Saturday
September 20, 2014

Posts by Reiny


Total # Posts: 27,130

Math
How about this pattern term(1) = 6 = 3(2^1) term(2) = 12 = 3(2^2) term(3) = 24 = 3(2^3) term(4) = 48 = 3(2^4) .... term(23) = .... = 3(2^23) term(n) = .....
April 7, 2014

Math
Q(t) = 200 (1/2)^(t/14.2) or Q(t) = 200(.5)^(.0704t) Q '(t) = (200/14.2) (.5)^(t/14.2) so when t = 21.5 Q ' (t) = (200/14.2) (.5)^(21.5/14.2) = 4.931 g/day
April 6, 2014

algebra 2
This produces an arithmetic series, where a = -5 and d = 8 sum(28) = (28/2)(-10 + 27(8)) = 2884
April 6, 2014

Math
I am sure you meant: Q(t) = 7000/(1 + 249 e^(-.6t) ) Q(10) = 7000/(1 + 249 e^(-.6(10) ) ) = appr 4328
April 6, 2014

algebra 2
so a = -12 , d = 5 sum(n) = (n/2)(2a + (n-1)d ) = (11/2)(-24 + 10(5)) = (11/2)(26) = 143 OR sum(n) = (n/2)(first + last) = (11/2)(-12 + 38) = 143
April 6, 2014

algebra 2
The famous mathematician Gauss, while he was in elementary school, notices the following 1+2+3+..+58+59+60 = (1+60) + (2+59) + (3+58) +.. (for a total of 30 of these pairs) = 30(61) = 1830
April 6, 2014

MATH
A polynomial must have a non-negative integer exponent. A and B contain square roots or exponents of 1/2 D: 11/(√x)^2 = 11/x or 11 x^-1 so none is a polynomial C: x - √11 yup, I would go with that one
April 6, 2014

Algebra
Did you mean: (2x+6)/(4x-8) ?? = 2(x+3)/(4(x-2)) = (x+3)/(2(x-2) or (x+3)/(2x - 4)
April 6, 2014

Math
I would consider it a "combination" , assuming that the order that you choose the appetizers should not matter Number of ways = C(4,2) x C(5,1) = 6x5 = 30
April 6, 2014

Calculas
P(4) = 100(4) - 3(16)ln(4) = .. I assume you have a calculator to get appr 333.46
April 4, 2014

Calculus Help Please!!!
dy/dx = 8x(1/2)(x-x^2)^(-1/2) (1 - 2x) + 8(x-x^2)^(1/2) = 4(x-x^2)^(-1/2) [ x(1-2x) + 2(x-x^2) ] = (4/√(x-x^2) ( x - 2x^2 + 2x - 2x^2) = (4/√(x-x^2) (3x - 4x^2) = 0 for a max/min 3x - 4x^2 = 0 x(3 - 4x) = 0 x = 0 ----> looks like it will yield a min x = 3/4 ---&...
April 4, 2014

typo - Calculus Help Please!!!
only valid for 0 ≤ x ≤ 1
April 4, 2014

Calculus Help Please!!!
only valid for 90 ≤ x ≤ 1 http://www.wolframalpha.com/input/?i=y+%3D+%3D+8x%28√%28x+−+x%5E2%29%29+%2C+0+%3C+x+%3C+1
April 4, 2014

Algebra
But you wanted to use the formula ... x = (-4 ± √100)/2 = (-4 ± 10)/2 = (-4+10)/2 or (-4-10)/2 = .....
April 4, 2014

Algebra
put it into standard form of a quadratic ... x^2 + 4x - 21 = 0 how nice that it factors .... (x+7)(x-3) = 0 so x = ... or x = ....
April 4, 2014

percentages/word problem
costprice = 80 after first markup, SP = 80(1.5) after 20% mark down = 8(1.5)(.8) another 15% markup = 8(1.5)(.8)(1.15) final markdown of 60% = 8(1.5)(.8)(1.15)(.4) = 8(.552) = 4.42
April 3, 2014

Calculus1
let the width of the beam be 2w and the depth be 2d S = k(2w)(4d^2) = 8k w(d^2) I drew a circle and incribed a rectangle with the defined dimensions. Notice the diagonal is 12 Construct a righ-angled triangle, with sides w, d, and hypotenuse 6 w^2 + d^2 = 36 d^2 = 36-w^2 in S...
April 3, 2014

Math - Algebra2
f(x)=3x+2 , g(x)=3/x^2+2 , h(x)=sqrt(x-2) (f∘g)(-5) to me means: f (g(x) ) so f(g(5)): g(-5) = 3/27 = 1/9 f(1/9) = 3(1/9) + 2 = 1/3 + 2 = 5/3 (f∘g)(-5) = 5/3 so the others the same way
April 3, 2014

Precalculus
w = -i - 2j describes the vector (-1,-2) so it the same way I showed you in the similar problem of unit length. YOu can do it in your head to get (-1/√5 , -2/√5)
April 3, 2014

Algebra
for any quadratic of the form y = ax^2 + bx + c the x of the vertex is -b/(2a) so for yours ... x of the vertex is -184/(-32) = 5.75 so it took 5.75 seconds, plug that into your original function to find the maximum height.
April 3, 2014

Pre calculus
correct notice you can check that the magnitude is 1 magnitude = √( (1/√2)^2 + (-1/√2)^2 ) =√( 1/2 + 1/2) = √1 = 1
April 3, 2014

Pre calculus
for any unit vector in the direction of (a,b) .... find the length of the vector = √(a^2+b^2) now divide each component by that magnitude to get (a/√(a^2+b^2) , b/√(a^2+b^2) or you could write it as (1/√(a^2+b^2) (a,b) apply this to your vector, let me ...
April 3, 2014

algebra
welcome
April 3, 2014

algebra
multiply each term by 2x(x+1) 6x - 2(x+1) = x(x+1) 6x - 2x - 2 = x^2 + x x^2 +3x + 2 = 0 (x-1)(x-3) = 0 x = 1 or x = 3
April 3, 2014

Calculus1
it would be a combination of the chain rule and the product rule, doing it as a single power the way I did it was easier as a product rule - chain rule for that term ..... x√x = x x^(1/2) derivative: x (1/2) x^(-1/2) + (1)x^(1/2) = x/(2√x) + √x = x/(2√x...
April 3, 2014

Calculus1
yes, of course, silly me, the exponent on the last one was 3/2
April 3, 2014

Calculus1
I would rewrite as h(x) = 3x^(1/2) - x^(3/2) h ' (x) = (3/2) x^(-1/2) - (2/3) x^(1/2) = 3/(2√x) - (2/3) √x
April 3, 2014

Algebra
it will hit the ground when the height h(t) = 0 -16t^2 + 144 = 0 16t^2 = 144 t^2 = 144/16 = 9 so t =√9 = 3 after 3 seconds
April 3, 2014

Pre calculus
welcome
April 3, 2014

Pre calculus
PS-3PQ = (-10,4) - 3(2,5) = (-10,4) + (-6,-15) = (-16,-11) magnitude is √((-16)^2 + (-11)^2) = √377
April 3, 2014

Algebra
since you want the height horizontally from the starting height, and that height was 5.4 metres, -.06x^2 + 9.6x + 5.4 = 5.4 the 5.4 drops out, so x(-.06x + 9.6) = 0 x = 0 , the starting time or x = 9.6/.06 = 160 it will land after 160 m
April 3, 2014

Geometry
let the chord AB = 2x then the diameter = 2x+2 or the radius = x+1 This allows me to draw a right-angled triangle with sides x and 9 and hypotenuse x+1 (x+1)^2 = x^2 + 9^2 x^2 + 2x + 1 = x^2 + 81 2x = 80 x = 40 AB = 80 check: diameter = 82 is 41^2 = 40^2 + 9^2 ? LS = 1681 RS...
April 2, 2014

Algebra II
rowing speed in still water ---- x mph speed of current ------------- 2 mph time to go 50 miles with the current = 50/(x+2) time to go 25 miles against current = 25/(x-2) the two times are the same, so ... 50/(x+2) = 25/(x-2) 50x - 100 = 25x + 50 25x = 150 x = 6 speed in still...
April 2, 2014

slope
y = 3x - 7 straight line with slope of 3 and y-intercept of -7 http://www.wolframalpha.com/input/?i=y+%3D+3x+-+7
April 2, 2014

Pre-calc
What are we doing with this hyperbola ?
April 2, 2014

Math help
look back at your previous post of this
April 2, 2014

Math
let the slant height of one side be h then using (1.2)base x height 1980 = (1/2)(35.4)h h = 3960/(35.4) = 111.8644 = appr 111.86 m this can't be. According to the given dimensions on the webpage, the base is about 35 by 35 and the height is 21.6 m, for a slant height of 27...
April 2, 2014

calculus
let the two equal width be x let the single side by y xy = 600 y = 600/x cost = 20y + 30x = 20(600/x) + 30x d(cost)/dx = -12000/x^2 + 30 = 0 for a min of cost 30 = 12000/x^2 x^2 = 400 x = 20 the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.
April 2, 2014

Word problem
the x of the vertex is -b/(2a) = -184/(-32) = 5.75 seconds plug that into the function h(5.75) = 16(5.75^2) + 184(5.75) + 20 = 549 ft
April 2, 2014

Finance
monthly rate = .041/12 = .00341666.. let the effective annual rate be i 1 + i = (1 + .00341666..)^12 1+i = 1.0417783 i = .0417783 or appr 4.18%
April 2, 2014

PRE CALC
using the standard notation: term(20) = a + 19d = 27 and a = -11 -11 + 19d = 27 19d = 38 d = 2 the common difference is 2 check: term(2) = a+19d =-11 + 19(2) = -11+38 = 27
April 2, 2014

calculus
I see that C(1990) is given as 271.9 What are you asking?
April 2, 2014

Equations
did it, look back
April 2, 2014

trig
after 1 hours, one ship has gone 25 km, the other 15 km make a sketch, let the distance between them be x straigh-forward case of the cosine law x^2 = 25^2 + 15^2 - 2(25)(15)cos 60° = .... you do the arithmetic. (I got appr 21.8 km)
April 2, 2014

Algebra Question~!
To be a factor, the division has to be exact, that is, the remainder must be zero works that way with numbers, works that way in algebra.
April 2, 2014

Calculus Help Please!!! Check
looks like you are using Newton's Formula for Cooling properly.
April 2, 2014

Derivatives
write it as: G(t) = 5200 (1+12e^(-.52t)^-1 G ' (t) = -5200(1+12e^(-.52t) )^-2 (-.52)(12)e^(-.52t) = + 32448 e^(-.52t) / (1+12e^(-.52t) )^2 I got a positive instead of your negative.
April 2, 2014

kaylah - math
kaylah, you can't draw a triangle with 2 sides parallel !!
April 2, 2014

math
Can you draw a 4-sided figure with 2 lines parallel ?
April 2, 2014

Equation help 2 questions
You state the equation as a function, so to speak of real number solutions makes no sense. There are an infinite number of solutions, any ordered pair satisfying the equation would be one. You probably want the solution to -4x^2 + 7x - 8 = 0 in both cases, it depends on the ...
April 2, 2014

Math
t(1) = 1/3 t(n) = 3term(n-1) , n>1
April 2, 2014

Calculus Help
I can add more rats!! last step: dx/dt = -6( csc^2 (π/3)) (-π/3) = -6((4/3)(-π/3) = 24π/9 km/min = 8π/3 km/min (which is Steve's answer)
April 2, 2014

Calculus Help
At a time of t min after the plane passed over the tracking telescope, let the horizontal distance be x km Let the angle of elevation be Ø Make a sketch, I get cot Ø = x/6 x = 6cotØ dx/dt = -6 csc^2 Ø dØ/dt when Ø = π/3 and d&...
April 2, 2014

Calculus Help Please!!!
given : dr/dt = 40 cm/s A = πr^2 dA/dt = 2π r dr/dt case 1: when s = 1, r = 40 dA/dt = 2π(40)(40) = 3200π cm^2/sec case 2: when s = 3, r = 3(4) = 120 cm dA/dt = 2π(120)(40) = 9600π cm^2/sec case 3: ... your turn .....
April 2, 2014

math
multiples of 5 and 8 from 1 to 110 : either 40 or 80 so prob of your event = 2/100 = 1/50
April 2, 2014

algebra 2
subtract them : 30y^2 - 96x = 192 5y^2 = 32 + 16x back into the first: 16x^2 - (32+16x) = 64 16x^2 -16x - 96 = 0 x^2 - x - 6 = 0 (x-3)(x+2) = 0 x = 3 or x = -2 if x = 3, 5y^2 = 32+48 = 80 y^2 = 16 y = ± 4 if x = -2 5y^2 = 32-32 = 0 y = 0 so we have 3 points: (-2,0) , (3...
April 2, 2014

Math
ignore the 2nd part of my answer to the above, the numbers don't even match. I cut and pasted from a previous solution but the numbers were not even the same Also note that even though 263 is a solution, it is one of an infinite number. But it said to find "a number&...
April 2, 2014

Math
look up "Chinese Remainder Theorem" and you will find many pages for this kind of problem You will have to know how to do arithmetic in "modular arithmetic" , and this forum is not suitable to teach you that. I just worked out the above problem using that ...
April 2, 2014

Equation help
you must have a typo, since all your terms are positive. Your rock will continue to rise higher and higher. I was expecting the square term to be negative. so I will assume that -.04x^2 + 1.3x + 56 = 0 (y is zero when it hits the ground) times -100 4x^2 - 130x - 5600 = 0 x = (...
April 2, 2014

math
number of boys --- 2x number of girls --- 5x after 12 new boys number of boys = 2x+12 girls , still 5x (2x+12)/(5x) = 4/9 18x + 108 = 20x 108 = 2x x = 54 So now the number of boys = 2x+12 = 108+12 = 120
April 2, 2014

math
your data just has to be entered here http://davidmlane.com/hyperstat/z_table.html
April 2, 2014

Math
forgot the link http://www.jiskha.com/display.cgi?id=1329034595
April 1, 2014

Math
looks like yours, just input 20 instead of the 60
April 1, 2014

Algebra II
number from A ---- x number from Bx+6000 solve for x: .04x + .03(x+6000) = 880
April 1, 2014

Math
did it here .... http://www.jiskha.com/display.cgi?id=1396401662 give your posts a bit of time. You reposted this with only about 20 minutes in between. If tutors are online they may be answering somebody else's question while yours is waiting.
April 1, 2014

Combinations Algebra Readiness
you should know these w definitions nCr = n!/( r!(n-r)! ) nPr = n!/(n-r)! 6C3 = 6!/(3!3!) = 20 6P4 = 6!/2! = 360 On most scientific calculators both of these functions are built-in on mine they are found below the 5 - key and the 6-key to do 6C3 enter 6 2ndF 5 3 = to get 20 ...
April 1, 2014

Algebra
√(y+3) - 4 = 5 what about it? are we solving for y? √(y+3) = 9 square both sides y+3 = 81 y = 78 test it.
April 1, 2014

Math!!!
4/100 = x/80 100x = 320 x = 3.20 or take .2($4) = $ .80 after discount, cost = $ 4.00 - .80 = $3.20
April 1, 2014

Calculus Help Please!!!
done http://www.jiskha.com/display.cgi?id=1396400942 are you switching names???
April 1, 2014

Calculus Help Please!!!
Use the product rule to get f ' (t) = -(t^2 - 32)/√(64-t^2) = 0 for a local max/min t^2 = 32 t = ±4√2 f(±4√2) = 0 f(-1) = -1√63 f(8) = 8(√0) = 0 there you go, you got your f(t)'s what do you think? Here is your graph, notice ...
April 1, 2014

MATH UGH WORD PROBLEM
capacity of tank = π r^2 h = π(100^2)(40) = 400000π number of gallons = 7.5(400000π) = appr .....
April 1, 2014

Calculus Help!
see http://www.jiskha.com/display.cgi?id=1396388805
April 1, 2014

not - trigonometry
Why are you calling this trig ? assuming his first deposit is NOW end of 1st year: 1000(1.06) + 1000 = 2060 end of 2nd year: 2060(1.06) + 1000 = 3183.60 ... end of 5th year: .......... = 6637.09 fill in the rest using your calculator
April 1, 2014

algebra
first one: add them, 2y = 6 y = 3 sub into the 2nd: (could have used the 1st, makes no difference) 2x - 3 = 1 2x = 4 x = 2 so x=2, y=3 do the 2nd one by adding them, follow my example
April 1, 2014

math..help again
look back at your previous post of this same question
April 1, 2014

Math- urgent
1st number --- x 2nd number --- y "The second of two numbers is five more than the twice first." ---> y = 2x+5 "the sum of the numbers is 44" ---> x+y = 44 x+y = 44 x + (2x+5) = 44 x + 2x + 5 = 44 3x = 39 x = 13 1st is 13, 2nd is 31 check: is 31 five ...
April 1, 2014

Math
area of whole thing is 120x60 = 7200 ft^2 so half of that is 3600 ft^2 make a sketch showing the first run area of 1st run = 120x4 + 120x4 + 52x4 + 52x4 = 1376 leaving 2224 make a sketch of the remaining rectangle which is 112 by 52 area of 2nd run = 112x4+112x4+48x4+48x4 = ...
April 1, 2014

Math
ummmhhh, how many sides does a hexagon have ?
April 1, 2014

trig
I assume you want the distance traveled along the hypotenuse, d, then sin30° = 5000/d d = 5000/sin30 d = ... if you want the horizontal distance traveled , x tan30 = 5000/x x = 5000/tan30 = ...
April 1, 2014

Urgent Calc Help!!! Thanks!
f ' (x) = x( xe^((−x^2)/98)(-2x/98) + e^((−x^2)/98) = e^((−x^2)/98) ( -x^2/49) + 1) = 0 for a max/min -x^2/49 +1 = 0 x^2 = 49 x = ± 7 evaluate f(7) f(-7) f(-6) f(14) and determine which is the largest and which is the smallest
April 1, 2014

Calculus
f ' (t) = -8sin t + 2(4 cos t) = -8sint + 8cost = 0 for a max/min 8sint = 8cost sint/cost = 1 tant = 1 t = 45° or 225° or t = π/4 , t = 5π/4 -->(outside our domain) so evaluate f(0) f(π/4) f(π/2) and determine which is the largest and which ...
April 1, 2014

Calculus Help Please!!!
so it the same way you were just given in your previous post. Let us know what you got
April 1, 2014

Calculus Help Please!!!
looks like we both messed up in the f(x) calculations should be f(4) = 2(64) - 3(16) - 72(4) + 7 = -201 f(-3) = 2(-27) - 3(9) - 72(-3)+7 = 142 end-values: f(-4) = 2(-64) - 3(16)( - 72(-4) + 7 = 119 f(5) = 2(125) - 3(25) - 72(5) + 7 = -178
April 1, 2014

Calculus Help Please!!!
f ' (x) = 6x^2 - 6x - 72 = 0 for a local max/min x^2 - x - 12 = 0 (x-4)(x+3) = 0 x = 4, or x = -3 f(4) = 2(64) - 3(16) - 72(4) + 7 = -201 f(-3) = 2(-27) - 3(9) - 72(-3)+7 = 115 end-values: f(-4) = 2(-64) - 2(16)( - 72(-4) + 7 = 135 f(5) = 2(125) - 3(25) - 72(5) + 7 = -178 ...
April 1, 2014

math
I gave it to you ... instead of y I have "cost" instead of x I have "n" y = mx + b <-----> cost = (1/10)n + 5
April 1, 2014

math
I will assume that your given ordered pair (10,6) is of the type (number , cost), then cost - 6 = (1/10)(number -10) cost = (1/10) number -1 + 6 cost = (1/10)n + 5 so if n = 25 cost = (1/10)(25) + 5 = 7.5 units of cost (you gave no units)
April 1, 2014

calculus and vectors
Add the 2 equations ... 6x + y = 6 y = 6-6x let x = 0 , y = 6 2(0) + 4(6) + z = 5 --> z = -19) we have a point (0,6,-19) on the line of intersection let x = 1, y = 0 2(1) + 4(0) + z = 5 --> z = 3 and (1,0,3) is another point on that line So a direction vector of that ...
April 1, 2014

Algebra II
just plug in your value: 24.2 = √(19.6 h) √h = 24.2/√19.6 h = (24.2/√19.6)^2 = 29.88 m or I know from physics that h = 4.905 t^2 gives you the height from which an object was dropped after t seconds , and v = 9.81 t gives you the velocity after t ...
April 1, 2014

maths geometry
let the distance of the shorter chord to the centre be x x^2 + 15^2 = 25^2 x^ = 400 , x = 20 let the distance between the longer chord and the centre by y y^2 + 24^2 = 25^2 y^2 = 49 , y = 7 so x+y = 27 the chords are 27 cm apart
April 1, 2014

Algebra
the way you typed it would be r = (2√5) L or did you mean r = 2√(5L) major difference between the 2 formulas, please clarify.
March 31, 2014

math
let the 3 numbers be a , b, and c, in order of size, c is the largest a+b+c = 36 c = 2a b = (a+c)/2 = (a+2a)/2 = 3a/3 back into the first a+b+c = 36 a + 3a/2 + 2a = 36 times 2 2a + 3a + 4a = 72 9a = 72 a = 8, then c = 16, and b = 12 Our 3 numbers are 8, 12, and 16 (all ...
March 31, 2014

Math
your answeres are correct so far. for the increasing/decreasing part, find dy/dx I got (-c((ax+b) + a(cx+d))/(cx+d)^2 = (ad - bc)/(cx + d)^2 since the denominator is always ≥ 0 we only have to look at the top for the function to increase , dy/dx > 0 ad - bc > 0 for...
March 31, 2014

Algebra 1
Didn't know baskets were worth 4 point, did you mean 2 or 3 points? I will assume that. number of 2-pointers ---x number of 3-pointers --- 9 2x + 3(9-x) = 22 2x + 27 - 3x = 22 x = 5 so 5 two-pointers and 4 three-pointers check" 5(2) + 4(3) = 22
March 31, 2014

math
Same structure as the one I just did for you. Try it, let me know what you got.
March 31, 2014

math
amount(1.03)^5 = 5(125000) I got $ 539,130.49
March 31, 2014

statistics
plug in your data here .... http://davidmlane.com/hyperstat/z_table.html to get .4013
March 31, 2014

Math
prob(spade facecard, then king) = (3/52)(4/52) = 3/676
March 31, 2014

math
3sin = 1.2 sinØ = .4 (set your calculator to RAD) Ø = .41152 or π-.41152 which is 2.73008 but you wanted from 0 to 4π so add a period , or 2π, to each of the above answers Ø = .41152 , 2.73008 , .6947, and 9.01326
March 31, 2014

trig
I drew a circle, and a vertical radius of 12 m In 40 s, it rotates 360°, so in 5 sec it rotated 45° let the vertical position from the centre be y cos45 = y/12 y = 8.485 m so he is 12-8.85 or appr 3.5 m high after 5 seconds
March 31, 2014

Math
just translate the English into Math, 4x - 6 = 2x + 4 then solve for x
March 30, 2014

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