Thursday
March 5, 2015

Posts by Reiny


Total # Posts: 29,207

Calculus
Let the height of the ballon be h ft then tanØ = h/60 h = 60tanØ dh/dt = 60 sec^2 Ø dØ/dt we know dh/dt = 8 when h = 25 tanØ = 25/60 = 5/12 construct a right-angled triangles with opposite side 5 and adjacent side 12. By Pythagoras the ...
October 29, 2014

math
What is the transformation ? Does it match with any of the "Related Questions" below? the first one has the same coordinates.
October 29, 2014

Math
look at some example 3/2= 6/4 = 60/40 = 12/8 = .. what do you think?
October 28, 2014

Trig
(1+sinx)=cos^2 x 1 + sinx = (1 - sin^2 x) (1 + sinx) = (1+sinx)(1-sinx) divide both sides by 1 + sinx 1 = 1 - sinx or sinx = 0 easy to solve if you have to solve
October 28, 2014

Math
volume of cylinder = π(5^2)(12) = ... volume of cone = (1/3)πr^2 h solve (1/3)π(5^2)h = π(5^2)(12) after getting your answer it should be obvious why it is so.
October 28, 2014

Math
insufficient data e.g. do the 12 boys play ONLY soccer ? etc
October 28, 2014

Algebra
ratio of movie to band posters = 120:100 = 6/5 after selling 24 movie posters she has 96 so 96/x = 6/5 6x = 480 x = 80 so she has to sell 100-80 or 20 band posters
October 28, 2014

Algebra
NA : SA = 5 : 3 , SA : E = 3 : 2 So, NA : SA : E = 5 : 3 : 2 = 5x : 3x : 2x given: NA = 30 5x = 30 x = 6 then NA = 30 SA = 18 E = 12
October 28, 2014

Algebra
correct
October 28, 2014

math
let the width of one of the pens be x, let its length be y so we have 8x + 5y = 720 y = (720 - 8x)/5 = 144 - 8x/5 area = 4xy = 4x(144 - 8x/5) = 576x - (32/5)x^2 d(area)/dx = 576 - 64x/5 = 0 for a max of area 64x/5 = 576 64x = 2880 x = 45 largest total area = 4(45)(144 - 8(45)/...
October 28, 2014

Cal.
Since you did not define what your x and y are, I have no way of checking what you did In my sketch, I let the distance from the man to the light be x m, and the length of his shadow as y m then by ratios , 2/x = y/12 xy = 24 x dy/dt + y dx/dt = 0 when x=4, y=6 and dx/dt = 2.2...
October 28, 2014

math
width --- x length --- 2x+6 2(x) + 2(2x+6) = 102 carry on
October 28, 2014

Algebra
pick any pair to find the "slope" I took the first two pairs slope = (1840-1000)/60-40) = 42 so using the 1st point: e-1000 = 42(t-40) e - 1000 = 42t - 1680 42t - e = 680 or e = 42t - 680 all "points" satisfy my equation
October 28, 2014

probability ?????
time = distance/rate = 121/65 = 1.8615 hrs = 1 hr and 51.7 minutes
October 28, 2014

math
1st simplified: x + 2y = -1/2 2nd simplified: x + 2y = -1/2 same line, so infinite number of solutions
October 28, 2014

trigonometry
Did you make a sketch? I have a right-angled triangle with hypotenuse of 54 and a base angle of 90-32 or 58° sin 58 = y/54 y = 54sin58° = ... (the north distance) cos58 = x/54 x = 54cos58 = .... (the west distance)
October 28, 2014

math
Fran --- x Pete ---- 6x Hannah --- y y + x = 120 y+6x = 230 subtract them 5x = 110 x = 22 then y = 98 Hannah has $98 (Fran has 22 and Pete has 132
October 27, 2014

Algebra
yes
October 27, 2014

math
5 nickels 4 nickels, 5 pennies 3 nickels, 10 pennies 2 nickels, 15 pennies 1 nickel, 20 pennies 25 pennies. so 6 combinations
October 27, 2014

math
geeeshhh .... 2 inches represent 35 miles 1 inch represents 35/2 or 17.5 miles, so 5 inches represent 17.5(5) or 87.5 miles
October 27, 2014

Calculus
In just about any introductory Calculus book this type of question appears as a lead-in to the topic of "rates of change" Make a diagram, label the height y and the the base length x then x^2 + y^2 = 13^2 differentiate with respect to t (time) 2x dx/dt + 2y dy/dt = 0...
October 27, 2014

Math
3^-1 m/min = (1/3) m/min so time = distance/rate = 33/(1/3) = 99 minutes
October 27, 2014

algebra. help!
1st correct 2nd ... Poorly worded make a Venn diagram and fill in the data, according to your data, 130 play only basketball, 120 play both and 100 play only baseball so 220 for all of baseball circle is correct
October 27, 2014

math
2/5x-9 < 9/10 times 10 4x - 90 < 9 4x < 99 x < 99/4 if you meant to type 2/(5x-9) < 9/10 we would have a totally different problem, but you didn't type that
October 27, 2014

NO Nicole -Trig
your step from cos8t=3sin8t to 8 = 3tan8t is totally invalid, that would be pure mathemagics test your value, it does not work
October 27, 2014

Trig
you are ok up to 8t = arctan 1/3 make sure your calculator is set to radians, and then 8t = .32145 or 8t = π + .32145 t = .04022 or t = .43292 we know the period of tan 8t is 2π/8 or .7854 so we could add this to any previous answer to get more correct answers, as ...
October 27, 2014

algebra
The only one slightly difficult is #2 |y+4| < 1 then y+4 < 1 AND -y-4 < 1 y < -3 AND -y < 5 y< -3 AND y > -5 so -5 < x -3 in general, for inequalities, if you have |some stuff| < k , then separate them with AND (the intersection) |some stuff| > k...
October 27, 2014

College Algebra
8% less ----> 100% - 8% = 92% or .92 .92x = 146000 x = 146000/.92 = $158,695.65
October 27, 2014

Pre-Calc/Trig
Both of your equations are quadratics the standard form, sometimes called the vertex form, of a quadratic takes the form y = a(x-h)^2 + k , where the vertex is (h,k) your first equation is in intercept form, so the x of the vertex must be midway between -3 and 4 which would be...
October 27, 2014

math
What am I looking at ? I this a matrix equation? What is x ?
October 27, 2014

algebra
factor top and bottom = (x-6)(x+5)/( (x-5)(x+5) ) = (x-6)/(x-5) , x ≠ -5
October 27, 2014

maths
take a $1 investment 1 + 1(5)r = 8/5 5r = 8/5 - 1 = 3/5 r = 3/25 or .12 or 12%
October 27, 2014

Calculus: need clarification to where the #'s go
looks like you defined d to be the distance of the point from the origin y = 2(4x+4)^(1/2) y^2 = 4(4x+4) = 16x + 16 d = √(x^2+y^2) = ( x^2 + 16x + 16)^(1/2 dd/dt = (1/2)(x^2 + 16x + 16)^(-1/2) (2x + 16) dx/dt so when x = 3, y = 8 and dx/dt = 5 . Plug away dd/dt = (1/2) (...
October 27, 2014

Math
I will assume you have a typo and on the third day she sold 1/4 of what was left and 1/4 of a peach, or else it does not follow the pattern let x be the number of peaches at the start. number sold in 1st hour = x/2 + 1/2 = (x+1)/2 number left after 1 hour = x - (x+1)/2 = (2x...
October 26, 2014

Calculus
f(x) = sinx ---> f ' (x) = cosx g(x) = cosx ---> g ' (x) = -sinx so we want -sinx = cosx -sinx/cosx = 1 tanx = -1 I know tan 3π/4 = -1 and tan 7π/4 = -1 and the period of tanx is π since 3π/4 + π = 7π/4 we can just state that first ...
October 26, 2014

algebra
done, look back
October 26, 2014

Algebra
I think you placed some of those brackets in the wrong places, I am sure you meant f(x) = 1/(x-64) + 1/(x^2 - 64) + 1/(x^3 - 64) (the way you have them, they serve no purpose) remember we can't divide by zero, so x-64 ≠ 0 , ---- x ≠ 64 x^2 - 64 ≠ 0 ----&...
October 26, 2014

Calculus
let y1 = r dy1/dr = 1 let y2 = r^3 dy2/dr = 3r^2 when is dy2/dr = 12(dy1/dr) ? 3r^2 = 12(1) ? r^2 = 4 r = 2
October 26, 2014

Calculus
Let P(x,y) be any point on the parabola. According to the stated condition √( (x-8)^2 + (y-6)^2 ) - √( (x-5)^2 + (y-2)^2 ) = c, where c is that constant we could find c by plugging in (8,6) , a point on the parabola, but there is no need for it messy looking ...
October 26, 2014

Calculus
x^2 - xy + y^2 = 9 2x - x dy/dx - y + 2y dy/dx = 0 dy/dx(2y - x) = y - 2x dy/dx = (y-2x)/(2y-x) at x-intercept: y = 0 x^2 - 0 + 0 = 9 x = ± 3 when x = 3, dy/dx = (0-6)/(0-3) = 2 equation of tangent: y = 2(x-3) y = 2x - 6 when x = -3 , dy/dx = (0 + 6)/(0+3) = 2 equation ...
October 26, 2014

Calculus (math)
Let the radius of the water level be r let the height of the water level be h by ratios, r/h = 12/23 12h = 23r r = 12h/23 V = (1/3)πr^2 h = (1/3)π(144h^2/529)h = (48π/529) h^3 dV/dt = (144π/529) h^2 dh/dt for the given data: 20 = (144π/529)(144) dh/dt ...
October 25, 2014

Math
just one tiny step needed: divide by -3 s ≤ -6 (remember when multiplying or dividing by a negative number, the inequality sign must be reversed)
October 25, 2014

trig
You will have to know the co-function properties notice that the 6 trig names come as sine vs cosine tan vs cotan sec vs cosecant we need only the first two sinx = cos(90-x) tanx = cot(90-x) secondly we have to know tan(-x) = -tanx and sin(-x) = -sinx tan(-17°) + sin24°...
October 25, 2014

Math
#1 and #2: isolate the term you are solving for e.g. 4y + 6x = 12 ---> 4y = -6x + 12 now divide everybody by the coefficient of the term you isolated divide by 4 y = (-6/4)x + 12/4 y = (-3/2)x + 3 for #3, I would first multiply every term by 2, the LCM 2y = x - 20 2y + 20...
October 25, 2014

math
What Sal is basically showing you in the video is this: look at the repeating decimal places , there are 2 digits in the repeating loop so, let x = .151515... because we have 2 digits repeating, let's multiply the equation by 100 100x = 15,151515... notice the decimal part...
October 25, 2014

Math
your volume is correct f) well , we know the block of ice must be 12 inches high , and must be a square of 15 in by 15 inches
October 25, 2014

Pre-Calc/Trig
Try to factor it as Steve told you in a previous post along the same type of question What methods have you learned? A common method these days seems to be "decomposition" multiply the first and last coefficients: 6(-35) = -210 Now look for 2 factors which when ...
October 25, 2014

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

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