Wednesday
April 16, 2014

Posts by Reiny


Total # Posts: 25,975

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' =...

math
let the dimensions of the first plot be x by y let the dimensions of the second plot be a by b where x,y, a, and b are all integers. so we want: xy + ab = 60, and x-y = a+b There are many combinations that will work e.g. 15 2 30 3 10 30 x=15 y=2 a=3 b=10 area of first = 30, ar...

Good one Bob - calculus
and Bob saw an even third interpretation of your typing (e^-x - 1)/(e^-x+ x )^2 http://integrals.wolfram.com/index.jsp?expr=%28e%5E-x+-+1%29%2F%28e%5E-x%2B+x+%29%5E2&random=false

calculus
my interpretation: (e^-x - 1)/(e^-x+x^2) , you have mis-matched brackets even the usual reliable Wolfram had difficulties with that one http://integrals.wolfram.com/index.jsp?expr=%28e%5E-x+-+1%29%2F%28e%5E-x%2Bx%5E2%29&random=false the way you typed it, fixing the missing bra...

Calculus
v(0) = 35(25)^2 = 21875 v(15) = 35(10)^2 = 3500 avg rate of change for those 15 minutes = (2500 - 21875)/(15-0) = -18375/15 L/min = -1225 L/min You are correct at t=15, you are looking for the instantaneous rate of change, that is, the derivative of v(t) v ' (t) = 70(25-t)...

math
Dimensions of the rectangle including the sidewalk is 290 by 730 , (added 5 feet on each side) surface area of sidwwalk = 290x730 - 280x720 =10100 ft^2 volume of sidwwalk = 10100(8/12) ft^3 = 20200/3 ft^3 but we are ordering 5% extra volume ordered = 20200/3 (1.05) = 7070 cubi...

Logarithmic Algebra
log 100 = log(25*4) = log 25 + log 4 = log 5^2 + log 2^2 = 2log5 + 2log2 = 2c + 2a

Algebra
= x^9 y^36

Math
let the angle be x then its complement is 90-x x = 4(90-x) x = 360 - 4x 5x = 360 x = 72 so the angle is 72° and its supplement is 180-72 = 108° check: our angle = 72 its complement = 18 is the angle 4 times its complement ? is 72 = 4(18) ? yes

Algebra
so .. [(x^2 + 8x + 15)/(x-4)] * [(x^2 – 16) / (2x + 6)] = (x+3)(x+5)/(x-4) * (x-4)(x+4)/(2(x+3) ) = (x+5)(x+4)/2 , x ≠ -3, 4 the temptation is to anticipate asymptotes at x = -3 and x = 4 but since we obtain 0/0 for these two values in the original, but an actual va...

math
You are probably not getting any replies because we might all be confused by " Find the number of ordered N samples of size 3: " I have no idea what you mean. Are there different sizes of lightbulbs? Are we choosing lightbulbs? ???

Calculus
so you are solving 2sin 2t + cos 2t = 0 2sin 2t = -cos 2t 2sin 2t/cos 2t = -1 tan 2t = -1/2 set your calculator to RAD and find 2nd function tan (tan^-1 (+1/2) to get .46365 we know that the tangent is negative in II and IV so 2t = π - .46365 = 2.6779 t = 1.339 or 2t = 2&...

math
z-score for the 169 = (169-180)/8 = -1.375 x-score for the 191 = (191-180)/8 = +1.375 look up value for 1.375 and the value for -1.375 subtract the two values You should get .8309 I recommend this webpage for these type of questions. http://www.wolframalpha.com/input/?i=plot+y...

math
number of dimes ---- x number of quarters --- 21-x by value: 10x + 25(21-x) = 405 10x + 525 - 25x = 405 -15x = -120 x = 8 so 8 dimes and 21-8 or 13 quarters or dimes ---- d quarters ---q based on numbers: d+q = 21 based on value: 10d + 25q = 405 --- 2d + 5q = 81 double the fir...

College Algebra
when is 2 = 1 (1.3)^t take ln of both sides ln 2 = ln (1.3)^t ln2 = t (ln 1.3) t = ln 2/ln 1.3 = appr 2.64 yrs or 2 years and 7.7 months check suppose there were 5 million sold now, in 2.64 years, the number sold is N = 5 (1.3)^2.64 = 9.995 million or double the original 5 mil...

Algebra
no unique answer. any pair of factors of 15x3 + 25x^2 would do 15x^3 +25x^2 = x^2(15x + 25) or = 5x(3x^2 + 5x) or = 5(5x^3 + 5x^2) etc for any answer, the two factors would be the length and width

9th grade math
divide each term by 4 and move all terms to the left x^2 - 20x + 100 = 0 (x - 10)^2 = 0 x-10 = 0 x = 10

9th grade math
did you notice the left side is a perfect square? (x+4)^2 = 25 take √ of both sides x+4 = ± 5 x = -4 ± 5 = 1 or -9

9th grade math
I would divide by 4 to get m^2 - 6m + 9 = 0 , and now see it as a perfect square (m-3)^2 = 0 m-3 = 0 m = 3

Calculus
yes

Calculus
You are right to have those two asymptotes. look at http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x%5E2%2B4x-5%29%2F%28x-2%29+%2C+y+%3D+x%2B6 What happens at the far right and the far left ?

Math
correct , there is only one choice, namely the 1

College algebra
white ones ---- x yellow ones ---- 31 - x solve for x 11.95x + 12.50(31-x) = 379.80

precal
I noticed that it factors quite easily using grouping f(x) = x^2(x - 2) - 15(x - 2) = (x-2)(x^2 - 15) so if (x-2)(x^2 - 15) = 0 then x-2 = 0 or x^2 - 15 = 0 x = 2 or x^2 - 15 = 0 x^2 = 15 x = ± √15 x^2 - 15 does not factor using rational numbers you could look it ...

Math (Please Help Ms. Sue)
The surface area of two similar solids is proportional to the square of their corresponding sides, so the square of the "doubling" is 2^2 or 4 So the surface area is quadrupled or let the original dimensions be l , w, and h surface area = 2lw + 2lh + 2 wh = 2(lw + lh...

Calculus Help Please!!!
a) very easy b) dy/dx = (π^x) * ln(π) c) tricky, first ln both sides lny y = ln(x^x) = xlnx y'/y = x(1/x) + lnx y' = x^x (1 + lnx) d) what is the derivative of a constant? e) xy = π x dy/dx + y = 0 dy/dx = -y/x

Calculus Help Please!!!
2x + 4x dy/dx + 4y + 2y dy/dx = 0 dy/dx(4x + 2y) = -2x - 4y dy/dx = -2(x+2y)/( 2(2x + y) = -(x+2y)/(2x+y) at (2,1) dy/dx = -4/5 so slope of tangent is 4/5 slope of normal is 5/4 tangent: y-1 = (-4/5)(x-2) y - 1 = (-4/5) + 8/5 y = (-4/5)x + 13/5 you do the normal is the same way.

maths Pls help trig
1. tanA = 1/3, and tanB = 1/7 I usually construct my triangles, (since the fraction gives you 2 of the sides of right-angled triangles, the third can always be found using Pythagoras) for tanA = 1/3, sinA = 1/√10 , cosA = 3/√10 for tanB = 1/7, sinB = 1/√50, c...

MathS triG
see solution above of the same question Please don't switch names.

Algebra
let her speed for the last two hours be x km/h total distance = 6(40) = 240 km 4(50) + 2(x) = 240 2x = 40 x = 20 speed of last part = 20 km/h

college algebra
So you are solving: 144 = 128t - 16t^2 16t^2 - 128t + 144 = 0 t^2 - 8t + 9 = 0 I will complete the square, (in this case faster than the formula) t^2 - 8t + 16 = -9+16 (t-4)^2 = 7 t-4 = ±√7 t = 4 ± √7 I get appr 6.65 and 1.35

maths - HCF
Did you notice that 119 = 7 x 17 , that is, its only factors are prime numbers. If we needed the HCF of 7 and 17 it would be 1 If we needed the LCM of 7 and 17 it would be 119 The product of 1 and 119 is 119 Our two numbers are 7 and 17 Further investigation: suppose we have t...

math
height/30 = sin 65 height = 30sin65° = .....

Geometry
A regular octagon forms 8 congruent isosceles triangles, where the central angles are 360/8° or 45° each. Your second part cannot be answered since you gave no data. Let the radius be r and consider one of the triangles.. If the base is 2s, then s/r = sin 67.5° s =...

Math
The way you worded it , we could form 3 letter words, or 5 letter words, etc. In other words, it becomes a "Scrabble" type question and not really a math question. Is that what you need ? or is it, "in how many ways can we arrange all the letters of the word ALG...

Pre-Algebra
I assume you meant 18 inches ( ' usually is the symbol for feet if I recall the imperial measure system) jenny --> x inches Demi--> half of that or x/2 inches Joel --> gets 3/4 of Jenny's or 3x/4 x + x/2 + 3x/4 = 18 times 4 4x + 2x + 3x = 72 9x = 72 x = 8 Jenn...

Calculus Help
let the height be h then the diameter of the base is 4h, thus the radius is 2h given: dV = 20 ft^3/min find: d(2h)/dt , when h = 12 V = (1/3)π r^2 h = (1/3) π (4h^2)(h) = (4/3) π h^3 dV/dt = 4π h^2 dh/dt 20 = 4π((144) dh/dt dh/dt = 5/(144π) so d(2...

Math
white / green = 3/2 w/18 = 3/2 2w = 54 w = 27 check: 27/18 = 3/2

Math
√(2x^2+5)=2 square both sides 2x^2 + 5 = 4 2x^2 = -1 x^2 = -1/2 no solution, since we cannot take the square root of a negative in the real number set.

Algebra - Help!
f(x)=(x^2+6x+5)/(x^2+3x−10) = (x+1)(x+5(/((x+5)(x-2) ) = (x+1)/(x-2) domain: any real value of x , x ≠ -5, 2 vertical asymptote: x = 2 hole: x = -5 horizontal asymptote: y = 1 see: http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x%5E2%2B6x%2B5%29%2F%28x%5E2%2B3x...

Algebra 2
Looks like you label your a to be associated with the major axis (the axis containing the foci) In that case: b^2 + c^2 = a^2 b^2 + (√19)^2 = 7^2 b^2 + 19 = 49 b^2 = 30 so are correct about the centre, so (x+7)^2 /30 + y^2/49 = 1 http://www.mathwarehouse.com/ellipse/equa...

uc-metc math16
let the length of the chord be y let the horizontal distance of the kite be x ft given: dx/dt = 5 ?? (looks like a typo in the units) I will assume you meant: 5 mph = 5280 ft/60 min = 88 ft/min y^2 = x^2 + 40^2 when y = 50 50^2 = x^2 + 40^2 x = 30 2y dy/dt = 2x dx/dt dy/dt = 2...

Calculus Help
dy/dØ = cos(π/√(Ø^2+5) * (-1/2)(Ø^2 + 5)^(-3/2) ) * (2Ø) =(-πØ/(Ø^2 + 5)^(3/2) * cos(π/√(Ø^2+5) so when Ø = 2 dy/dØ = ... You do the button - pushing. Make sure to set your calculator to RAD

Math
1n + 7p = 5.55 3n + 2p = 12.28 from the first: n = 5.55-7p sub into the 2nd 3(5.55-7p) + 2p = 12.28 16.65 - 21p + 2p = 12.28 -19p = -4.37 p = .23 then n = 5.55 - 7(.23) = 3.94 check: 1 notebook + 7 pencils = 3.94 + 7(.23) = 5.55 3 notebooks + 2 pencils = 3(3.94) + 2(.23) = 12....

Math
Right now, (-2,-5) is 5 units below the x-axis so reflecting it over the x-axis would put it how many units above the x-axis ? And the total distance would be ...... ?

foundation differential calculus
I suspect a typo why would you have 2 terms in t^2 without adding them together? Is the last term supposed to be t^3 ? Clarify before I attempt it.

Math
sin 2x - sinx =0 2sinx cosx - sinx = 0 sinx(2cosx - 1) = 0 sinx = 0 or cosx = 1/2 for sinx = 0 x = 0, 180°, 360° for cosx = 1/2 x = 60° , 300° so for 0 ≤ x ≤ 360° x = 0, 60, 180, 300, 360 in radians: x = 0 , π/3 , π , 5π/3 , 2π

Maths
Did you make your sketch? Let the distance from the longer chord to the circle be x then the distance from the shorter chord to the circle is 17-x Let the radius be r then r^2 = x^2 + 12^2 and r^2 = (17-x)^2 + 5^2 so x^2 + 144 = (17-x)^2 + 25 x^2 + 144 = 289 - 34x + x^2 + 25 3...

Math
Ahh, looks like neither one of us read the question carefully. P(t) given the percentage that will FAIL, which is 30.2% But it says, "what percentage ... is usable " so 100 - 30.2 or 69.8%

Math
just plug in t = 3 P(3) = 100(1 - e^-.36) = 30.23 So appr 30.2%

Math
3(0.4h+5)>4(0.2h+7) 1.2h + 15 > .8h + 56 1.2h - .8h > 56 - 15 .4h > 41 h > 41/.4 h > 102.5

math
1 rotation = 360° = 2π radians at 7:00 the minute hand is on the 12 (straight up) and the hour hand has moved 7/12 of a rotation (7/12)(2π) = 7π/6 radians ---> or 210° so the smaller angle between the two hands = 2π - 7π/6 = 5π/6 radian...

Math (check)
Interpretation #1 : Slant height is the edge of the pyramid Consider the right-angled (internal) triangle formed by the height , half the diagonal of the base and hypotenuse being the slant height. let the slant height be x let the diagonal of the base be d d^2 = 1^2 + 12^2 = ...

Algebra
number of dach's --- x number of labs ----- 3x solve for x .... x + 3x = 200000

Math
I labelled the position of the church as C. angle C = 85° by the sine law: CP/sin35 = 600/sin85 CP = 600sin35°/sin85° = appr 345.5 m you do CQ

Math
Erin has 36 Julia has 2/3 as many as Erin ---> she has (2/3)(36) or 24 Julia also has 1/3 as many as Robert 24 = (1/3)(Robert) Robert has 72 Erin has 36 Julia has 24 Robert has 72 for a total of 132

Algebra
I suspect a typo and you meant: (x^2 - 25)/(x^2 - 3x - 10) , since that factors nicely into (x+5)(x-5)/( (x-5)(x+2) = (x+5)/(x-2) , x ≠ 5

Math
How about this pattern term(1) = 6 = 3(2^1) term(2) = 12 = 3(2^2) term(3) = 24 = 3(2^3) term(4) = 48 = 3(2^4) .... term(23) = .... = 3(2^23) term(n) = .....

Math
Q(t) = 200 (1/2)^(t/14.2) or Q(t) = 200(.5)^(.0704t) Q '(t) = (200/14.2) (.5)^(t/14.2) so when t = 21.5 Q ' (t) = (200/14.2) (.5)^(21.5/14.2) = 4.931 g/day

algebra 2
This produces an arithmetic series, where a = -5 and d = 8 sum(28) = (28/2)(-10 + 27(8)) = 2884

Math
I am sure you meant: Q(t) = 7000/(1 + 249 e^(-.6t) ) Q(10) = 7000/(1 + 249 e^(-.6(10) ) ) = appr 4328

algebra 2
so a = -12 , d = 5 sum(n) = (n/2)(2a + (n-1)d ) = (11/2)(-24 + 10(5)) = (11/2)(26) = 143 OR sum(n) = (n/2)(first + last) = (11/2)(-12 + 38) = 143

algebra 2
The famous mathematician Gauss, while he was in elementary school, notices the following 1+2+3+..+58+59+60 = (1+60) + (2+59) + (3+58) +.. (for a total of 30 of these pairs) = 30(61) = 1830

MATH
A polynomial must have a non-negative integer exponent. A and B contain square roots or exponents of 1/2 D: 11/(√x)^2 = 11/x or 11 x^-1 so none is a polynomial C: x - √11 yup, I would go with that one

Algebra
Did you mean: (2x+6)/(4x-8) ?? = 2(x+3)/(4(x-2)) = (x+3)/(2(x-2) or (x+3)/(2x - 4)

Math
I would consider it a "combination" , assuming that the order that you choose the appetizers should not matter Number of ways = C(4,2) x C(5,1) = 6x5 = 30

Calculas
P(4) = 100(4) - 3(16)ln(4) = .. I assume you have a calculator to get appr 333.46

Calculus Help Please!!!
dy/dx = 8x(1/2)(x-x^2)^(-1/2) (1 - 2x) + 8(x-x^2)^(1/2) = 4(x-x^2)^(-1/2) [ x(1-2x) + 2(x-x^2) ] = (4/√(x-x^2) ( x - 2x^2 + 2x - 2x^2) = (4/√(x-x^2) (3x - 4x^2) = 0 for a max/min 3x - 4x^2 = 0 x(3 - 4x) = 0 x = 0 ----> looks like it will yield a min x = 3/4 ---&...

typo - Calculus Help Please!!!
only valid for 0 ≤ x ≤ 1

Calculus Help Please!!!
only valid for 90 ≤ x ≤ 1 http://www.wolframalpha.com/input/?i=y+%3D+%3D+8x%28√%28x+−+x%5E2%29%29+%2C+0+%3C+x+%3C+1

Algebra
But you wanted to use the formula ... x = (-4 ± √100)/2 = (-4 ± 10)/2 = (-4+10)/2 or (-4-10)/2 = .....

Algebra
put it into standard form of a quadratic ... x^2 + 4x - 21 = 0 how nice that it factors .... (x+7)(x-3) = 0 so x = ... or x = ....

percentages/word problem
costprice = 80 after first markup, SP = 80(1.5) after 20% mark down = 8(1.5)(.8) another 15% markup = 8(1.5)(.8)(1.15) final markdown of 60% = 8(1.5)(.8)(1.15)(.4) = 8(.552) = 4.42

Calculus1
let the width of the beam be 2w and the depth be 2d S = k(2w)(4d^2) = 8k w(d^2) I drew a circle and incribed a rectangle with the defined dimensions. Notice the diagonal is 12 Construct a righ-angled triangle, with sides w, d, and hypotenuse 6 w^2 + d^2 = 36 d^2 = 36-w^2 in S...

Math - Algebra2
f(x)=3x+2 , g(x)=3/x^2+2 , h(x)=sqrt(x-2) (f∘g)(-5) to me means: f (g(x) ) so f(g(5)): g(-5) = 3/27 = 1/9 f(1/9) = 3(1/9) + 2 = 1/3 + 2 = 5/3 (f∘g)(-5) = 5/3 so the others the same way

Precalculus
w = -i - 2j describes the vector (-1,-2) so it the same way I showed you in the similar problem of unit length. YOu can do it in your head to get (-1/√5 , -2/√5)

Algebra
for any quadratic of the form y = ax^2 + bx + c the x of the vertex is -b/(2a) so for yours ... x of the vertex is -184/(-32) = 5.75 so it took 5.75 seconds, plug that into your original function to find the maximum height.

Pre calculus
correct notice you can check that the magnitude is 1 magnitude = √( (1/√2)^2 + (-1/√2)^2 ) =√( 1/2 + 1/2) = √1 = 1

Pre calculus
for any unit vector in the direction of (a,b) .... find the length of the vector = √(a^2+b^2) now divide each component by that magnitude to get (a/√(a^2+b^2) , b/√(a^2+b^2) or you could write it as (1/√(a^2+b^2) (a,b) apply this to your vector, let me ...

algebra
welcome

algebra
multiply each term by 2x(x+1) 6x - 2(x+1) = x(x+1) 6x - 2x - 2 = x^2 + x x^2 +3x + 2 = 0 (x-1)(x-3) = 0 x = 1 or x = 3

Calculus1
it would be a combination of the chain rule and the product rule, doing it as a single power the way I did it was easier as a product rule - chain rule for that term ..... x√x = x x^(1/2) derivative: x (1/2) x^(-1/2) + (1)x^(1/2) = x/(2√x) + √x = x/(2√x...

Calculus1
yes, of course, silly me, the exponent on the last one was 3/2

Calculus1
I would rewrite as h(x) = 3x^(1/2) - x^(3/2) h ' (x) = (3/2) x^(-1/2) - (2/3) x^(1/2) = 3/(2√x) - (2/3) √x

Algebra
it will hit the ground when the height h(t) = 0 -16t^2 + 144 = 0 16t^2 = 144 t^2 = 144/16 = 9 so t =√9 = 3 after 3 seconds

Pre calculus
welcome

Pre calculus
PS-3PQ = (-10,4) - 3(2,5) = (-10,4) + (-6,-15) = (-16,-11) magnitude is √((-16)^2 + (-11)^2) = √377

Algebra
since you want the height horizontally from the starting height, and that height was 5.4 metres, -.06x^2 + 9.6x + 5.4 = 5.4 the 5.4 drops out, so x(-.06x + 9.6) = 0 x = 0 , the starting time or x = 9.6/.06 = 160 it will land after 160 m

Geometry
let the chord AB = 2x then the diameter = 2x+2 or the radius = x+1 This allows me to draw a right-angled triangle with sides x and 9 and hypotenuse x+1 (x+1)^2 = x^2 + 9^2 x^2 + 2x + 1 = x^2 + 81 2x = 80 x = 40 AB = 80 check: diameter = 82 is 41^2 = 40^2 + 9^2 ? LS = 1681 RS =...

Algebra II
rowing speed in still water ---- x mph speed of current ------------- 2 mph time to go 50 miles with the current = 50/(x+2) time to go 25 miles against current = 25/(x-2) the two times are the same, so ... 50/(x+2) = 25/(x-2) 50x - 100 = 25x + 50 25x = 150 x = 6 speed in still...

slope
y = 3x - 7 straight line with slope of 3 and y-intercept of -7 http://www.wolframalpha.com/input/?i=y+%3D+3x+-+7

Pre-calc
What are we doing with this hyperbola ?

Math help
look back at your previous post of this

Math
let the slant height of one side be h then using (1.2)base x height 1980 = (1/2)(35.4)h h = 3960/(35.4) = 111.8644 = appr 111.86 m this can't be. According to the given dimensions on the webpage, the base is about 35 by 35 and the height is 21.6 m, for a slant height of 27...

calculus
let the two equal width be x let the single side by y xy = 600 y = 600/x cost = 20y + 30x = 20(600/x) + 30x d(cost)/dx = -12000/x^2 + 30 = 0 for a min of cost 30 = 12000/x^2 x^2 = 400 x = 20 the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.

Word problem
the x of the vertex is -b/(2a) = -184/(-32) = 5.75 seconds plug that into the function h(5.75) = 16(5.75^2) + 184(5.75) + 20 = 549 ft

Finance
monthly rate = .041/12 = .00341666.. let the effective annual rate be i 1 + i = (1 + .00341666..)^12 1+i = 1.0417783 i = .0417783 or appr 4.18%

PRE CALC
using the standard notation: term(20) = a + 19d = 27 and a = -11 -11 + 19d = 27 19d = 38 d = 2 the common difference is 2 check: term(2) = a+19d =-11 + 19(2) = -11+38 = 27

calculus
I see that C(1990) is given as 271.9 What are you asking?

Equations
did it, look back

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