Tuesday
September 1, 2015

Posts by Reiny


Total # Posts: 30,694

Math
volume is dependent on the mass the volume of similar solids varies directly as the cube of their heights, so 16000/2000 = 30^3/h^3 8 = 27000/h^3 take cube root of both sides 2 = 30/h h = 15 ------> the height of the smaller is 15 m check: let the base of larger be x by x (...
May 19, 2015

Math Help
a^2 = 9 and b^2 = 16 so the major axis is the y-axis and the foci will lie on the y-axis c^2 + 9 = 16 c^2 = 7 c = ±√7 the foci are (0 , ± √7)
May 19, 2015

Math
take 1/2 of the x coefficient, then square that so 1/2 of √3 = √3/2 after squaring ---> 3/4 so x^2 + √3x + 3/4 is a perfect square the 2nd one is even easier, follow my steps
May 19, 2015

Calc 1
y^3 - x^2 = 2xy 3y^2 dy/dx - 2x = 2x dy/dx + 2y dy/dx(3y^2 - 2x) = 2y + 2x dy/dx = 2(x+y)/(3y^2 - 2x)
May 19, 2015

algebra
I am going off line for the afternoon. Hope somebody else picks up your questions. for this one, Hint: = (x-6)(x+3)/(x+3) = ...
May 19, 2015

algebra
#1 (x + 7)/(x^2 + 4x - 21) = (x+7)/((x+7)(x-3)) = 1/(x-3) , x ≠ -7, 3 you had 7, but that would make the denominator 14 , which is perfectly ok to divide by Hint: take the denomiator and solve it for zero. Whatever the solution, that x becomes the restricted value And ...
May 19, 2015

algebra
You should try the first one yourself These are usually done by factoring, as you can see in my other replies to your previous questions. For this one, look at the numerator of x+7 It has disappeared in all the choices of answers. That should give you a hint that it probably ...
May 19, 2015

algebra
Which other problems, you don't state your name identify the post by name and time posted
May 19, 2015

algebra
factor out 5w^5 from the top and then cancel it with the denominator 5w^5( -w^5 + 2w^3 + w)/(5w^5) = -w^5 + 2w^3 + w , w ≠ 0 (or else we divided by zero)
May 19, 2015

Geometry
Make it a point to memorize the ratios of sides for a 30-60-90 triangle The side opposite the 30° side is 1 the side opposite the 60° is √3 and the hypotenuse is 2 check: 1^2 + √3^2 = 2^2 so in yours: the side opposite the 30° is c the side opposite the...
May 19, 2015

College Algebra
You did not state the equation that you should use. Since you are not using metric units, I would have to look up the non-metric formula. I will let you do that.
May 19, 2015

algebra
use / to show division (x^2 + 6x + 9 )/(x-1) ÷ ((x+3)(x-3))/(x-1)^2 = (x+3)^2 /(x-1) * (x-1)^2/((x-3)(x+3)) = (x+3)(x-1)/(x-3) , x ≠ 1, ± 3
May 19, 2015

Calculus
Here is the sketch, the bottom diagram shows it best http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+%2B+1%2C+y+%3D+2x%5E2+-+2 We need their intersection: 2x^2 - 2 = x^2 + 1 x^2 = 3 x = ± √3 , y = 4 I will do it in two parts, 1. horizontal discs from y = -2 ...
May 19, 2015

algebra
factor the bottom ... = -14x^3/(x^3(1 - 5x)) now we can divide top and bottom by x^3 = -14/(1 - 5x) , where x ≠ 0
May 19, 2015

math
x+y = 5 , or y = 5-x xy = 5 x(5-x) = 5 x^2 - 5x + 5 = 0 x = (5 ± √5)/2 = appr 3.62 or 1.38 if x = appr 3.62 , y = 1.38 if x = 1.38 , then y = 3.62 the two number are 1.38 and 3.62 check: 1.38+3.62 = 5 (1.38)(3.62) = 4.9956 , pretty good with 2 decimal places of x ...
May 19, 2015

Math!!! Please help!!!
general term(r+1) = C(11,r) x^(11-r)(-3)^r so 11-r = 7 r = 4 term(5) = C(11,4) x^7 (-3)^4 = 26730 x^7 making the coefficient 26730 check with Wolfram http://www.wolframalpha.com/input/?i=%28x-3%29%5E11 (2y-3x)^5 = (2y)^5 + C(5,1)(2y)^4 (-3x) + C(5,2)(2y)^3 (-3x)^2 + C(5,3)(2y...
May 17, 2015

Math
No, 8 different girls can finish first, for each of those 7 can finish second and for each of those 6 can finish third, so 8*7*6 = 366
May 17, 2015

Calculus
Steve answered a similar question like this back in 2013 Just change the corresponding number to this problem http://www.jiskha.com/display.cgi?id=1386655263
May 17, 2015

Math
According to your wording, the area of the shaded circle is 36π ft^2 The small circle has an area of 4π ft^2 if you want the area of the shaded circle minus the smaller circle is would simply be 32π ft^2
May 17, 2015

math
Answered by Jai http://www.jiskha.com/display.cgi?id=1431875792
May 17, 2015

math
sum(15) = (15/2)(2a + 14d) = 1290 2a + 14d =172 sum(16) = (16/2)(2a + 15d) = 1464 2a + 15d = 183 subtract them: d = 11 sub into 2a + 14d = 172 2a + 154 = 172 2a = 18 a = 9 term(16) = a + 15d = 174 sum(20) = 10(2a + 19d) = 10(18+209) = 2270 BTW, we could have found term (16) by...
May 17, 2015

maths
Looks like both Jai and I both forgot an angle I left out 0 and Jai left out 2π Final answer: for -2π ≤ Ø ≤ 2π Ø = 0, ±π, ±2π
May 17, 2015

maths
2 cos(2Ø-π) = -2 cos (2Ø-π) = -1 2Ø-π = π 2Ø = 2π Ø = π the period of cos 2Ø = π , so adding/subtracting multiples of π will yield another answer so solutions for -2π ≤ Ø ≤...
May 17, 2015

Algebra
1st half speed --- x 2nd half speed -- 1.25x Since time = distance/rate time for 1st part = 150/x time for 2nd part = 150/1.25x total time = 150/x + 150/1.25x LCD = 1.25x total time = (150(1.25) + 150)/1.25x = 337.5/1.25x = 270/x
May 16, 2015

Algerbra please help
Unfortunately #4 is wrong too. Looks like some major review and studying lies ahead of you.
May 16, 2015

Algebra
good job, you are correct
May 16, 2015

Trig
you might want to say let cosØ = x, then x^2 + x - 1 = 0 x = (-1 ± √5)/2 = .618033 or -1.618.. cosØ = .618033 or cosØ = -1.6.. , which is not possible since -1 ≤ cosx ≤ 1 and since our domain is between 0° and 180°, we only...
May 16, 2015

algebra
time of first leg --- x hrs time of 2nd leg --- 7-x hrs solve for x, then sub into 7-x 40x + 55(7-x) = 295
May 16, 2015

calculus
s = 4t^3 + 6t + 2 ds/dt = v = 12t^2 + 6 when t = 1, v = 12(1^2) + 6 = 18 when t = 2, v = .... when t = 3 ....... when t = a , b = 12a^2 + 6
May 16, 2015

calculus
same as the one before
May 16, 2015

calculus
v(t) = dy/dt so find dy/dt, (that's a very easy one), then sub in t = 2
May 16, 2015

calculus
or f(x) = x^(-1/2) f ' (x) = (-1/2)x^(-3/2) = (-1/2) /√(x^3) sub in x = 4
May 16, 2015

Trig
Your 4 solutions are correct for the primary domain suppose we add the next 4, and we have 60, 120, 240, 300, 420, 480, 600, 660 notice that the 1st, the 3rd, the 5th, and the 7th, are obtained by adding consecutive multiples of 180°to 60° and the 2nd, 4th, 6th, and ...
May 16, 2015

Math
comparing it with the standard form x^2 /a^2 + y^2/b^ = 1 a^2 = 9 ----> a = 3 b^2 = 4 ---> b = 2 and with an ellipse with major axis along the x-axis: b^2 + c^2 = a^2 4 + c^2 = 9 c^2 = 5 c = √5
May 16, 2015

math
if y = 125 e^(8sin 2t) , then dy/dt = 125 e^(8sin 2t) (8cos 2t) (2) = 2000cos (2t) ( e^(8sin (2t)) )
May 16, 2015

Math natural logarithms
so you are solving, .55 = 1 - (7.5)^(1-y) 7.5^(1-y) = .45 take log of both sides, and use rules of logs (1-y)log 7.5 = log .45 1-y = log .45/log7.5 y = 1 - (log.45/log7.5) I got appr 1.3963
May 16, 2015

algebra
= (28/5) / (10/7) = (28/5)(7/10) = 196/50 = 98/25
May 15, 2015

Math
looking at the choices of answer I must conclude that you meant: logw (w^2/w^6) = logw w^2 - logw (w^6) = 2 logww/(6logww) = 2/6 = 1/3
May 15, 2015

Math
so a^2 = 9 ---> a = 3 b^2 = 4 ---> b = 2 for a horizontal ellipse like the given, b^2 + c^2 = a^2 4 + c^2 = 9 c^2 = 5 c = √5 e = c/a = √5/3 or appr .745
May 15, 2015

algebra
I = k(1/d^2) when I = 45, d = 5 45 = k/25 k =1125 so I = 1125/d^2 when d = 7 I = 1125/49 = appr 22.96
May 15, 2015

Math Check
The only one we actually have to work with is A let's complete the square: x^2+y^2-6x+8y-9=0 x^2 - 6x + ... + y^2 + 8y + ... = 9 x^2 - 6x + 9 + y^2 + 8y + 16 = 9+9+16 (x-3)^2 + (y+4)^2 = 34, so its radius is √34 my order from smallest to largest is D, C, B, A The ...
May 15, 2015

Math
take 1/2 of the x coefficient and square it, so (1/2)√3 = √3/2 square it ---> 3/4 Do the same with the 2nd
May 15, 2015

Algebra, please help
#2 is C, -3f^2 + 8f^2 = +5f^2 #4 debatable point here. Coefficient usually refers to the constant in front of a variable, so the last -3 does not have a variable, thus it is a constant I would say: 4,3 , which makes it B #6, the x term is -7x, so the coefficient is -7 which is...
May 15, 2015

math
I agree The wording of the question should have been: "What is the range of ages from the 2nd youngest to the oldest" to make it more clear.
May 15, 2015

math
Your question makes no sense to me. A linear function is a straight line. Tha't like asking, "What is the shape of a straight line?"
May 15, 2015

Math
original: Dakota --- x Ethan ----- x+8 after give-away: Dakota --- x + (1/4)(x+8) = (4x + x+8)/4 = (5x+8)/4 Ethan ---- (3/4)x = 3x/4 3x/4 : (5x+8)/4 = 5 : 7 3x : 5x+8 = 5/7 3x/(5x+8) = 5/7 25x+40 = 21x we will get a negative value of x, so this question is bogus, not possible
May 15, 2015

Caclulus
look at it as: f(x) = (sin(3x^2))^3 f ' (x) = 3(sin(3x^2))^2 cos(3x^2) (6x) = 18x sin^2 (3x^2) cos(3x^2) or = 9x sin(6x^2) cos(3x^2), using property sin 2A = 2sinAcosA
May 15, 2015

algebra
let the distance be x miles time for first leg = x/176 time for return leg = x/308 solve for x: x/176 + x/308 = 5 multiply by 1232 , the LCM 7x + 4x = 6160 x = 560 miles
May 14, 2015

math
1 C 2 B 3 D looks like you were just wildly guessing
May 14, 2015

Math
Why is this confusing? Make a table, showing C(hildren), A(dults), T(otal) C A T 6 0 $18.00 5 1 $20.00 4 2 $22.00 3 3 $24.00 2 4 $26.00 1 5 $28.00 0 6 $30.00 How many different amounts do you see ?
May 14, 2015

maths
Jean --- x Bob ---- 3x Paul ---- 6x x+3x+6x = 5590 take over
May 14, 2015

Calculus
take derivative first e^x - 3x^2 + 2y dy/dx = 0 dy/dx = (3x^2 - e^x)/2y at (0,3) dy/dx = (0 - 1)/6 = -1/6 so the slope of the tangent at the given point is -1/6 thus the slope of the normal at that point is +6
May 14, 2015

Math
g ' (x) = ln5 (5^x) g ' (2) = ln5 (5^2) = 25 ln 5
May 14, 2015

Math
Sami ... 3 ?? (1/40)(120) = 30 (whatever units "to a" are) Once you establish what those units were with the 120, convert 30 of whatever those are to pounds
May 14, 2015

math
I will assume that the sprinkler is a circular one, although some like the sweeping kind, are not. area of rectangle = 30x40 or 1200 ft^2 the area covered by the sprinkler is 1/4 of a circle with radius 26 area of watered lawn = (1/4)π(26)^ = 169π so area not covered...
May 14, 2015

my bad - Math
OF COURSE!! got my a's and b's reversed. I should have said: a^2 = 144 and b^2 = 25 giving a = ±12 and b = ±5 so I would go up 5 and down 5 from the centre so (-6,5) and (-6,-5) the same would be true for the co-vertices, should be (6,0) and (-18,0) http...
May 14, 2015

Math
standard notation: (x+6)^2/144 - y^2/25 = -1 so the hyperbola is vertical and its centre is (-6,0) a^2 = 25 and b^2 = 144 a = ±5 and b = ± 12 vertices are 12 up and 12 down from (-6,0) which is (-6,12) and (-6,-12) If I recall the co-vertices, although not points...
May 14, 2015

Math
I helped you in detail with your other hyperbola using the properties of the curve. What have you done so far for this one? Where did you run into difficulties?
May 14, 2015

correction - Math
oops, messed up in the last few lines the end should be: a^2 = 9 then b^2 = 4a^2 /9 = 36/9 = 4 (x-2)^2 /9 - (y+2)^2/4 = 1 is the equation
May 14, 2015

Math
I assume you want the equation of a hyperbola so we know: (x-2)^2 /a^2 - (y+2)^2 /b^2 = 1 for point(2+3√2,0) (3√2)^2 /a^2 - 2^2 /b^2 = 1 18/a^2 - 4/b^2 = 1 18b^2 - 4a^2 = a^2 b^2 for point(2+3√10,4) (3√10)^2 /a^2 - 6^2/ b^2 = 1 90b^2 - 36a^2 = a^2b^2 so...
May 14, 2015

MATH PLEASE HELP THIS IS A TEST!!!!!!!!!!!!!!!!
It would help if you numbered your questions. 1. your last choice is dependent , thus NOT independent D 2. prob(heads and 3) = (1/2)(1/6) = 1/12 D 3. prob = 1/4, so of 36 cases, we can expect 9 C 4. prob(4door) = .56, so of 300 asked we expect 168 B 5. Prob(defective) = 7/50 ...
May 14, 2015

Geometry
no idea Is there some kind of relationship between these angles?
May 14, 2015

MATH PLEASE HELP
1. there are 5 numbers other than 6 prob(getting one of those) = 5/6 your choice is wrong 2. there are 3 numbers less than 4, 1,2, or 3 prob(a number less than 4) = 3/6 = 1/2 your choice is wrong 3. rolling a 2 or 3 happened 80 times prob(of the stated event) = 80/360 = 2/9...
May 14, 2015

math
I will interpret "northward 59° " as N31°E Since the two distances are the same, we have an isosceles triangle and the angles at A and C would each be 29.5° let x = (1/2)AC ----< AC = 2x cos 29.5 = x/60 x = 60cos29.5 = 52.22.. so AC = appr 104.44 miles...
May 14, 2015

triginometry
how about sin 57°29' = h/9 ?
May 14, 2015

Math1210
let the width be y m and each of the lengths x m so 2x + 2y = 300 x + y = 150 y = 150-x cost = 50(2x+y+ = 50(2x + 150-x) = 50x + 7500 then 50x + 7500 = 12000 50x = 4500 x = 90 y = 150-90 = 60 the field is 60 m by 90 m
May 14, 2015

maths
any square contains at least a PAIR of equal factors e.g 1600 = 5x5 x 8x8 so ... 103875 = 25x4155 = 25 x 5 x 831 = 25 x 5 x 3 x 277 , and 277 is prime so to make pairs, we need a 5, a 3, and a 277 5(3)(277) = 4155 so if 103875 is multiplied by 4155 the result is a perfect ...
May 14, 2015

geometry
Your question makes no sense. To me congruent circles would be circles that have the same radius. What do you mean by "one has a lenght of 8ft" Is that supposed to be the circumference ? If the second has a "length" of 4 ft, then it must be smaller, ...
May 13, 2015

Math @Reiny
This must be re your previous post from above: centre is (2,0) c is from centre to focus or c = 2 2a = 8 a = 4 you should know that for a horizontal ellipse, a^2 = b^2 + c^2 16 = b^2 + 4 b^2 = 12 (x-2)^2 /16 + y^2 /12 = 1
May 13, 2015

math
let the base be x by x after cut out, base is (x-3) by (x-3) and the height is 3 3(x-6)(x-6) = 243 (x-6)^2 = 81 x-6 = ±9 x = 15 or x is a negative which would make no sense so the base was 15 by 15 inches check: after cutting out 3 inches from each end, the base is 9 by...
May 13, 2015

Algebra 2 Honors
you did your first 3 questions by using ratios. This is fine as long as you know where to put the numbers. since you appear to understand that direct variation ---> y = kx inverse variation ---> y = k/x perhaps that is the approach you might take at the beginning. 1. It ...
May 13, 2015

Math
since the change is in only one of the dimensions, the change of the volume must be linear. height was tripled, so the volume is doubled or new volume is 54 in^3 or old volume = 3(l)(w) = 3lw = 27 lw = 9 new volume = 6(l)(w) = 6lw = 6(9) = 54
May 13, 2015

Math
tomatoes: (1/4)(12) = 3 remainder = 9 pears = (1/3)(9) = 3 remainder = 6 radishes = (1/2) of 6 = 3 leaving 3 for the lettuce so 3 ft^2 of radishes
May 13, 2015

algebra - please help!
P(1 - (1 + .08/4)^-20)/(.08/4) = 2400 P(1 - 1.02^-20)/.02 = 2400 P = 146.78
May 13, 2015

Math
correct
May 13, 2015

Math
Not enough information for 1. all we know is that the centre is (2,0) and c = 2 (x-2)^2 /a^2 + y^2 / b^2 = 1 where a^2 = b^2 + 4 2. centre is (0,1) , a = 2 , c = 3 in a hyperbola: a^2 + b^2 = c^2 4 + b^2 = 9 b^2 = 5 x^2 /4 - (y-1)^2 /5 = 1
May 13, 2015

Math Check
a^2 = 3 , b^2 = 4 a = √3 , b = 2 so you have a vertical major axis, thus the x's must be the same , eliminating A and C y^2 + √3 ^2 = 2^2 y^2 = 4 - 3 = 1 y = ± 1 so the centre is (2,2) moving one up and one down from there gives us (2,3) and (2,1) e = c/...
May 13, 2015

math help please
no on both counts x^9/x^2 = x^9 ÷ x^2 to divide powers with the same base, keep the base and subtract the exponents, so x^7 #2, h^9
May 13, 2015

Please help
Yes, the combination of alliances and counter-alliances as well as the national pride, ignorance and arrogance of the leaders of Germany, Britain, France, Austria-Hungary, and Russia were the primary cause of World War I Just finished an excellent book: The War That Ended ...
May 13, 2015

Math
-tanØ = √3 tanØ = -√3 , so Ø is in II or IV first primary answer = 120° 2nd primary answer = 300° , notice the difference between them is 180° and the tangent curve has a period of 180° so we can get away with a single general ...
May 13, 2015

Math Ms.Sue???
You will need the slant height s , the hypotenuse s^2 = 4^2 + 6^2 = √52 surface area = πrs + (πr^2) , using the formula on Ms Sue's page = 4√52π + 16π You didn't state if the circular base is to be included, so .... your choice.
May 13, 2015

math help please
The area of a rectangle = length x width = 8x(7x+1) expand to see which matches btw, it is a rectangle not an angel
May 13, 2015

Geometry/Math
volume of 1st = π(36)(12) = 432π volume of 2nd = π(64)h 64π h = 432π h = 432π/(64π) = 27/4
May 13, 2015

Math
Your answers are correct. Be careful with brackets on a site such as this. e.g. in #1 you will have to type it as (x+5)/(x^2 + 6x + 5) and your answer is 1/(x+1), x ≠ -1 As to the x ≠ ?? the concern is the denominator, e.g. in #1, we have x+1 as a denominator. What...
May 13, 2015

MATH I NEED HELP
let the number of deer be x (16/800)x = 120 (1/5)x = 120 x = 5(120) = 6000 or use a ratio: 16/800 = 120/x 1/5 = 120/x x = 5(120) x = 6000
May 13, 2015

Geometry
I will assume you meant (20+x)/x = 6/5 (those brackets are essential) now cross-multiply ... 6x = 100 + 5x x = 100
May 13, 2015

Math
3 consecutive questions dealing with varied topics. Are you expecting us to do an assignment for you? What are your difficulties, and what steps have you to show me ?
May 13, 2015

Math
I suggest you graph on the same grid 1. y = x+1 , which is a very simple straight line 2. y = cosx , which is the basic standard cosine curve and see what happens
May 13, 2015

math
This is the same style of question I just answered for you in the previous post. Just follow the same steps.
May 13, 2015

math
Volume of well = π r^2 h = π(3.5)^2 (40) = 490π cubic metres let the height of the plateform be h 28(22)h = 490π h = 490π/616 = 35π/44 metres or appr 2.5 m
May 13, 2015

Math
general term = term(r+1) =C(10,r) (x^2)^(10-r) (1/x)^r = C(10,r) x^(20 - 2r) x^(-r) = C(10,r) x^(20 -3r) so 20 -3r = 11 -3r = -9 r = 3 C(10,3) = 120 the term containing x^11 is 120x^11 and it is the 4th term confirmation by Wolfram: http://www.wolframalpha.com/input/?i=expand...
May 13, 2015

Math
I answered this http://www.jiskha.com/display.cgi?id=1431486984
May 12, 2015

geometry
it is called the hypotenuse (you give no values or variables, so who knows ?)
May 12, 2015

Math
sinØ = -2/13 and we are told Ø is in III so y = -2, r = 13 x^2 + y^2 = r^2 x^2 + 4 = 169 x= ±√165 , but in III x = -√165 cosØ = -√165/13 cos 2Ø = cos^2 Ø - sin^2 Ø = 165/169 - 4/169 = 161/169
May 12, 2015

Geomerty
The mystery remains unsolved with only one bit of information about the triangle.
May 12, 2015

Math
Expand it That would be your other version
May 12, 2015

Math
Let the positive square number be x 2x^2 + 3x = 14 solve for x: 2x^2 + 3x - 14 = 0 hint: it factors, remember to reject the negative answer.
May 12, 2015

Pre-Algebra
1. how did you get 24 ? f(x) = x^2 - 3x + 2 f(-2) = (-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12 2. E = 12m 3. correct 4. y = 1.15 + .95(x-1)
May 12, 2015

math
If you plot the points you will get a rectangle of length 6 and height of 4 so the perimeter is 12 + 8 or 20 units take over
May 12, 2015

Math
recall the difference of squares: a^2 - b^2 = (a+b)(a-b) this has the same pattern (x+y)^2-(x-y)^2 = (x+y + x-y)(x+y - (x-y)) = 2x(2y) = 4xy or you could just expand the original ... (x+y)^2-(x-y)^2 = x^2 + 2xy + y^2 - (x^2 - 2xy + y^2) = 4xy
May 12, 2015

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