Saturday
December 20, 2014

Posts by Reiny


Total # Posts: 28,259

Calculs I
y(t) = a e^(kt) , where a is the intitial count, and k is a constant, and t is in minutes You have two ordered pairs, (15,16000) and (45,22000) for (15,16000) 16000 = a e(15k) for (45,22000) 22000 = a e^(45k) divide the 2nd by the 1st 1.375 =e^(30k) ln both sides , that is : (...
November 2, 2014

Calculus
k(t)=(t^2-4)^2 = (t^2 - 4)(t^2 - 4) now do as instructed
November 2, 2014

Calculus
let the time after their split be t hrs I see a triangle with sides 10t and 6t and an angle of 120° between them let the distance between them be d miles by the cosine law: d^2 = (6t)^2 + (10t)^2 - 2(6t)(10t)cos120° = 136t^2 + 60t^2 d2 = 196t^2 d = 14t dd/dt = 14 mph...
November 2, 2014

Calculus
2x dx/dt + x dy/dt + y dx/dt + 2y dy/dt = 0 (dy/dt)(x + 2y) = -2x dx/dt - y dx/dt dy/dt(2 + 6) = -4(3) - 3(3) dy/dt = -21/8 the ant is moving DOWN at 21/8 cm/s
November 2, 2014

Calculus
C = 2πr dC/dt = 2π dr/dt A = πr^2 dr/dt dA = 2πr dr/dt you have the values to plug in for both rates.
November 2, 2014

Calculus
dV/dt = πr^2 dh/dt + 2πrh dr/dt plug in the given values SA = 2πrh , are you not considering the ends ? differentiate with respect to t using the product rule like I did for the volume, then plug in the values
November 2, 2014

Calculus
let the length be x inches let the width by y inches A = xy dA/dt = x dy/dt + y dx/dt for the given data... dA/dt = 24(-3) + 15(4) = -12 inches^2/min the area is decreasing at 12 square inches/min P = 2x + 2y dP/dt = 2 dx/dt + 2 dy/dt = 2(-3) + 2(4) = 2 inches/min
November 2, 2014

Math
i = .049/12 = .00408333... n= 15(12) = 180 amount = 10000(1.00408333..)^180 = $ 20,823.63
November 2, 2014

Algebra
notice that for every increase of 1 in the x, the y increases by 2 so slope = 2 or, more formally, take the fist two points (1,1) and (2,3) slope = (3-1)/(2-1) = 2 so y = 2x + b sub in the first point (1,1) 1 = 2(1) + b b = -1 y = 2x - 1 check the remaining points to make they...
November 1, 2014

Algebra
I assume you want it 'simplified' and that you forgot the brackets (8-6i)/(3i) = (8-6i)/(3i) * i/i = (8i - 6i^2)/(3i^2) = (6 + 8i)/-3 or =( -6 - 8i)/3 hint for the second... multiply top and bottom by (4-2i)/(4-2i)
November 1, 2014

Math
simply solve ... .07x + .15(x+1500) = 1545 where x is the amount invested at 7%
November 1, 2014

Maths
Please type your question in proper English. "d" is the common variable for the difference between consecutive terms of an AP and not as a substitute for "the".
November 1, 2014

math
Finding the distance between 2 points and finding the midpoint between 2 points should be part of your repertoire of common and memory-recall-ready formulas if you want to study math for (a,b) and (c,d) Distance = √( (c-a)^2 + (d-b)^2 ) midpoint = ( (a+c)/2 , (b+d)/2 ) ...
November 1, 2014

Algebra
so a#b =(a+b)/2 then ((1#2)#2)#4 = (1.5#2)#4 = 1.75#4 = 2.875 or = 23/8 or ((1#2)#2)#4 = (3/2#2)#4 = (7/4)#4 = 23/8
November 1, 2014

Algebra
P(g(x)) = p(4-3x) = 4 + 2√(4 - 3x + 2) = 4 + 2√(6-3x) remember we cannot take the square root of a negative, so 6-3x≥0 -3x ≥ -6 x ≤ 2 so the largest value of a is 2
November 1, 2014

MATHS
I will need 2 zeros (0 can't be in front) 3 ones 3 twos 3 fours ... 3 sevens 2 eights 2 nines total = 29 for b) we can save the 2 nines, (the 3 sixes will suffice) so they can save 2 cards
November 1, 2014

Maths
Prob(m) = 1/5 prob(S) = 4/5 Possible outcomes in best of three" MM --- (1/5)(1/5) = 1/25 MSM -- ((1/5)(4/5)(1/5) = 4/125 SMM -- ((4/5)(1/5)(1/5) = 4/125 SS ---- (4/5)(4/5) = 16/25 ----> Sue wins SMS -- (4/5)(1/5)(4/5) = 16/125 ----> Sue wins MSS -- ((1/5)(4/5)(4/5...
November 1, 2014

Algebra
πr^2 = 2πr r^2 - 2r = 0 r(r-2) = 0 r = 0 , the trivial answer or r = 2 So the diameter is 4 a/b = 2/3 or 2b = 3a, or b = 3a/2 (a+5)/b = 5/6 5b = 6a + 30 5(3a/2) = 6a + 30 times 2 15a = 12a + 60 a = 20 and b = 3(20)/2 = 30 the fraction was 20/30 y < √x by 4 y...
October 31, 2014

Math
factor is 10^8.8/10^7.1 = 10^1.7 = appr 50 times as strong
October 31, 2014

Math
number of quarters ---- x " he has one more dime than he has quarters" ---> dimes ---- x+1 now for the "value" of coins equation: 25x + 10(x+1) = 115 25x + 10x + 10 = 115 35x = 105 x = 3 etc
October 31, 2014

Width of a square
How can 45/10 = 3.5 ?? 45/10 = 4.5
October 31, 2014

math
You are looking for those values of x, so that y = (x+5)/(x-2) lies above the x-axis first of all, x ≠ 2 or else we are dividing by zero critical values are -5 and 2 investigate x < -5, say x = -10 then y = -/- = + , that's good investigate between -5 and 2, say x...
October 31, 2014

maths
I will assume you meant: 1/( (x+2)(x+3) ) - 1/( (x-4)(x-5) ) what about it? are you simplifying?
October 31, 2014

Math, Can someone check my answers?
all 3 are correct
October 31, 2014

Thanks Steve - Pre Calculous
for keeping an eye on me. I just have to read more carefully, I read it as sinx = 1/4
October 31, 2014

Pre Calculous
my keystrokes on my calculator: 2nd sin .25 = to get 14.478° but the sine is positive in I and II so x could also be 180 - 14.478 = 165.522° there are an infinite number of solutions, just add/subtract 360° to any existing answer to produce more.
October 31, 2014

Math Calc
divide by 7 sinØ = 6/7 Ø = arcsin (6/7) = appr 58.997° Did you use a calculator? my keystrokes: 6 ÷ 7 = 2nd sin = to get my answer
October 31, 2014

Math Arc Length
circumf = 2πr = 2π(4.9) = 9.8π so 360° of arc = 9.8π units and 1° of arc length = 9.8π/360 = 49π/1800 units Maybe they didn't like your decimal, but your answer is correct
October 31, 2014

Calculus
dy/dx = 4x + 5 dy = (4x + 5)dx so for your given data dy= (20+5)(.1) = 2.5 so the other one the same way
October 31, 2014

math
amount poured into canister --- x g amount in canister = 5026 + x amount left in bag = 4157-x g 5026+x = 2(4157-x) 5026 + x = 8314 -2x 3x = 3288 x = 1096 amount left in bag = 4157-1096 = 3061 g
October 31, 2014

trigonometry
LS = sinx(cos2x) + cosx(sin 2x) RS = sin(3x) = sin(2x + x) = (sin 2x)cosx + (cos 2x) sinx = LS I am using sin(A+B) = sinAcosB + cosAsinB
October 31, 2014

Math Please Check
you have found the variables which will yield the maximum and minimum , but you have not found the actual max or min When t = 0 (you had x = 0) h(0) = 0-0 = 0 when t = 2, h(2) = 8 - 12 = -4 also h(-1) = -1 - 3 = -4 so you have a local max at (0,0) and a local min at (2,-4) for...
October 30, 2014

business maths
I have no idea what your equation is supposed to say or do. Since you are talking about a "focal date", I will assume you have learned to make a time line. label it "now" or 0, 1,2,3 months I place the debt above the line , and the payments below the line, ...
October 30, 2014

geometry
not enough data all we know is that the total area of pool plus walkway is 72 units^2 so 9x8=72 , perimeter = 34 6x12 = 72 , perimeter = 36 4x18 , perimeter = 44 etc
October 30, 2014

pre-algebra
so the area of each of the smaller squares = 100/25 = 4 ft^2 so each side of the smaller square must be 2 ft
October 30, 2014

can't figure it out
Bob, looks like you missed that silly little negative sign in front of the 5 too, just like I did when I answered this question the first time for Ernie, John, and now Charlie . One would assume that he would check back to his previous post before posting the same question ...
October 30, 2014

Math 11
So you have a tetrahedron area of one of the triangles = (1/2)(16)(16)sin60 = 128(√3/2) = 64√3 Counting the base there are 4 faces, so surface area = 4(64√3) = 256√3 = appr 443.4 cm^2 If you don't want to count the base, multiply by 3 instead of by 4
October 30, 2014

Math
A two-term ratio can not be equal to a constant looks like a typo
October 30, 2014

math really need help!
done, look back
October 30, 2014

oops math please help
didn't notice that little - in front of the 5 f(x+2) = -5(x+2) + 6 you finish it this time
October 30, 2014

math please help
replace the x with x+2 f(x+2 = 5(x+2) + 6 = 5x + 16
October 30, 2014

Math-urgent-
huh? how many times are we to subtract ? on the other hand ... 11/12 ÷ 3/4 = (11/12)(4/3) = 44/36 = 11/9
October 30, 2014

algebra
times 2 14 + 6t = 6 - t 7t = -8 t = -8/7
October 30, 2014

Math
should have been y-1 = (1/4)(x-1) y = (1/4)x - 1/4 + 1 = (1/4)x + 3/4
October 30, 2014

Algebra
ahhh, your slope is not zero look at your 3/0 we CAN'T divide by zero , 3/0 is undefined If you look at your sketch , your line will be a vertical line Anytime you have a vertical line, your slope will be undefined and the equation will simply be x = some constant look at ...
October 30, 2014

math
c + 2s = 10.30 3c + 2s = 18 subtract them 2c = 7.7 c = 3.85 sub back into the first equation to get 3.85 + 2s = 10.3 2s = 6.45 s = 3.23 so c + s = 7.08
October 30, 2014

Equation ratio
if 5x = 4.5y then y/x = 5/4.5 = 10/9 y : x = 10 : 9
October 30, 2014

Math
7/3 = rear/2 3rear = 14 rear = 14/3 or 4 2/3 turns or 3 pedal turns = 7 rears 1 pedal turn = 7/3 rears 2 pedal turns = 14/3 rears
October 29, 2014

Math
yes (4/3)π r^3 = 1767.1 r^3 = 21.864.. r = 7.4999 or appr 7.5 m check: (4/3)π(7.5)^3 =1767.145..
October 29, 2014

Math
The least common multiply (LCM) of 12 and 20 is 60 So to make 60 burgers, we need 60/12 or 5 patty packages, and 60/20 or 3 bun packages.
October 29, 2014

Math
According to your equation, the object was 125 m above ground (t=0) , when it was shot solve for h = 0 , this will give you the two times it is on the ground -5t^2 + 120t + 125 = 0 divide by -5 t^2 - 24t - 25 = 0 (t-25)(t+1) = 0 t = -1 or t = 25 but, this only makes sense for ...
October 29, 2014

Trigonometry
2cosxcsc2x = cscx LS = 2cosx(1/sin 2x) = 2cosx(1/(2sinxcosx) = 1/sinx = csc x = RS sin^2 2x = 4 sin^2 x cos^2 x will use the same identity as in the first one: namely, sin 2x = 2sinxcosx LS = sin^2 2x = (sin 2x)(sin 2x) = (2sinxcosx)(2sinxcosx) = 4 sin^2 x cos^2 x = RS cot 2&...
October 29, 2014

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

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