Wednesday
April 23, 2014

Posts by Reiny


Total # Posts: 26,103

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

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

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

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

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

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.

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.

graphing
not enough information is your parabola vertical or horizontal? Was there a graph?

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/h...

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 ...

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

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

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

ALGEBRA
What is the x value of your vertex ?

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)

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)

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 ...

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

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.

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

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.

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

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...

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

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...

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 und...

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...

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 s...

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 = ....

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