Wednesday
November 26, 2014

Posts by Reiny


Total # Posts: 27,960

Math
f(x) and y are interchangable so instead of f(x) = 3x^2 - x - 2 you can say y = 3x^2 - x - 2 so when x = 2 , y = 12 - 2 -2 = 8 which you had so you are dealing with the point (2, 8) the x is 2, the y is 8
October 25, 2014

precalculus
make you sketch in such a way that the roadway is the x-axis and the center of the cable is along the y-axis So the vertex of your parabola is (0,10) and your equation is y = ax^2 + 10 we know (200,90) must be a point on it, so 90 = a(40000) + 10 a = 80/40000 = (1/500)x^2 + 10...
October 25, 2014

Precalculus
according to my quick sketch you have to use the cosine law x^2 = 180^2 + 90^2 - 2(180)(90)cos 75° ... x = appr 179 miles
October 25, 2014

geometry
No idea what your diagram looks like.
October 25, 2014

correction - Math
original : x at end of 1st week we have 1/3 x left at end of 2nd week we have (1/3)(1/3 x) left = (1/3)^2 x at end of 3rd week we have (1/3)^3 x left so (1/27)x = 37 x = 999 So there were 999 leaves check: number falling off 1st week = (2/3)(999) = 666 number left = 333 number...
October 25, 2014

math
Amount it is less by = 45-25 = 20 as a percentage that is 20/45 =.44444.. or appr 44.4%
October 25, 2014

maths
Assuming you are just picking one card from the full deck each time It will always be out of 52 all you have to know is how many cards there are in your subject. e.g. b) there are 4 aces, so prob(ace card) = 4/52 = 1/13 d) yellow is not a basic property of a deck of cards so I...
October 25, 2014

Math
depends on the value of the discriminant D where D = b^2 - 4ac remember that if D > 0 we have 2 distinct real roots D = 0 we have 1 real root D <0 we have no real roots So take all 3 cases , I will do one them, you do the rest. D > 0 10^2 - 4(5)d > 0 -20d > -100...
October 24, 2014

algebra
done, check your other post
October 24, 2014

algebra
first of all, 2-x > 0 -x > -2 x < 2 furthermore, 1-√(2-x) > 0 1 > √(2-x) √(2-x) < 1 so 0 < 2-x < 1 -2 < -x < -1 2 > x > 1 or 1 < x < 2 so if x < 2 AND 1 < x < 2 then 1 < x < 2 test: take a value outside...
October 24, 2014

calculus
A = 4πr^2 dA/dt = 8πr dr/dt when d = 8, r = 4, dA/dt = -2 -2 = 8π(4)dr/dt dr/dt = -1/(16π) so dd/dt = -1(8π) cm/min
October 24, 2014

algebra
y - 5 = 1(x - 4) etc
October 24, 2014

algebra
slope = (7-3)/(4-5) = -4 using the point (5,3) y - 3 = -4(x - 5) dress it up any way you want to
October 24, 2014

algebra
undefined x = 4 (how does that compare with the results of your previous post ? )
October 24, 2014

algebra
Any horizontal line has the form y = b, where b is the y value of the point it passes through so yours is y = 5 think of it as y = 0x + 5
October 24, 2014

college algebra
5 5 -1/5
October 24, 2014

algebra
since the relation is supposed to be linear, let's pick an "easy" pair, (20,2100) and (30,2000) slope= (2100 - 2000)/(20-30) = 100/-10 = - 10 so temp = -10t + b , where t is time in minutes 2000 = -10(30) + b b = 2300 temp - =10t + 2300 b) for 3 hrs, temp = -10(...
October 24, 2014

Last BrainMath :(
by the time you typed out your reply you could have easily counted from 99 to 131 and back again.
October 24, 2014

math
look at the answer I just gave Casey one post below.
October 24, 2014

Algebra 1
What is the value of y at the x-intercept? what is the value of x at the y-intercept? just plug in y = 0 and you have the x-intercept or notice that the constant is 0 So the line must pass through the origin.
October 24, 2014

Algebra 1
2 steps: 1. isolate the y term 2y = -x - 6 2. divide by the coefficient of the y term y = (-1/2)x - 3
October 24, 2014

Math
times 18 2x - 72 = 5 2x = 77 x = 77/2 or 38.5
October 24, 2014

applied maths
to be orthogonal, the dot product must be zero -2b + 4b^2 + 2 = 0 2b^2 - b + 1 = 0 b = (1 ± √-7)/4 No real value of b will make your two given vectors orthogonal
October 24, 2014

Please Help asap for math
u dot w = |u| |w| cosØ [-2,-1,2]dot[4,3,-2] = √9√29cosØ (-8 -3 -4)/3√29 = cosØ Ø = appr 158.2° to be coplanar, w must be a linear combination of u and v, that is w = au +bv [4,3,-2] = a[-2,-1,2] + b[1,-1,-4] so -2a + b = 4 and...
October 24, 2014

math
you are given the equation y = -4.3x and in each point, one of the variables is given, so just plug that in and evaluate. e.g. for B x = 5, so y = -4.3(5) = -21.5 you do the first one
October 23, 2014

Math
slope = (-1-4)/(2-(-3)) = -5/5 = -1
October 23, 2014

Trig / Calc
well, once around a circle is 360° 2 times around a circle is 2(360) or 720° ... 18.96 times around a circle is .....
October 23, 2014

Math 222
Since you don't have equations, you can't "solve" either one of them Your probably want them simplified 1. (g^2 - 6g - 55)/g = (g-11)(g+5)/g nothing else can be done with that one. 2. (k^3 + k)/(k^2 + k - 42) = k(k^2 + 1)/( (k+7)(k-6) ) again, not much more ...
October 23, 2014

algebra
let the length parallel to the wall by y m let the other two lengths be x m 2x + y = 24 y = 24-2x area = xy = x(24-2x) = -2x^2 + 24x this is a downwards opening parabola, we have to find the vertex. I don't know which method you use but the easiest way is to find the x of ...
October 23, 2014

algebra
looks like some kind of typo did you mean: r(x) = 1/(1-x)^2 ?
October 23, 2014

algebra
let the amount invested at 10% be x let the amount invested at 6% be 10000-x so ... .1x + .06(10000-x) = .08(10000) .1x + 600 - .06x = 800 .04x = 200 x = 5000 just read the question again, an saw that you wanted a system of equations, that is, two variable let 10% money be x ...
October 23, 2014

Algebra
l(y) = 1/(y-8) + (y+8) If we define domain as your choice of numbers for the independent variable, then any real number , y ≠ 1
October 23, 2014

math
if you are using the standard notiation to label a vector with [i, j, k] then 5j would be [0, 5, 0] a) |vector u + vector v - 5j | = |[1,-3,-2] + [4,-5,3] - [0,5,0] | = | [5, -13, 1] = √(25+169+1) = √195 b) let Q be (x,y,z) then PQ = [x+7,y-5,z+1] but PQ = 2u = [2...
October 23, 2014

Algebra
looks like you meant to type a partial continued fraction 1/( 1+ (1+1/x) ) , so x≠0 = 1/(1 +(x+1)/x) --> (x+1)/x ≠ -1 , or x ≠ -2 = 1/(x + x+1)/x = 1/(2x+1)/x = x/(2x+1) , x ≠ -1/2 so x ≠ 0, -1/2 , -2 the sum of those 3 restricted values = -2 1...
October 23, 2014

arithmetic
Did you not look at the answer I gave you for this same type question I gave you yesterday? http://www.jiskha.com/display.cgi?id=1414030711 follow the same reasoning.
October 23, 2014

Algebra
no, the same x value of 0.3 has 2 different y values
October 23, 2014

Geometry- thanks reiny
more data needed
October 22, 2014

Math
What five shelves ? depends on each of the five shelves.
October 22, 2014

math
distance at 70 mph = .65(300) or 195 miles trip left = .20(105) = 21 miles distance traveled between 35 and 70 = 300-195-21 = 84
October 22, 2014

algebra, factoring
I will assume you mean x^3 + .9x^2 - .9x = 0 times 10 10x^3 + 9x^2 - 9x = 0 x(10x^2 + 9x - 9) = 0 x = 0 or x = (-9 ± √441)/20 x = 0 or x = (-9 ± 21 )/20 x = 0 or x = .6 or x = -1.5
October 22, 2014

math
let the height be x then the base is x area of triangle = (1/2)x^2 sum = 2x 2x = (1/2)x^2 - 16 4x = x^2 - 32 x^2 - 4x - 32 = 0 (x-8)(x+4) = 0 x = 8 or x = -4, the latter makes no sense, so if x=8, area = (1/2)64 = 32 check is their sum 16 less than the area? or is 16 less than...
October 22, 2014

algebra
3x^2 + x = 2 3x^2 + x - 1 = 0 no integer solution, (use the formula, it will not come out to be a whole number)
October 22, 2014

Math
2215.1( 1 - (1+i)^-72)/i = 135000 very nasty equation to solve, since there is no "formula" way to do this Wolfram is our saviour. (notice I changed the i to x) the reasonable answer is i = .00470829 for the monthly rate so annual rate = 12(.0047...) = .056499.. or ...
October 22, 2014

arithmetic
the minute hand rotates 360° in 60 minutes or 6° per minute or 3° in 30 seconds. area swept by minute hand in one rotation = π(19^2) = 361π mm^2 so by ratios: 3/360 = area/361π area = 361π(1/120) = 361π/120 mm^2 = appr 9.45 mm^2 check my ...
October 22, 2014

math
How about thinking like this: You want to hand out 1 1/2 dollars or 3/2 dollars in coins If you want to use only quarters (1/4 of a dollar), how many coins (quarters) will you need ? obvious 6 quarters so 1 1/2 ÷ 1/4 = 6
October 22, 2014

pre calc
h = -16t^2 + 16t + 370 -16t^2 + 16t + 370 ≥ 50 16t^2 - 16t -320 ≥ 0 t^2 - t - 20 > 0 (t-5)(t+4) > 0 since this makes sense only for t ≥ 0 you would have 0 ≤ t ≤ 5 ( your first inequality sign is incorrect)
October 22, 2014

pre calc
no big deal, so 1995 --- > 0 but what did he/she change 1990 to ? make the suitable changes
October 22, 2014

pre calc
at x = 0 --- we have 1975 R(0) = 3500 http://www.wolframalpha.com/input/?i=f%28x%29+%3D++-0.121x%5E5%2B2.952x%5E4%2B3500+for+x+%3D+0 http://www.wolframalpha.com/input/?i=f%28x%29+%3D++-0.121x%5E5%2B2.952x%5E4%2B3500+for+x+%3D+1 http://www.wolframalpha.com/input/?i=f%28x%29+%3D...
October 22, 2014

4th Grade math
3x2x1 = 6 different ways
October 22, 2014

7th grade math
2x+3≤-3 2x ≤ -6 x ≤ -3 AND 5x-2<3 5x < 5 x < 1 so -3 ≤ x < 1 looks like {-3, -2, -1, 0 }
October 22, 2014

algebra
yes, I hope you weren't just guessing.
October 22, 2014

metric conversion
kilogram kg = 1000 g hectogram hg = 100 g dekagram dg = 10 g gram g 1 decigram dg = .1 g centigram cg = .01 g milligram mg = .01 g kilometre km hectometre hm dekametre dm metre m decimetre dm centimetre cm millimetre mm same for litre , etc all you need is the prefixes each is...
October 22, 2014

Trigonometry
Ahhh, good observation bob I did a similar type the long way few posts back, could have done it this way as well, would have been shorter
October 22, 2014

Math
Think of it as money. Suppose 12 friends have $5 each how much total money would there be ? ...... $60 So if one person would get all that money, how much would he/she get? ..... $60 If you had to share all the money with 20 people, how much would each get ? ..... 60/20 = $3 ...
October 22, 2014

Trigonometry
I know, I was able to do my diagram. I want YOU to try it, let me know what you get
October 22, 2014

Trigonometry
Looks like a bit of "home-work " dumping here I have done 2 of them for you, you have shown no indication of any of your own work. You try this one. hint: make a diagram to show triangle ABC All the angles in the triangle can be found, and you know one side AB = 300 ...
October 22, 2014

Trigonometry
(cos^2 x - sin^2 x)(cosx) - (2sinxcosx)(sinx) = 0 divide by cosx cos^2 x - sin^2 x - 2sin^2 x = 0 cos^2 x = 3sin^2 x sin^2 x/cos^2 x = 1/3 tan^2 x = 1/3 tanx = ± 1/√3 so x could in in any of the 4 quadrants I know tan 30° = 1/√3 and 30° = π/6 ...
October 22, 2014

Trigonometry
3sinx = 1 + 3cosx square both sides 9sin^2 x = 1 + 6cosx + 9cos^2 x 9(1 - cos^2 x) = 1 + 6cosx + 9cos^2 x 9 - 9cos^2 x = 1 + 6x + 9cos^2 x 18cos^2 x + 6x - 8 = 0 9cos^2 x + 3x - 4 = 0 cosx = ( -3 ± √153)/18 = -.85385 or .5205 if cosx = -.85385 x = 148.6° or x...
October 22, 2014

Algebra
yes
October 21, 2014

math,algebra,fractions, decimals
1/2 = .5 2/3 = .66666.... so terminating decimal between is .58 repeating decimal between is .567676767...
October 21, 2014

math
then I am right check: area of one triangle = (1/2)(3.5)(10.7857 = 18.875 4 such triangle = 4(18.875) = 75.5
October 21, 2014

math
define what you mean by slant height.
October 21, 2014

math
Clearly the surface area would consist only of the 4 triangles. area of one of them = 75.5/4 or 18.875 m^2 area = (1/2)base x height 18.875 = (1/2)(3.5)h h = 2(18.875)/3.5 = appr 10.7857 clean up to whatever accuracy is expected I would say 10.8 , since the original data had ...
October 21, 2014

Algebra
the original value does not matter e.g. let's start with 100,000 after 3 years: value = 100,000(.9)^3 after 3 more years: value = 100,000(.9)^3 (1.1)^3 = 97,029.9 so what do you think? Here is a new question for you. Would it matter if the value first increased by 10% for ...
October 21, 2014

math
any number that can be expressed as a simple fraction of the form a/b, where b ≠ 0 is rational rational --- from ratio --- a: b or a/b A number which cannot be expressed as a simple fraction in the above form is irrational irrational --> not rational (irresponsible...
October 21, 2014

Calculus
f ' (x) = ( (x-2)(2x) - (x^2 + 1)(1) )/(x-2)^2 = (2x^2 - 4x - x^2 - 1/(x-2)^2 = (x^2 - 4x - 1)/(x-2)^2 so f ' (a) = (a^2 - 4a - 1)/(a-2)^2
October 21, 2014

math
correct
October 21, 2014

math
simple interest = PRT = 5000(.09)(2) = $ 900 compound interest = 5000( 1.09)^2 - 5000 = $ 940.50
October 21, 2014

math
-7x^2 + 4x + 9 = 0 7x^2 - 4x - 9 = 0 using the formula ... x = (4 ± √268)/14 = appr 1.455 or x = - .884 the only one that comes close is the last choice Do the other one in the same way
October 21, 2014

math
done, look at your other post
October 21, 2014

Maths
f' (x) = x^(2/3) + (2/3)x^(-1/3) (x-1) = (1/3)x^(-1/3) [ 3x - 2(x-1) ] = (1/3)x^(-1/3) [ x + 2] = 0 for a max/min x = 0 or x = -2 checking the f(x) for those and the endvalues f(0) = 0 f(-2) = (-2)^(2/3) (-2-1) = -3(-2)^(2/3) = appr 4.76 f(4) = 4^(2/3) (4-1) = appr 7.56 so...
October 21, 2014

algebra
amount at 4% --- x amount at 3% --- 15000 - x solve for x .... .04x + .03(15000-x) = 550
October 21, 2014

Algebra
if 9>-3w-51>60 add 51 60 > -3w > 111 divide by -3 -20 < w < -37 which of course is not possible, since we can't have a number which is greater than -20 AND less than -37 (try to place such a number on a number line)
October 21, 2014

Math
at a time of t minutes, let the height of the water be h ft V = π(6^2)(h) = 36π h dV/dt = 36π dh/dt subbing in our values 3 = 36π dh/dt dh/dt = 1/(12π) ft/min Did you notice that the rate was constant (it did not depend on what h was) ?
October 21, 2014

Math HELP!!!!!
????
October 21, 2014

Algebra
I do not understand your long first sentence. I will attempt to make sense out of it let number of 5 centavo coins be x let the number of 10 centavo coins be y let the number of 25 centavo coins be z "25 centavo coin is 3 times as many 5 coinand" ---- z = 3x "...
October 21, 2014

algebra
another ---- x one integer ---- 4x-3 x(4x-3) = 27 4x^2 - 3x - 27 = 0 (x-3)(4x+9) = 0 x = 3 or x = -9/4 but x was to be an integer so x =3 3 and 9
October 20, 2014

Math
Math is a language Just translate: 25 is --- "25 =" three times a number ---- "3w" , if w is the number decreased ---- " - " 8 --------- " 8 " so what do we have ?
October 20, 2014

math
let x be the total number of beads 2x/3 + 4x/21 + whites = x times 21 14x + 4x + 21whites = 21x 21whites = 3x whites = (1/7)x or (1/7) of the total
October 20, 2014

Pre-Calc
your given point is in quad II, so the cosine of the angle will have to negative. x = -1/5 , y = 1/2 r^2 = 1/25 + 1/4 = 29/100 r = √29/10 cosØ = x/r = (-1/5)/(√29/10) = (-1/5)(10/√29) = -2/√29 they might expect it to be rationalized and want the ...
October 20, 2014

calculus
your dy/dx should be -2sint + 2cos2t = 0 recall that one of the equivalents for cos 2t is 1 - 2sin^2 t so -2sint + 2(1 - 2sin^2 t) = 0 -sint + 1 - 2sin^2 t = 0 2sin^2 t + sint - 1= 0 (2sint - 1)(sint + 1) = 0 sint = 1/2 or sint = -1 but we want quadant I ,so sint = 1/2 t = &#...
October 20, 2014

geometry
You did not state which sides are parallel, so we can't tell If QT || RS, then obviously angle T = 180-23
October 20, 2014

Math
2z dz/dt = 2x dx/dt + 2y dy/dt when x=4 and y = 3 z^2 = 4^2 + 3^2 = 25 z = 5 Now that you have 5 of the 6 terms, just sub those in and solve for dz/dt
October 20, 2014

Calculus
I will guess you meant: f(x) = x^(1/6) - x^(-5/6) then f'(x) = (1/6)x^(-5/6 + (5/6)x^(-11/6) = 0 for critical values factor it .. (1/6)x^(-11/6)[ x + 5] = 0 x = 0 or x = - 5 sub those values back into the original function if you need the y values
October 20, 2014

Calculus
I will give you the derivative, you should be able to take it from there f ' (x) = (x^6(1/x) - lnx(6x^5) )/x^12 = (x5 - 6x^5(lnx))/x^12
October 20, 2014

Calculus
f'(x) = 12x^2 - 36x - 480 =0 for max/mins divide by 12 x^2 - 3x - 40=0 (x-8)(x+5) = 0 x = 8 or x = -5 You should know the general behaviour of cubic curve with a positive x^3 term and critical values at -5 and 8 I will give you the decreasing interval, it is between -5 and...
October 20, 2014

arithmetic
(7(9) + x)/8 = 6 63 + x = 48 x = -15 So you would have to add a negative number ?
October 20, 2014

Trigonometry
So A in in quadrant III tan 2A = 2tanA/(1 - tan^2 A) = 2(1/3)/(1 - 1/9) = (2/3) / (8/9) = (2/3)(9/8) = 18/24 = 3/4
October 20, 2014

Calculus
Your dy/dx should be (2y-4x)/(3y^2 - 2x) (the way you have it, only the -4x is divided by 3y^2 ) so when y = 2 , in the original, 2x^2 - 4x + 8 = 14 2x^2 - 4x - 6 = 0 x^2 - 2x - 3 = 0 (x-3)(x+1) = 0 x = 3 or x = -1 b) you probably meant to say: Find the equation of the tangent...
October 20, 2014

Math
You are right. It is not so much of an equation, but rather a statement. I would simply say: cost per child = 192/16 as the "equation"
October 20, 2014

math
let the sides be x , 3x , 5x, and 7x x+3x+5x+7x = 64 solve for x back-substitute to find any or all sides
October 20, 2014

calculus
Question makes no sense. It appears whole words are missing.
October 20, 2014

maths
term7 = a+6d = 6d-8 term9 = a+8d = 8d-8 (6d-8)/(8d-8) = 5/8 48d - 64 = 40d - 40 8d = 24 d = 3
October 20, 2014

Math
From the identity sin^2 x + cos^2 x = 1 if we divide both sides by sin^2 x , we get 1 + cot^2 x = csc^2 x so csc^2 x - 1 = cot^2 x RS = cot^2 x LS = csc^2(x)cos^2(x) = (1/sin^2 x)(cos^2 x) = cot^2 x = RS All done
October 20, 2014

Algebra
slope = (1-0)/(3-(-3)) = 1/6 so y = (1/6)x + b plug in (-3,0) 0 = (1/6)(-3) + b b = 1/2 y = (1/6)x + 1/2
October 20, 2014

math
since a = 2m/s^2 , note you have a typo there. v = 2t + c when t = 3, v = 6 6 = 2(3) + c c = 0 v = 2t so at top of hill, t = 0 then v = 0
October 20, 2014

algebra
3/(5-i) = 3/(5-i) * (5+i)/(5+i) = (15 + 3i)/(25-i^2) = (15+3i)/26
October 19, 2014

Math
contradiction: you say the diameter of the cone is the same as the diameter of the ice crream, but then you say 4 cm scoop of ice cream vs 7 cm of diameter of cone
October 19, 2014

math
Ø = tan^-1 (4/3) so you have right-angled trianle with opposite side = 4 and adjacent side = 3 You should recognize the 3-4-5 right-angled triangle, so sinØ = 4/5
October 19, 2014

algebra
Really ???? 10-4x = 0 -4x = -10 x = -10/-4 = 2.5
October 19, 2014

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