg is used to measure mass, not volume Please fix your question, since a suitable unit for the circumference would be cm (centimetre)
April 12, 2014

Pre-Calculus
10000(1.03)^n = 11000 , where n is half=years 1.03^n = 1.1 n log 1.03 = log 1.1 n = log 1.1/log 1.03 = 3.224 half years it will take 1.612 years or about 1 1/2 years
April 12, 2014

Algebra
Surely you meant: F(t)= 30000/(1+20e^-1.5t ) a) let t = - F(0) = 30000/(1+20) = appr 1429 b) when t = 4 F(4) = 30000/(1 + 20e^-6) = 28,583 check my "button-pushing" on the calculator
April 12, 2014

Algebra
done, see below, please don't switch names
April 12, 2014

algebra
you are solving 6 e^12.77x = 20 e^12.77x = 10/3 ln both sides and use rules of logs 12.77x lne = ln(10/3) , recall that ln e = 1 x = ln(10/3) /12.77 = appr .094
April 12, 2014

Algebra
log2 x + log2 (x-7) = 3 log2( x/(x-7) ) = 3 x/(x-7) = 2^3 = 8 8x - 56 = x 7x = 56 x = 8
April 12, 2014

Algebra
ln( x+2)/(4x+3) ) = ln (/x) (x+2)/(4x+3) = 1/x x^2 + 2x = 4x+3 x^2 - 2x - 3 = 0 (x-3)(x+1) = 0 x = 3 or x = -1 but if x = -1 , ln(4x+3) is undefined, so x = 3
April 11, 2014

algebra
ln ( (x+3)/(x-5) ) = ln 7 (x+3)/(x-5) = 7 7x - 35 = x+3 6x = 38 x = 38/6 = 19/3
April 11, 2014

Algebra Word Problem
let the number of men be x original share of debt = 100/x men actually paying back = x-5 new share = 100/(x-5) 100/(x-5) - 100/x = 1 100x - 100x + 500 = x(x-5) x^2 - 5x - 500 = 0 (x - 25)(x+20) = 0 x = 25 or x = a negative, which is not admissible So there were 25 men, of ...
April 11, 2014

Algebra
let speed of steamer in still water be x mph let the speed of the current be y mph 108/(x-y) - 108/(x+y) = 3 108x + 108y - 108x + 108y = 3(x^2 - y^2) 216y = 3(x^2 - y^2) 72y = x^2 - y^2 ---- #1 let speed of "boat" be x-6 108/(x-6 - y) - 108/(x-6 + y) = 9 108x - 648...
April 11, 2014

Algebra - functions
Here is a "picture" of your graph It should help you to answer your questions. http://www.wolframalpha.com/input/?i=plot+y%3D+5%2F%28x-1%29%5E2+
April 11, 2014

Algebra
Your first version is correct, the "others" are wrong To interpret along the second version it would have been (-16)^(1/4) , but there were no brackets just like in -2x^2 , it is only the x that is squared, not the -2 There is a major difference between -2x^2 and (-...
April 11, 2014

Statistics
Using this webpage you don't even have to find the z-scores (you may if you wish) just enter the mean, the SD, click on "below" and enter 2 in that field and "recalculate" to get .2743 http://davidmlane.com/hyperstat/z_table.html perfect substitute for ...
April 11, 2014

math
|2n^2 - 7| < 1 We could go into a formal solution with all the AND and OR operators, but clearly n must be a small integer, so lets just try some values of n n = 0 ---> |-7| < 1 , no n = ± 1 --> |2-7| < 1 , no n = ± 2 ---> |8-7| < 1 , no n...
April 11, 2014

finance
PV = 163291.18 (1 - 1.075)^-20)/.075 = $ 1,664,670.52
April 11, 2014

algebra
follow this method, yours is even easier than the one in the link http://www.jiskha.com/display.cgi?id=1397241650
April 11, 2014

algebra
You should really memorize the 3 main rules of logs log(AB) = ... log (A/B) = .. log A^n = ... log(x y^3 z^7) = logx + log y^3 + log z^7 = logx + 3logy + 7logz
April 11, 2014

algebra
using the rule: log (AB) = logA + logB log x + log(x+15)=2 log(x(x+15)) = 2 x(x+15) = 10^2 x^2 + 15x - 100 = 0 (x + 20)(x-5) = 0 x = -20 or x = 5 BUT if x = -20 , we would have log (-20) in our expression, and log(a negative) is undefined so , x = 5
April 11, 2014

algebra
7 ^(x+3) =519 take logs of both sides log 7^(x+3) = log 519 using rules of logs ... (x+3)(log7) = log519 x+3 =log 519/log 7 x = log519/log7 - 3 = appr .2128
April 11, 2014

math
40e^(0.6x) - 3=237 40e^(.6x) = 240 e^.6x = 6 ln both sides ln e^.6x = ln 6 .6x ln e = ln 6 .6x = ln 6 , remember ln e = 1 x = ln 6/.6 = appr 2.986
April 11, 2014

math
height = -16t^2 + 344 when height = 200 16t^2 = 144 t^2 = 144/16 t = 3 after 3 seconds it will be 200 ft high
April 11, 2014

Math
My goodness, misread it and missed its simplicity. Here I thought it might be some kind of exponential growth. Funny thing is, I had the right answer of 1.71 at the beginning.
April 11, 2014

Math
time - height 0 ---- 1.6 m 7 ---- 1.71 "find the current height... " --- when is "current" Is the growth a linear function , (not realistic) Is it exponential ? More information needed.
April 11, 2014

graphing
not enough information is your parabola vertical or horizontal? Was there a graph?
April 11, 2014

statistics
97.5% must be below or in your "tables" find the probability closest to 0.975 You should have a z-score of 4.9625 depending on the accuracy of your tables then (x - 460)/80 = 1.9625 x-460 = 157 x = 157+460 = 617 OR, use this wonderful webpage: http://davidmlane.com/...
April 11, 2014

math
I will do the question the way I would do it. I will let you sort out which part becomes your a) , b) , etc let x be as defined above. number of units rented = 80 - x rent for each unit = 300+20x (80 - x)(300+20x) = 35000 24000 +1300x - 20x^2 = 35000 -20x^2 + 1300x -11000 = 0 ...
April 11, 2014

Hanus
centre of circle is (17,9) so slope of radius to tangent = (14-9)/(12-17) = 5/-5 = -1 so the slope of the tangent is +1 (the negative reciprocal) equation of tangent: y-14 = +1(x-12) y = x - 12 + 14 y = x + 2 the y-inercept is 2
April 11, 2014

ALGEBRA
I am 100% sure that I am correct the axis of symmetry is x = 0 For any vertical parabola , (like yours), if the vertex is (p , q), the axis of symmetry is x = p
April 11, 2014

ALGEBRA
so the vertex is (0,8) and the axis of symmetry is x = 0 , or the y-axis
April 11, 2014

ALGEBRA
What is the x value of your vertex ?
April 11, 2014

College alg.
easy to graph, just grab some ordered pairs Parabola opening downwards, domain of any standard parabola is the set of real numbers, (any x you want to choose) the domain in this case : all values of y ≤ the maximum y (you will need the vertex)
April 11, 2014

College Algebra
Since you labeled it "college" algebra, I will assume you know Calculus s(t) = -4.9t^2 + 7.1t + 10 v(t) = -9.8t + 7.1 = 0 for a max of s(t) 9.8t = 7.1 t = 71/98 s(71/98) = -4.9*71/98)^2 + 7.1(71/98) + 10 = appr 12.58 m or 12.6 m above water (to the nearest tenth)
April 11, 2014

pre algebra
#1. first equation: LS = -12 RS = 6(-4) + 12 = -12 2nd equation: LS = 2(-4) - (-12) = -8 + 12 = 4 RS = 4 So, yes , it is a solution. #2. since y = x+4 and y = 3x , then 3x = x+4 2x = 4 x = 2 sub into either one of the two original equations ... if x = 2, y = 6 so the solution ...
April 11, 2014

prealgebra
correct, subbing in x=-1 has to give you +5 for both equations.
April 11, 2014

math
teachers --- t students --- s from first case: 8.5t + 2s = 29 from the 2nd case: 34t + 8.5s = 119 System of 2 equations in 2 unknowns. Just your favourite method of solving.
April 11, 2014

Math
Using standard alphabet, number of possibilities for the 4 numbers = 10^4 number of possibilities for the letters = 26^3 Three more numbers = 10^3 Number of possible plates = (10^4)(26^3)(10^3) = 175,760,000,000 note: this includes plates such as 0000ZZZ000
April 11, 2014

Calculus
I agree with your choice of b) for #1 If the slope of the tangent is zero, then the tangent must be a horizontal line and you are at either a maximum or a minimum point of the curve.
April 9, 2014

Math
I observed that the derivative of the inside of the bracket sits out front as a multiple of that. If that is the case, I just reverse by "thinking" if dy/dx = x^2(5x^3 + 9)^3 y = (x^2/(15x^2)) (5x^3 +9)^4 * (1/4)+ c = (1/60) (5x^3 + 9)^4 + c
April 9, 2014

Math
N '(t) = 2e-0.02t N = (2/-.02) e^-.02t + c N = -100 e^-.02t + c when t=0 , N = 45 45 = -100(1) + c c = 145 N = -100 e^-.02t + 145 testing: if t = 0 N = -100 e^0 +145 = 45 , good if t = 5 N = -100 e^-.1 + 145 = -90.5 + 145 = 54.5 , improving if t = 20 N = 78 , looks logical...
April 9, 2014

Math
if dy/dx = 6(2x-7)^5 y = (6/6) (2x-7)^6 (1/2) + c y = (1/2)(2x-7)^6 + c but (4 , 3/2) lies on it, so 3/2 = (1/2)(1)^6 + c 3/2 = 1/2 + c c = 1 f(x) = (1/2)(2x-7)^6 + 1
April 9, 2014

MATH Algebra
You must use brackets to establish the correct order of operation. According to your steps, the question was: (48x + 32y)/32 = 48x/32 + 32y/32 = 3x/2 + y you have the correct answer. <Also 25a + 5b + 15c/10 would I be correct to divide by 5?> yes, but again you will need...
April 9, 2014

math
number of miles ---- m .15m + 22.5 ≤ 50 .15m ≤ 27.5 m ≤ 183.333.. Suppose you drive 183 miles cost = 183(.15) + 22.50 = 49.95 , still good suppose you drive 184 miles cost = 184(.15) + 22.5 =50.10, oops, we are over so you can drive 183 miles and still be ...
April 9, 2014

Calculus1
Since we are including the waste for cutting the circles from squares, we need 2 squares and a rectangle if the radius is r, and our square is 2r by 2r, we can cut 2 circles from 2squares. Let the height be h , (all units in cm) we must have: 1000 =π r^2 h h = 1000/(π...
April 9, 2014

math
I will assume you are not taking Calculus, but have studied the quadratic function, and know how to complete the square y = -16(x^2 - 2x) = -16(x^2 - 2x + 1 - 1) = -16( (x-1)^2 - 1) = -16(x-1)^2 + 16 so the vertex is (1,16) suggesting that the max height is 16 after 1 second ...
April 9, 2014

calculus
This one is more obvious than your last one (e^-x - 1)/(e^-x + x) notice that the derivative of (e^-x + x) is (-1)e^-x + 1 = -1(e^-x - 1) you have exactly the opposite of that sitting in your numerator. Which , by observation alone, suggest a log integration since for y'...
April 9, 2014

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