Thursday
July 24, 2014

Posts by Reiny


Total # Posts: 26,863

Alegbra
I suspect a typo

math
ummh, that would be (0,0) You should know the properties of this , the simplest form of the equation of a circle.

Math 117
done, check back on your previous post of this

Math 117
I interpret (fg)(x) as (-6x-1)(4x^2) = -24x^3 - 4x^2

Math 117
I bet you mean: f(x) = (x+10)^2 new equation: g(x) = (x+10 - 12)^2 = (x-2)^2

math
radius of each bubble = .005 m or (1/2) cm volume of each bubble = (4/3)π(1/2)^3 cm^3 so 1 million of them = 1000000(4/3)π(1/2)^3 = appr 523598.78 cm^3 = appr .5236 m^3 a bit over 1/2 cubic metre

trig
2tanA+6=tanA+3 tanA = -3 so A must be in II or IV using tanx = +3 x = 71.565° so A = 180-71.564 = appr 108.4 or A = 360 - 71.565 = appr 288.4°

Math 134
rate = 4760/34000 = .14 so .14(36000) = $ 5040

Math
Make the rectangle sit on the diameter. Let its base be 2x and its height be y then x^2 + y^2 = 27^2 y = √(729 - x^2) area = 2xy area^2 = 4x^2y^2 = 4x^2(729-x^2) = 2916x^2 - 4x^4 d(area^2)/dx = 5832x - 16x^3 = 0 for a max of area (if area is the largest of all areas, the...

Algebra
A variety of 9 different questions with no apparent effort shown by you, indicates that you just want us to do this assignment for you. Tell me what answers you obtained, and where you are having difficulty. Are you telling me that you can't do #2 ?

Math
Just realized that I answered this same question back in 2011 http://www.jiskha.com/display.cgi?id=1306326095

Math
Did you make a diagram? Did you not realize that the direction of the plane and the wind form a right angle ? How did you get 266.4 for the groundspeed ? (I got 241.86)

Math 2 questions
volume of 2 similar solids is proportional to the cube of their corresponding sides, so x/240 = 23^3/92^3 = (23/92)^3 = (1/4)^3 = 1/64 64x = 240 x = 3.75 the new volume is 3.75 ft^3 If I told you that the surface area of 2 similar solids is proportional to the square of their ...

Math
number of chairs --- x number of tables --- 14-x 30x + 70(14-x) = 660 solve for x, pretty straightforward.

can u explain? 1 question
volume of pyramid = (1/3) area of base x height

i need yur help with this..
look at my answer to your first question here http://www.jiskha.com/display.cgi?id=1394926846 In calculating the area of the triangle, the height is not 15. make a sketch of the triangle to see that 15 is the hypotenuse.

Calc
quick way: for a given point (p,q) , the shortest distance from that point to the line Ax + By + C = 0 is |Ap + Bq + C|/)√(A^2+B^2) so we have (p,q) = (-4,-4) and line 2x - 2y + 3 = 0 distance =|-8 +8 + 3|/(4+4) = 3/√8 = 3/√8*√8/√8 = 3√8/8 =...

math
could be a very nasty equation but .... 3^x + 4^x = 5^x by inspection and recall, I know that 3^2 + 4^2 = 5^2 (did you recognize the 3-4-5 right-angled triangle) so x = 2 now suppose it had been 3^x + 4^x = 6^x look at Wolfram's solution http://www.wolframalpha.com/input/?...

Math help plz check my answers!
Surface area of a square pyramid usually just adds up the surface area of the 4 isosceles triangles, not including the base one of them: base = 11 hypotenuse = 15 height^2 + 5.5^2 = 15^2 height^2 = 194.75 height = √194.75 area of one of them = (1/2)(11)√194.75 = ap...

Algebra II
I am sure you meant: (4-7i)/(2+5i) = (4-7i)/(2+5i)*(2-5i)/(2-5i) = (8 -20i - 14i + 35i^2 )/(4 - 5) = 8 - 34i - 35)/-1 = 27 + 34i

Pre-Calculus
5 - 12i r = 13 , but we want it in the form r(cosØ + isinØ) cosØ = 5/13 , so Ø could be in I or IV sinØ = -12/13, so Ø could be in III or IV so Ø must be in IV taking Damon's angle of 292.6° 5 - 12i = 13(cos292.6 + i sin...

Algebra Question~!
x^2 + 7x - 30 = (x+10)(x-3) so the sides could be (x+10) and (x-3) , were x > 3 or x^2 + 7x - 30 = (x-2)(x+9 - 12/(x-2) ) so the sides could be x-2 and x+9 - 12/(x-2) or x^2 + 7x - 30 = (x+5)((x+2 - 40/(x+5) ) so the sides could be x+5 and x+2 - 40/(x+5) or ... as you can s...

Algebra Question~!
you should know the formula for the area of a circle just plug in 3x+2 for r and look at your choices (which you did not give us)

math
did that one for you, look for your previous post

mathematics
tough one! are you sure you did not mean 4^x = 8^x ? that would be easy. What you typed requires some sort of sophisticated method such as "Newton's Method" but an intuitively obvious answer would be x = 2 however there is another one between 0 and 1 let me know ...

math
looks like a lot of nonsense and mathematical gibberish.

geometry
make a sketch, join the centre to A, and complete the right-angled triangle. let the distance from the centre to the chord be x x^2 + 5^2 = 13^2 x^2 = 169-25 = 144 x = √144 = 12 Where does CD enter the picture? Where is D ? Your opening sentence of "center C has a r...

math
all lines of the type y = (-3/2)x + b , where b is any real number would be perpendicular to your given line Where there any choices? so just make sure the answer starts with y = (-3/2)x ...

Algebra Question~!
area of lot = (6x)(9x) = 54x^2 area of circle = π(4x)^2 = 16πx^2 amount left over = 54x^2 - 16πx^2 = (54-16π)x^2

math
let the original cost of one shirt be x so three shirts cost 3x reduced by 30% leaves you with .7(3x) .7(3x) = 63 2.1x = 63 x = 63/2.1 = 30 Just noticed this same question was asked last year. http://www.jiskha.com/display.cgi?id=1361331485 Now you have 3 different solutions, ...

math
What is 8/9 - 3/5 ?

geometry
As I understand the question, you simply want the circumference of a sector of central angle 7(15°) or 105° with a radius of 24 cm circumference of a circle with radius 24 is 48π cm so using a simple ratio ... 105/360 = x/48π gives an arc length of 105(48`...

Finance
You have conflicting information. At the beginning of his "retirement period" he will need: 35000( 1 - 1.08^-15)/.08 = 299,581.75 so he would not need $400,000 at that time. To assure that he will have that $299,581.75 available 20 years from now , he needs a present...

Trigonometry
using sin(A+B) = sinAcosB + cosAsinB 4sin(π/2+x) = 4(sin(π/2)cosx + cos(π/2)sinx) = 4( (1)cosx + (0)sinx) = 4 cosx

Probability
I too made a Venn diagram and after filling in the given information , found two missing sections 1. Those that only walked 2. Those that took the bus or the car, but did not walk confirm this please #2, dA/dr means the rate of change of the surface area with respect to the ra...

math
I = PRT 960 =4000(R)(3) solve for R (I got 8%)

Calculus
Steve is right, I made a silly adding vs subtracting error in the 3rd last line 3y + 27/5 = 2x - 48/5 3y - 2x = -21/5 should be 3y + 27/5 = 2x - 48/5 3y - 2x = -75/5 to give 10x - 15y = 75 , reducing to 2x - 3y = 15

Calculus
the the point of contact be P(x,y) Make a sketch to see that there would be two points P 2x + 8y dy/dx = 0 dy/dx = -2x/(8y) = -x/(4y) slope of tangent = (y-3)/(x-12) then (y-3)/(x-12) = -x/(4y) 4y^2 - 12y = -x^2 + 12x x^2 + 4y^2 = 12x + 12y but x^2 + 4y^2 = 36 12x + 12y = 36 x...

Happy Pi Day
OOPS, good catch, my apologies to the good people of Illinois.

Happy Pi Day
From the article: "The Illinois Science Council and Fleet Feet Sports are hosting a 3.14-mile walk/run Friday night, ." It is ironic that the state of Illinois actually introduced a bill , the notorious #246, which attempted to declare the value of π to be 3. ht...

math
from the given: term(3) = ar^2 = 28 term(4) = ar^3 = -56 so ar^3/(ar^2) = -56/28 r = -2 then in ar^2 = 28 a(4) = 28 a = 7 sum(6) = a(r^6 - 1)/(r-1) = 7((-2)^6 - 1)/(-2-1) = 7(63/-3) = -147 check: GP is 7, -14 , 28 , - 56 , 112, - 224 sum of that is -147

math
You state different interest rates for the 1st and 3rd debt, but state no rate for the 2nd debt of $2000 due in 2 years. Other than , choose a time as a reference or focal date I picked the present time, so at present, the value of the debt = value of payments 500(1.03)^-2 + 2...

Math
cost of 1st machine = 250000 + 30000( 1 - 1.085^-10)/.085 - 75000(1.085)^-10 = 413,669.04 cost of 2nd machine = 400000 + 225000(1.085)^-5 - 175000(1.085)^-10 = 472,235.27 1st is cheaper, I used the present time as my "focal point in time" check my arithmetic

Algebra 1
so we want a^2 = b^3 a = b^(3/2) or (√b)^3 so pick b = a perfect square, e.g. b = 4 , then a = 8 so 8^2 = 4^3 = 64 let b = 9 , a = 27 9^3 = 27^2 = 729 let b = 16 , then a = 64 16^3 = 64^2 = 4096 let b = 25 , a = 125 25^3 = 125^2 = 15625 So the first few numbers with that...

Albegra
I would first of all divide both sides by 20 to get the numbers a bit smaller 121/(570+r) = 107(570-r) now cross-multiply 60990 + 107r = 68970 - 121r 228r = 7980 r = 7980/228 = 35 or, look at it this way: the LCD is (570+r)(570-r) so in effect I just multiplied both sides of t...

applied algebra
what is 800(1.0275)^14 ?

math
3x^2 - 24x + 45 =0 first divide by 3 to simply x^2 - 8x + 15 = 0 (x-3)(x-5) = 0 x = 3 or x = 5 check: http://www.wolframalpha.com/input/?i=plot+y+%3D+3x%5E2+-+24x+%2B+45

math
To have more than 30 cents, the right pocket must have the quarter and the dime. possible cases, order does not matter: L --- left pocket, R -- right pocket L -- R QP ND QN PD QD PN PN QD PD QN ND QP -----> so we have 6 cases prob = 1/6

Math
y = 2(x^2 - 2x +1 -1) - 6 = 2( (x-1)^2 - 1) - 6 = 2(x-1)^2 - 2 - 8 = 2(x-1)^2 - 10 the vertex is ........

Math
y=x^2 - 4x-21 = (x^2 - 4x + 4 - 4) - 21 = ( (x-2)^2 - 4) - 21 = (x-2)^2 - 4 - 21 = (x-2)^2 - 25 take over

MATH
I agree with Damon that your gravitational constant is off. Since you are using metric , your equation should be h = -4.905t^2 + 16t + 9 let's ballpark it to h = -5t^2 + 16 + 9 a) ..... b) sub in t = 1 , h = -5+16+9 = 20 m c) for t of the vertex ... t =-b/(2a) = -16/-10 = ...

Statistics
I thought I had given you the answer. finding the z-score results in a mean of 0 and a standard deviation of 1 so in the link I gave you .... http://davidmlane.com/hyperstat/z_table.html enter 0 for the mean 1 for the sd click on "below" and enter -.75 click on "...

further maths
calculate the area of a circle with 23 m - area of circle with 20 m. = (23^2)π - (20^2)π = .....

Statistics
Fun to play around with this excellent site http://davidmlane.com/hyperstat/z_table.html

Statitics
prob(lost) = 5/1000 = 1/200 prob(not lost) = 199/200 prob( 2 of 22 are lost) = C(22,2) (1/200)^2 (199/200)^20 = .005224.. Question for you. would this be the same as "....a group of people who have 11 pieces of luggage. What is the probability that 1 of these are lost? &q...

Statistics
Use David's excellent "normal distribution" calculator http://davidmlane.com/hyperstat/z_table.html click on "area from a value" enter the data, click on "between" and enter 8 and 11 to get .4467 You can enter the data directly, no need to fin...

maths
There are 2 ways to get a sum of 11 in a throw of 2 dice --- 6,5 or 5,6 prob of sum of 11 = 2/36 = 1/18

Algebra
Hint for the factors: Can you think of 2 numbers, one positive and the other negative, which when multiplied give you -30 and when added give you +7 ?

Algebra 1 Answer Check (Reiny)
you are welcome

Algebra 1 Answer Check (Reiny)
all 3 are correct.

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

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