Tuesday
July 29, 2014

Posts by Reiny


Total # Posts: 26,903

Calc :(((((
first cross-multiply y + y x^2 = x dy/dx + y(2x) + 2x dy/dx = 1 dy/dx(1 + 2x) = 1 - 2xy dy/dx = (1-2xy)/(1+2x) at (4, 1/4) dy/dx = (1 - 2(4)(1/4))/(1 + 2(4)) = -1/9 equation of tangent: y = (-1/9)x + b at (4,1/4) 1/4 = (-1/9)(4) + b b = 5/9 equation is y = (-1/9)x + 5/9 slope ...

Calculus Help
dy/dx = 2ax + bx when x = 1, 2a + b = 6 when x = -1 -2a +b = -14 add them 2b = -8 b= -4, then a = 5 to find c, sub in (2,17) into the original: 17 = 4a + 2b + c 17 = 20 -8 + c c = 5 y = 5x^2 - 4x + 5 check: for (2,17) 17 = 20 - 8 + 5 ---> true dy/dx = 10x - 4 at x = 1, dy/d...

Algebra word problem
x^2 + 6x - 27 = (x+9)(x-3) So possible sides are x+9 and x-3 however, that would not be the only possibility. e.g. suppose one side is x-2 then the other side is (x^2 + 6x - 27)/(x-2) or ( x+8 - 11/(x-2) ) or with actual values suppose the area is 27 and one side is 3 then we ...

Probability
let N be a normal coin, and let DH be a double - headed coin let DT be double-tailed H -- heads, T --- tails for N, prob(H) = 1/2, prob(T) = 1/2 for DH, prob(H down) = 1, prob(Tdown) = 0 for DT, prob(H down) = 0, prob(Tdown) = 1 so you could draw N or DH or DT prob(heads down)...

Algebra
area of lot = (6x)(10x) = 60x^2 area of field = x(4x) = 4x^2 area left for bleachers = 60x^2 - 4x^2 = 56x^2

maths
we know tht sin (-Ø) = -sinØ so if sinA = 3/5 sin(-A) = -3/5 check: from the given, A = 143.13.. sin(-143.13..) = -.6

Trig
In my sketch I see a non-rightangled triangle with angles 42° , 110° and 28° with the side opposite the 42° as the guy wire by the sine law: x/sin42 = 25/sin28 x = 25sin42/sin28 = .....

Calculus Please help!
f(-3) = 54 + 18 + 9 + 2 = 83 f(-1) = -2 + 2 + 3 + 2 = 5 slope = (5-83)/(-1+3) = -39 f ' (x) = -6x^2 + 4x - 3 then -6x^2 + 4x - 3 = -39 6x^2 - 4x -36 = 0 3x^2 - 2x - 18 = 0 x = (2 ± √220)/6 = appr 2.8054 or appr -2.1388

Calculus...URGENT..show steps please
The "solving" becomes a bit easier if you change the original equation to (x-y)^2 - 6x + 2y + 17 = 0 sub in : y = x - 3 (x - (x-3))^2 - 6x + 2(x-3) + 17 = 0 9 - 6x + 2x - 6 + 17 = 0 -4x = -20 x = 5 then y = 2 the horizontal asymptote touches at (5,2) I will do the ve...

math
change in volume of tank = (5000)(4400)(21) cm^3 = 462,000,000 cm^3 = 462,000 L 15 km/hr = 1,500,000 cm/hr Volume moved = 1,500,000(49π) cm^3/hr time to fill 462,000,000 = 462,000,000/1,500,000 hrs = 308 hrs check my arithmetic

Algebra Question
Of course not! expand each of your factored expression. Notice that the middle terms are not the same

Math
part left = 1 - 3/8 - 1/3 = 24/24 - 9/24 - 8/24 = 7/24

Trig
absurd angles, check your typing. did you mean 70° instead of 700 ?

Math(check answer)
odds and probability are not quite the same odds in favour of some event = prob of that event : prob of NOT that event so ... prob of picking a green = 9/20 prob of not picking green = 11/20 odds in favour of picking a green = 9/20 : 11/20 = 9 : 11 which is D

MATH
radius after 24 hrs = 500(24) = 12000 m or 12 km area after 24 hrs = π(12)^2 = 144π square km radius after 48 hrs = 500(48) = 24000 m - 24 km area after 48 hrs = π(24^2) = 576 km^2 growth of spill between 24 hrs and 48 hrs = 432 km^2

Math
What is C(16,3) ?

Math
distance covered by faster driver --- x km distance covered by slower driver --- 320-x km The must have driven the same abount of time, so x/95 = (320 - x)/65 65x = 30400 - 95x 160x = 30400 x = 190 time = 190/95 = 2 hrs check: time of faster driver = 190/95 = 2 time of slower ...

Math
same old

Math
Are you reading my other replies to your questions with the same concept?

Math
A prime has no factors other than 1 and itself 5x^2 + x - 2 does not factor, so ....

Math
Using distance = rate x time 105t = 45(t+4) 105t = 45t + 180 60t = 180 t = 3 distance covered by each = 105(3) = 45(7) = 315 miles

Math
Very similar to the other I just answered for you. Difference in this one: the item is not replaced Prob = (6/20)(2/19) = 12/380 = 3/95

Math
oops , you wanted 3 decimals, 5.791 or 1.209

Math
use the formula x = (7 ± √21)/2 ---- > this is exact or appr, 5.79 or appr 1.21

Algebra
look at it as 2 ordered pairs (1/2 , 480) and (3/4 , 720) and find the linear equation slope = (720-480)/(3/4 - 1/2) = 240/(1/4) = 960 S = 960g + b , (using y = mx + b ) for (1/2, 480) 480 = 960(1/2) + b 480 = 480 + b b = 0 S = 960G (tells me 1 gallon covers 960 square feet)

Math
P(red, then blue) = (9/41(10/41) = 90/1681

Math
starting number --- x Anita's method 2x + x = 3x Amit: (x+x)(2) = 4x 4x - 3x = 9 x = 9 My algebra becomes the explanation. check: Anita ---> 2(9) + 9 = 27 Amit ---> (9+9)(2) = 36 difference = 36-27 = 9 all is good!

Correction - Math(Check answer)
Both are wrong Odds and probability are not the same thing you have found the prob(picking a vowel) Odds in favour of picking a vowel = prob of picking a vowel : prob of NOT picking a vowel = 3/7 : 4/7 = 3 : 4 the second question simply reverses the odds should be 4 : 3

Algebra
variance is defined as the square root of the standard deviation since variance is 4, sd = 16 go to http://davidmlane.com/hyperstat/z_table.html enter , 195 for the mean and 16 for sd click on below, and enter 190.2 to get .3821

Alg help
I had that too, hit the 4 instead of the 2, sorry.

Alg help
What is √(12^2 + 4^2 + 9^2) ?? I get √441 , which is not any of your choices.

math
what about it ?

algebra
amount invested at 5% --- x amount invested at 8% --- y x+y = 5000 (5/100)x + (8/100)y = 331 times 100 5x + 8y = 33100 first equation times 5 5x + 5y = 25000 subtract them: 3y = 8100 y = 2700 take over....

algebra
x+y = 30 x-y = 2 add them 2x = 32 x = 16 then, mentally, y = 14 check: 16+14 = 30 16-14 = 2 , yeahhh!

Differential Equations
".. by making many small deposits throughout the year. " I don't know what you mean by that. - how often are they made ? - are the payments the same ?

Algebra
volume = length x width x height = (2x+3)(x+2)(x-3) or, if it needs to be expanded .... = (2x+3)(x^2 - x - 6) = 2x^3 - 2x^2 - 12x + 3x^2 -3x - 18 = 2x^3 + x^2 - 15x -18

Math
600 g + 1 kg = 600 g + 1000 g = 1600 g = 1.6 kg

algebra (solve for y)
treat it like a quadratic equation ... let e^y = x then your equation becomes 0 = 2x^2 - x x(2x - 1) = 0 x = 0 or x = 1/2 then e^y = 0 -----> no solution or e^y = 1/2 take ln of both sides and use the rules of logs y lne = ln1 - ln2 y (1) = 0 - ln 2 y = -ln2 or e^y( 2e^y - ...

math
I will define x in a different way, the way you suggest introduces unnecessary complicated fractions. The the radius of the circle be r, let each side of the square be x 4x + 2πr = 24 2x + πr = 12 x = 6 - (π/2)r let A be the total area A = πr^2 + (6 - (`...

math
y = cosx tanx = cosx (sinx/cosx) y = sinx

Geometry
no, it is b SSA often results in 2 different triangles with the same properties, thus no congruency.

math
square: a quadrilateral with 4 equal sides, all angles 90° rhombus: a quadrilateral with 4 equal sides. A square is a rhombus, but a rhombus is not necessarily a square. http://www.mathsisfun.com/quadrilaterals.html

Algebra - Domain
I see a few problems here. 1. In the usual terminology, the word "function" implies the relationship between two variables, usually x and y, where the value of y depends on x. You have an equation that contains only one variable y (the "solution" to your eq...

Algebra
correct

math
By sheer coincidence this same question was posted on March3 , three years ago http://www.jiskha.com/display.cgi?id=1299163469

Algebra
ascending powers of b ----> the terms containing b with exponents from smallest to largest, so -7dm + 25 b^5 - 6 d b^6 + 3 b^10 your answer makes no sense, there were 4 terms, so you still have to have 4 terms.

Algebra
descending means from highest to lowest. just look at the exponents of p

Math
speed = distance /time speed ≥ 420/8 ≥ 52.5 mph

Geometry
Did you not read our objection to your problem. Why would you repost exactly the same way ? http://www.jiskha.com/display.cgi?id=1393701722 Steve gave you a solution according to one interpretation.

geometric progresions
sum of first 8 terms = a(r^8 - 1)/(r-1) sum of first 4 terms = a(r^4 - 1)/(r-1 ( a(r^8 - 1)/(r-1) ) / ( a(r^4 - 1)/(r-1) ) = 97/81 (r^8 - 1) / (r^4 - 1) = 97 / 81 81r^8 - 81 = 97r^4 - 97 81^8 - 97r^4 + 16 = 0 let r^4 = x 81x^2 - 97x+16 = 0 x = (97 ± √4225)/162 = (...

algebra
Will there be some kind of question ?

math(algebra)
Or you could say that each costs $1.99 with the first 4 costing a dollar more so .. y =1.99x + 4 that would be the simplest equation, Too bad they don't have it

Algebra 1--Please, help me!
show that slope AB = slope DC and slope AD = slope BC I will do the first pair, you do the second slope AB = (5-5)/6+2) = 0/8 = 0 slope DC = (-3+3)/(-4-4) = 0/-8 = 0 so AB || DC test if AD || BC if so, then by definition, it is a parallogram.

Geometry
Strange wording. How high is the lighthouse above the sea level ?

Algebra 1--Step-by-Step
3 and 4 are correct #2 14q^2 - 21q + 6 - 4q = 7q(2q - 3) + 2(3-2q) = 7q(2q-3) - 2(2q-3) = (2q-3)(7q-2)

Algebra 1--Step-by-Step
look at my answer ... (r-3)(2r-4) = (r-3)(2)(r-2) = 2(r-3)(r-2)

Algebra 1--Step-by-Step
Surely you could see that 2 was an additional common factor contained in my (2r-4) factor.

Algebra 1--Step-by-Step
1. 2r(r - 3) + 4(3 - r) , ahhh, did you notice that the brackets are opposite? , so .. = 2r(r-3) - 4(r - 3) = (r-3)(2r-4) Use the same "trick" on the others if you have to.

algebra
sub the first into the 2nd ... 3x - 18y = 4 3(6y+2) - 18y = 4 18y + 6 - 18y = 4 6 = 4 , which of course is nonsese, so .. there is no solution (You have two parallel lines)

algebra
number of people---- x cost = 20x + 35 20x + 35 ≤ 350 20 x ≤ 315 x ≤ 315/20 ≤ 15.75 So he can invite 15 people maximum test: if he invites 15 cost = 20(15) + 35 = 335 , within his budget if he invites 16 cost = 20(16) + 35 = 355 , above budget.

algebra
Does the fence run on 4 sides or on 3 sides ?

Math
|2x-7|=11 2x-7 = 11 OR -2x+7 = 11 2x = 18 OR -2x = 4 x = 9 OR x = -2 so the sum of the solutions is 9-2 = 7

Algebra
I = k(1/R), where I current, R is resistance and k is a constant given: I = 5, R = 20 5 = k(1/20) k = 100 I = 100(1/R) so when R = 25 I = 100(1/25) = 4

Trigonometry
from last night at 10:06 pm RS = (1-sinØ)/(1+ sinØ) = (1-sinØ)/(1+ sinØ) * (1-sinØ)/(1- sinØ) = (1 - 2sinØ + sin^2 Ø)/(1 - sin^2 Ø) = (1 - 2sinØ + sin^2 Ø)/cos^2 Ø = 1/cos^2 Ø - 2sin&Osl...

Trigonometry
ok I usually start with the more complicated looking side and try to change it to the more simplified LS = cosØ/(sinØ - 1) + cosØ(sinØ + 1) , note it didn't matter to change the order of that last denominator common denominator of (sinØ-1...

Trigonometry
I see no equal signs What are we verifying ?

MATH
5√8 - 3√18 + √3 in general to change √k to a mixed radical, look for factors of k which are perfect squares e.g. 18 = (3)(6) or 2(9) the choice of (3)(6) does not do us any good, since neither factor is a perfect square so your problem can be written as...

MATH
4√2 + 6√4 = 4√2 + 6(2) = 4√2 + 12

Probability
let S be the event of being dealt a spade, x the event of a non-spade One such 5 spade hand could be SSSSSXXXXXXXX The prob of that is (13/52*12/51*11/50*10/49*9/48)(39/47*38/46*37/45*36/44*35/43*34/33*33/32*32/31) a quicker way would be to say prob(exactly 5 spades) = ( C(13,...

Trig
That's a better job of typing it. I did the first of these in your previous post.. the 2nd: LS = (1-sinØ)/(1+ sinØ) = (1-sinØ)/(1+ sinØ) * (1-sinØ)/(1- sinØ) = (1 - 2sinØ + sin^2 Ø)/(1 - sin^2 Ø) = (1 - 2sin&Os...

Math
how about just treating it like 2 ordered pairs (1991, 4.25) and (1997, 5.15) ? rate of change = (5.15-4.25)/(1997-1991) = .15

Trig
Don't try to build up fractional equations using your method, the spacing will not work out instead do something like this: 1/(tanØ - secØ) + 1/(tanØ + secØ) = -2tanØ LS = (tanØ + secØ + tanØ - secØ)/(tan2 &Osl...

Pre-Calculus
we know x =rcosØ and y = rsinØ -3rcosØ + (1/2)rsinØ = 2 -6rcosØ + rsinØ = 2 r(sinØ - 6cosØ) = 2 or r = 2/(sinØ - 6cosØ) looks good: http://www.wolframalpha.com/input/?i=polar+r+%3D+2%2F%28sinx+-+6cosx%29

Calculus Please help!
dy/dx = 3(x^2 + 6)^2 dy = 3(x^2 + 6)^2 dx when x = 2 and dx = .05 dy = ...... just plug in the above values.

Probability
#1 is correct, in effect what you are doing is C(60,60) (.99^60 (.01)^0 = .547 #2, you want to have 59 correct and one wrong = C(60,59) (.99)^59 (.01)^1 = 60(.55268..)(.01) = .33161 #3 , same way, 58 correct, 2 wrong prob = C(60,58) (.99)^58 (.01)^2 = .09881 #4 , at least 2 mi...

Probability
at least 4 means 4 or 5 or 6 or ... or 20 are colourblind so exclude cases of none, 1 , 2, and 3 colourblind = .05 not colourblind = .95 None: C(20,0) (.05)^0 (.95)^20 = .358486 one: C(20,1) (.05) (.95)^19 = .37735.. two: C(20,2) (.05)^2 (.95)^18 = .1886768 three: C(20,3)(.05)...

Math:Probability
1. could be 1 in math or 1 in history or 1 in Spanish that is (math)(no history)(no Spanish) + .... prob = .9(.4)(.25) + .6(.1)(.25) + .25(.1)(.4) = .115 Exclude the case of no homework in any which is (.1)(.4)(.25) = .01 prob(homework in at least 1 class) 1 - .01 = .99

Math (Statistics)
Perfect data, one standard of devation below and above. so appr 68% or prob of .68 confirmed by David's webpage http://davidmlane.com/hyperstat/z_table.html fill in the data to see and get .6827

Calculus Please help!
Let the radius be r, so the diameter is 2r then the height is 2r V = (1/3)π r^2 h = (1/3) π r^2 (2r) = (2/3)π r^3 dV/dt = 2π r^2 dr/dt when h = 24 2r = 24 r = 12 and dV/dt = 30 30 = 2π (144) dr/dt dr/dt = 30/(288π) = 5/(48π) ft/min or appr .0...

Calculus Please help!
darn them brackets 23t^2 vs (23t)^2

Calculus Please help!
let the time be t hours past noon. I see a right-angled triangle , with sides 23t and 50 + 18t, with D as the distance between them D^2 = (23t)^2 + (50+18t)^2 D^2 = 529t^2 + 2500 + 1800t + 324t^2 = 853t^2 + 1800t + 2500 2D dD/dt = 1706t + 1800 dD/t = (853t + 900)/D , #1 at 3:0...

Algebra 2 Help!
No, since the disc I negative, you will have 2 complex roots

Algebra 2 Help!
f(x) = 5x^2 - 10x + 3 , notice how we use exponents in this format = 5(x^2 - 2x + 1 - 1) + 3 = 5 ( (x-1)^2 - 1) + 3 = 5(x-1)^2 - 5 - 3 = 5(x-1)^2 - 8 6= 4x - 5x^2 5x^2 - 4x + 6 = 0 b^2 - 4ac = 16 - 4(5)(6) = -104 What do you think ?

Algebra 2 Help!
[sqrt3 + 2i][sqrt3 - 2i] = 3 - 2i√3 + 2i√3 - 4i^2 = 3 - 4(-1) = 7 (y - 4)^2 = -18 y - 4 = ± √18 y = 4 ± 3√-2 = 4± 3√2 i

math
36 hrs, 12 minutes <---> 1 day + 12 hrs , 12 min 6:12 pm + 12:12 = 6:24 am (wouldn't it be nice it time was metric ??)

Math
pigs--- x horses --- 2x cows--- 4(2x) or 8x 8x + 2x + x = 99 11x = 99 x = 9 9 pigs, 18 horses, and 72 cows

math --- can someone help me pls?
I assume you mean the diameter of the circular base of the cone, so the radius is 4 slant-height^2 = 9^2 + 4^2 = 97 slant-height = √97 = appr 9.85 your second question is correct

Math
Pablo --- x yrs old Chita ---- x- 15/4 4(x -15/4) = 43 4x- 15= 43 4x = 58 x = 14 1/2 years old

algebra
The corresponding sides of a regular polygon are in the same ratio, so 8/2 = 29/x 8x = 58 x = 58/8 = 29/4

Algebra
You should be familiar with the vertex form of a parabola as y = a(x-p)^2 + q , where (p,q) is the vertex, so we have: y = a(x-4)^2 - 4 using any of the other given points will give us the a let's use the easiest, (2,0) 0 = a(2-4)^2 - 4 0 = 4a - 4 a= 1 y = (x-4)^2 - 4 is y...

Ethiopia(AAU)
A) f(x) = x^2 e^x , notice how I indicated exponents? f ' (x) = x^2 e^x + 2x e^x = e^x(x^2 + 2x) f'' (x) = x^2 e^x + 2x e^x + 2x e^x + 2 e^x = e^x (x^2+ 4x + 2) here is a graph of your first function http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+e%5Ex type in yo...

math
number of men ---- x number of boys ---- 20-x solve for x 60x + 35(20-x) = 900 You should get 8 men .... etc

Math
That was a coincidence and only happens when r = 4 When r = 2, the area and the circumference just happen to be equal, again a coincidence.

math
I like that equation. What about it ?

Algebra
5x^2 - 526 = -651 5x^2 = -125 x^2 = -25 Unless you have another typo, there is no real number solution, since we cannot take the square root of a negative. If you equation was supposed to be 5x^2 - 526x= -651 5x^2 - 526x + 651 = 0 x = (526 ± √263656)/10 = appr 103...

Math
If my middle term is even and it starts with x^2, I always complete the square. x^2 + 14x + 49 = -4 + 49 (x+7)^2 = 40 x+7 = ± √40 = ± 2√10 x = -7 ± 2√10

Math
Use the formula exact values: x = (5 ± √13)/2 Use your calculator to find appr. values

Finance
PV = 235 (1 - 1.006458333..^-48)/.006458333 = $ 9672.48

Maths
A - B = 51 ---> A = B+51 A - C = 108 subtract them -C + B = 57 B = C + 57 C = (15/100)(A+B+C) C = (3A + 3B + 3C)/20 20C = 3A + 3B + 3C 17C = 3A+ 3B 17C = 3(B+51) + 3(C+57) 17C = 3B + 153 + 3C + 171 17C = 3(C+57) + 153 + 3C + 171 17C = 3C + 171 + 153 + 3C + 171 11C = 495 C =...

Geometry A
The line y+4 = 3(x+6) does expand and simplify it if you have to

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