Tuesday
July 7, 2015

Posts by Reiny


Total # Posts: 30,338

Math
Since you want the distance horizontally from the starting point, you want y to be 4.3m which is the initial height, thus 0 = -.04x^2 + 8.3x x(.04x - 8.3) = 0 x = 0 , which would be our starting point and x = 8.3/.04 or 207.5 m your answer would be the distance from a height ...
May 25, 2015

Math
the t of the vertex is -b/(2a) = -92/-10 = 9.2 you had that sub in t = 9/2, h = 439.2 you were right, good job
May 25, 2015

Math
we know r^2 = x^2 + y^2 and sinØ = y/r so we have x^2 + y^2 = 1 + y/r x^2 + y^2 = 1 + y/√(x^2+y^2) I don't know to what level you want to simplify this, I will leave it up to you
May 25, 2015

trigonometry
cosØ = 9/10 Ø = appr 25.8°
May 24, 2015

math
I disagree with marks answer The crust can be chosen in C(3,1) ways or 3 ways the cheese can be chosen in C(3,1) or 3 ways if you want only one cheese But the 3 toppings can be chosen in C(7,3) or 35 ways So the number of possible pizzas with 3 toppings and 1 cheese with 3 ...
May 24, 2015

Calculus
let the base be x by x ft and the height be h ft Volume = x^2h 32 = x^2 h h = 32/x^2 SA = x^2 + 4xh = x^2 + 4x(32/x^2) = x^2 + 128/x d(SA)/dx = 2x - 128/x^2 = 0 for a max/min of SA 2x = 128/x^2 2x^3= 128 x^3 = 64 x = 4 then h = 32/16 = 2 so the box should have a base of 4ft by...
May 24, 2015

Math
correct
May 24, 2015

Combinatorics
The lowest sum will be 19 , (all 1's) the largest sum will be 114 (all 6's) each number between them will be possible, so the total number of sums = 114-19 + 1 = 96
May 24, 2015

Math
So let's cut out an x by x square from each corner. so the base we would be left with would be an (20-2x) by (20-2x) cm but 20-2x > 0 -2x > -20 x < 10, since you want x to be a natural number, that would be a 9 by 9 cm square
May 24, 2015

maths
btw, this is true not just for the median AM In fact, the same steps can be used to prove it true if M is any point on BC.
May 23, 2015

maths
In any triangle, the sum of any two sides > the third side so in triangle ABM: AB + BM > AM in triangle ACM AC + MC > AM adding: AB + AC + BM+MC > 2AM AB + AC + BC >2AM
May 23, 2015

correction - Algebra
Anon has it wrong 9^12 ÷9^3 = 9^9 , which is rather large To divide powers with the same base, keep the base and subtract the exponents.
May 22, 2015

math
amount = 1040(1.12)^6 = 2052.78 interest on the initial principal = 2052.78 - 1040 = 1012.78
May 22, 2015

geomotry
If angle C had been 60°, then we would have an equilateral triangle and all sides would have been equal. But, since angle C > 62, the side opposite C must be the greatest. (the largest side is opposite the largest angle)
May 22, 2015

maths
Please use proper English in your posts. This is an arrangement, so number = 15x14x13 = 2730
May 22, 2015

math
It specified "completing the square", so v(x) = 25x^2 - 750x + 10000 , you had v(t) but no t showed up in your function. = 25(x^2 - 30x) + 10000 = 25(x^2 - 30x + 225 - 225) + 10000 = 25( (x-15)^2 - 225) + 10000 = 25(x-15)^2 - 5625+10000 = 25(x-15)^2 + 4375 lowest ...
May 22, 2015

algebra
I believe the physics formula for comparisons of sound intensity in decibels is 10^(112/10) / 10^(118/10) = 10^11.2 / 10^11.8 = 10^-.6 = .2511... or appr 1/4 of the intensity
May 22, 2015

Calculus math
btw, these were not quadratics I find it strange that a person taking Calculus would not know how to solve two linear equations with two unknowns.
May 21, 2015

Calculus math
Step #1 is to replace c with 10000 in both equations to get 9a + 3b = -2025 ---> 3a + b = -675 36a + 6b = -3600 --> 6a + b = -600 subtract the two equations: 3a = 75 a = 25 plug that into 3a + b = -675 75 + b = -675 b = -750 check: 9(25) + 3(-750) + 10000 = 7975 check! ...
May 21, 2015

Algebra
since (2,1) lies on it 2A + B = 7 or B = 7 - 2a slope of 2x-7=3 is 2/7 slope of Ax + By = 7 is -A/B so -A/B = 2/7 2B = -7A 2(7-2A) = -7A 14 - 4A = -7A 3A = -14 A = -14/3 B = 7-2(-14/3) = 49/3 B - A = 49/3 - (-14/3) = 21
May 21, 2015

Calculus
a) is the correct choice
May 21, 2015

trigonometry
I have a triangle with sides 1000 and 1200 with an angle of 130° between them. Clearly a cosine law problem d^2 = 1000^2 + 1200^2 - 2(1000)(1200) cos 130° = ... d = √... = let me know what you get.
May 21, 2015

math
Did you mean the effective annual interest rate ? if so, then (1+i) = (1.02)^4 1+i = 1.0824.. i = .0824 or appr 8.24% per annum
May 21, 2015

Math
A quick sketch shows that your base is 25 units and the height is 7 units area = (1/2)(25)(7) = 87.5 units^2 or 87.5 m^2
May 21, 2015

Math
Damon did this yesterday in the first of the "Related Questions" below.
May 21, 2015

Maths
let's define everything in terms of the number of 10 cent coins, and then just translate the English into Math. let the number of 10 cent coins be x "The number of 20-cent pieces is twice the number of 10-cent pieces" --> number of 20 cent pieces = 2x "...
May 21, 2015

school
time to fill with smaller pipe --- x minutes rate of smaller pipe = 1/x units/min time to fill with larger pipe --- x-10 minutes rate of larger pipe = 1/(x-10) units/min combined rate = 1/x + 1/(x-10) = (x-10 + x)/(x(x-10)) = (2x-10)/(x^2 - 10x) 1/[ (2x-10)/(x^2 - 10x)] = 12 (...
May 21, 2015

Maths
I was only on my second cup of coffee when I did this .... equation should have been x/4 + (25-x)/12 = 3.75 multiply by 12 3x + (25-x) = 45 3x + 25 - x = 45 2x = 20 x = 10 So she walked 10 km by linear equations: let the distance walked be x let the distance biked by y x + y...
May 21, 2015

Maths
distance walked --- x km distance biked ----- 25-x km 4x + 12(25-x) = 3.75 solve for x
May 21, 2015

Math Please Help
Recall that cosØ = x/r but we are given that x = cosØ then y = cos^2 Ø + 8cosØ y = x^2 + 8x
May 20, 2015

Math
Right now, rise/run = 9/156 so tanØ = 9/156 Ø = 3.302° So she wants the angle to be 6.604° Then, assuming the rise will remain the same, tan 6.604° = 9/length length = 9/tan6.604 = 77.7 inches or 78 inches
May 20, 2015

Trig
So we know Ø is in quad III , where both sine and cosine are negative given : cosØ = -12/13 and recognizing the 5,12,13 right-angled triangle we know that sinØ = -5/13 sin 2Ø = 2sinØcosØ = 2(-5/13)(-12/13) = 120/169 cos 2Ø = cos...
May 20, 2015

math
what is (17/4)^3 ??
May 20, 2015

Trig
sinØ = √(1 - (-5/13)^2) = .923 which is none of the choices or sketch a triangle in the 2nd quad, x = -5 r = 13 x^2 + y^2 = r^2 25 + y^2 = 169 y^2 = 144 y = ± 12, but in quad II , y +12 so sinØ = 12/13 or appr .923 (same as above) your choices: 1 and...
May 20, 2015

Algebra 2
looks like each side is 4/5 of its previous , so 20(4/5)^n = 8 (.8)^(n-1) = .4 using logs (n-1) log .8 = log .4 n - 1 = 4.1 n = 5.1 so the 5th would be less than 8 and the 6th would be greater than 8 e.g. 1st --- 20 2nd -- 16 3rd -- 12.8 4th -- 10.24 5th -- 8.192 6th -- 6.5536...
May 20, 2015

ALG 2
you are looking at a hyperbola with its major axis on the x-axis. a^2 = 16 , a = ± 4 b^2 = 25 , b = ± 5 so the vertices are (4,0) and (-4,0) foci: c^2 = 16+25 = 41 c = ± √41 so foci are (√41,0) and (-√41, 0) The asymptotes are y = (5/4)x ...
May 20, 2015

Math
1. clearly A , since 4^8 < 4^12 2. clearly C, since 3^6 > 3^5
May 20, 2015

math
kids tickets ---- x adult tix's ----- 2x solve for x: 20x + 35(2x) = 1890
May 20, 2015

algebra
for #2, Steve meant to say: (x-6)(x+3)/(x+3) = x-6 , x ≠ -3
May 20, 2015

Algebra 2
ok, that makes it easy √2/2 + √2 = √2( 1/2 + 1) = √2(3/2) = 3√2/2
May 20, 2015

Algebra 2
Don't know what you want done with "solve" We solve equations, but you don't have one. Did you mean "evaluate" ? Also , did you mean it the way you typed it, or did you mean √2/(2+√2) ? Back before we had calculators, it was often useful...
May 20, 2015

College Algebra
mmmhhh, didn't you post this same question this morning. I told you what the problem was, and you did nothing about it http://www.jiskha.com/display.cgi?id=1432046868
May 19, 2015

algebra
or slope = (y-4)/5 = 5 (y-4)/5 = 5 y-4 = 25 y = 29
May 19, 2015

Algebra
1. no, I see a constant 2. yes, which you had but your "reasoning" statement makes no sense did you mean to say, "because (0,0) satisfies the equation?
May 19, 2015

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

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