Wednesday
October 22, 2014

Posts by Reiny


Total # Posts: 27,509

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

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, ...
April 9, 2014

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
April 9, 2014

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 ...
April 9, 2014

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...
April 9, 2014

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 ...
April 9, 2014

Logarithmic Algebra
log 100 = log(25*4) = log 25 + log 4 = log 5^2 + log 2^2 = 2log5 + 2log2 = 2c + 2a
April 9, 2014

Algebra
= x^9 y^36
April 9, 2014

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
April 9, 2014

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 ...
April 9, 2014

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? ???
April 9, 2014

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...
April 9, 2014

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...
April 9, 2014

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 ...
April 9, 2014

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 ...
April 9, 2014

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
April 8, 2014

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
April 8, 2014

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
April 8, 2014

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
April 8, 2014

Calculus
yes
April 8, 2014

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 ?
April 8, 2014

Math
correct , there is only one choice, namely the 1
April 8, 2014

College algebra
white ones ---- x yellow ones ---- 31 - x solve for x 11.95x + 12.50(31-x) = 379.80
April 8, 2014

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 ...
April 8, 2014

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...
April 8, 2014

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
April 8, 2014

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.
April 8, 2014

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, ...
April 8, 2014

MathS triG
see solution above of the same question Please don't switch names.
April 8, 2014

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
April 8, 2014

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
April 8, 2014

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 ...
April 8, 2014

math
height/30 = sin 65 height = 30sin65° = .....
April 8, 2014

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...
April 8, 2014

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 ...
April 8, 2014

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 ...
April 8, 2014

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(...
April 7, 2014

Math
white / green = 3/2 w/18 = 3/2 2w = 54 w = 27 check: 27/18 = 3/2
April 7, 2014

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.
April 7, 2014

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...
April 7, 2014

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/...
April 7, 2014

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 = ...
April 7, 2014

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
April 7, 2014

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....
April 7, 2014

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 ...... ?
April 7, 2014

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.
April 7, 2014

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
April 7, 2014

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 ...
April 7, 2014

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%
April 7, 2014

Math
just plug in t = 3 P(3) = 100(1 - e^-.36) = 30.23 So appr 30.2%
April 7, 2014

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
April 7, 2014

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 ...
April 7, 2014

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 = ...
April 7, 2014

Algebra
number of dach's --- x number of labs ----- 3x solve for x .... x + 3x = 200000
April 7, 2014

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
April 7, 2014

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
April 7, 2014

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
April 7, 2014

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) = .....
April 7, 2014

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
April 6, 2014

algebra 2
This produces an arithmetic series, where a = -5 and d = 8 sum(28) = (28/2)(-10 + 27(8)) = 2884
April 6, 2014

Math
I am sure you meant: Q(t) = 7000/(1 + 249 e^(-.6t) ) Q(10) = 7000/(1 + 249 e^(-.6(10) ) ) = appr 4328
April 6, 2014

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
April 6, 2014

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
April 6, 2014

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
April 6, 2014

Algebra
Did you mean: (2x+6)/(4x-8) ?? = 2(x+3)/(4(x-2)) = (x+3)/(2(x-2) or (x+3)/(2x - 4)
April 6, 2014

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
April 6, 2014

Calculas
P(4) = 100(4) - 3(16)ln(4) = .. I assume you have a calculator to get appr 333.46
April 4, 2014

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 ---&...
April 4, 2014

typo - Calculus Help Please!!!
only valid for 0 ≤ x ≤ 1
April 4, 2014

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
April 4, 2014

Algebra
But you wanted to use the formula ... x = (-4 ± √100)/2 = (-4 ± 10)/2 = (-4+10)/2 or (-4-10)/2 = .....
April 4, 2014

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 = ....
April 4, 2014

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
April 3, 2014

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...
April 3, 2014

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
April 3, 2014

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)
April 3, 2014

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.
April 3, 2014

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
April 3, 2014

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