Tuesday
September 30, 2014

Posts by Reiny


Total # Posts: 27,190

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

Algebra
y-5 = -5x + 10 5x + y = 15
March 30, 2014

math
We will need to find the sides angle P = 180 - 60 - 75 = 45° let PQ=x , QR = y , PR = z x/sin75 = y/sin45 = z/sin60 let's assign an arbitrary value of y = 1 to our smallest side using x/sin75 = 1/sin45 we get x = .1.366025 using 1/sin45 = z/sin60 z = 1.224745 so sum of...
March 30, 2014

Math
ways to choose 5 of the 6 multiple choices = C(9,5) = 126 number of ways to choose 2 of the 6 essay questions = C(6,2) = 15 number of ways to answer the test = 126x15 or 1890 ways
March 29, 2014

Finance
I have now answered 2 of these kind of questions for you. Exactly where are you finding difficulties with these? Do you know the 4 basic formulas we have to use for these ?
March 29, 2014

Finance
PV = 10000(1 - 1.08)^-10)/.08 + 20000(1 - 1.08^-30)/.08 (1.08)^-10 = 171391.45 or pretend you are gettting 20,000 for 40 years - the 10,000 for the first 10 years = 20000(1 - 1.08^-40)/.08 - 10000(1 - 1.08^-10)/.08 = 171391.45
March 29, 2014

Finance
150000 =PAY( 1 - 1.07^-20)/.07 solving for PAY, I got $ 14,158.94 Balance owing after 7 years = 150000(1.07)^7 - 14158.94( 1.07^7 - 1)/.07 = $ 118.335.46
March 29, 2014

math
I will assume you meant: log3 (2x + 5) = 1 then 2x+5 = 3^1 2x = -2 x = -1 If otherwise, let me know
March 29, 2014

survey math 140
Number of ways to select 5 of 19 is C(19,5) = 19!/(5!14!) = 11628 most calculators have that function built-in look for something like nCr
March 29, 2014

algebra
James, I gave you a detailed solution yesterday for the same question on the assumption that your symbol was supposed to be ≥ You later told me that it was to be ≤ So why don't you just switch all the conditions e.g. all the domain that worked before, now will ...
March 29, 2014

Math
I am guessing that P(number < 2) is supposed to mean probability that the number is less than 2 What number ???? Are you tossing a die ? confirm
March 28, 2014

calcules
let base be x by x let the height be y x^2 y = 8 y = 8/x^2 SA = base + 4 sides = x^2 + 4xy = x^2 + 4(8/x^2) = x^2 + 32/x d(SA)/dx = 2x - 32/x^2 = 0 for a minimum of SA 2x = 32/x^2 2x^3 = 32 x^3 = 16 x = cuberoot(16) = appr 2.52 then y = 1.26 the base is 2.52 by 2.52 and the ...
March 28, 2014

Algebra 2
same idea as before, factor first, then divide, restrict what you divided by Again, I am putting in the brackets, they are extremely important here h(x)=(x^2-9)/(x^2-4x+3) = (x+3)(x-3)/(x-1)(x-3)) = (x+3)/(x-1) , x ≠ 3
March 28, 2014

Algebra 2
I have a feeling you meant: (49X^6+7X^7)/(28X^8) take out a common factor = 7x^6( 7 + x)/(28x^8) now divide = (7+x)/(4x^2) now we divided top and bottom by a variable. If that variable is zero, we just divided by zero, which is a mathematical no-no. so we have to state a ...
March 28, 2014

algebra
I have a strong feeling you meant (x-4)(x+2)/( (x-3)(x+5) ) ≥ 0 I good and fast way is to look at the graph of y = (x-4)( (x+2)/(x-3)(x+5) ) http://www.wolframalpha.com/input/?i=y+%3D+%28x-4%29%28x%2B2%29%2F%28%28x-3%29%28x%2B5%29%29 It shows the graph to be above the x-...
March 28, 2014

Geometry
You are missing one of the dimensions of the floor, its length Once you have that, Cost = 105 ( 33 * 1/2 * ??)/27 units of money where ?? in your length we divide by 27 since there are 27 cubic feet in 1 cubic yard If the concrete is sold in whole cubic yards, you will have to...
March 28, 2014

ALGEBRA
the t of the vertex of your parabola is -b/(2a) = -20/-32 = 5/8 at t = 5/8 h = -16(25/64)+20(5/8) + 6 = 12.25 nope!
March 28, 2014

math
avg rate of change = (23500 - 8750)/(8 = ...
March 27, 2014

Math
treat it as two ordered pairs (t, c) where t is temperature and c is consumption so we have (90,220) and (76, 178) slope = (220-178)(/(90-76) = 42/14 = 3 so: c-220 = 3(t-90) c = 3t - 270+220 c = 3t - 50 check: if t = 90, c = 270-50 = 220 if t = 76, c = 228 - 50 = 178
March 27, 2014

Math
no, 26x^2 ≠ x√26 Whatever made you think so. let x = 4 26(4^2) = 26*16 = 416 xV26 = 4√26 = appr 20.4 is 416 = 20.4 ???? However, you could write 26x^ as (x√26)^2
March 27, 2014

Math
Imagine "opening up" a cylinder, what would you get? 2 equal circles + a rectangle whose length is the circumference of the circle and whose height is the height of the cylinder. so SA = 2π(6^2) + 2π(6)(20) = 72π + 240π = 312π = appr 980 No ...
March 27, 2014

Math
I assume you pick a card, then throw the die primes from 1-10 : 2,3,5,7 , so 4 of them primes on a die: 2 3 5, so 3 of them prob(2 primes) = (4/10)(3/6) = 1/5 prob(not 2 primes) = 4/5 odds in favour of getting two primes = (1/5) : (4/5 = 1 : 4
March 27, 2014

2nd question - math help!!
(x+y)^2-x-y = (x+y)^2 - (x+y) = (x+y)(x + y - 1)
March 27, 2014

math help!!
To make it easier to see, let 2x^2 - x = a so you have 2a^2 - 3a - 9 = (a-3)(2a+3) put the original back in = (2x^2 - x - 3)(4x^2 - 2x + 3) = (x + 1)(2x - 3)(4x^2 - 2x + 3)
March 27, 2014

Math
cosine law .... 5.4^2 = 6.2^2 + 3.6^2 - 2(6.2)(3.6)cosR cosR = 22.24/44.64 = .4982.. R = 60.1°
March 27, 2014

Math
direct application of the sine law: x/sin41 = 96/sin71 x = 96sin41/sin71 = ....
March 27, 2014

Calculus Help Please!!!
According to Newton's Law of Cooling T(t) = roomtemp + (37 - 20)e^(-kt) , where t is the time in hours and k is a constant so we get two equations: 32.5 = 20 + 17e^(-kt) ---> 12.5 = 17e^(-kt) and 30.3 = 20 + 17e^(-k(t+1)) ---> 10.3 = 17e^(-kt - k) divide them: 115/...
March 27, 2014

Algebra
did you try factoring both expressions? They factor quite easily. Then divide out the common factor, don't forget to state the restriction.
March 27, 2014

trig
Not sure what notation you are using when you say "blowing in at 53° " is North your 0° and you are going clockwise, or is 0° your positive x - axis and you are going counterclockwise ?
March 27, 2014

Calculus
just using ln a^b = b ln a ln (243^3/5 *32^4/5) = ln ( (3^5)^(3/5) * (2^5)^(4/5) ) = ln ( 3^3 * 2^4) = ln (27*16) = ln(432) 1/5 ln (243^3 * 32^4) = ln [ (243^3 * 32^4) ^(1/5) ] = ln (243^(3/5) * 32^(4/5) ) = .... = ln(432)
March 27, 2014

Calculus
I agree with Damon's "huh" since ln (243^3/5 *32^4/5) = 1/5 ln (243^3 * 32^4)
March 27, 2014

FINANCE
choice A: pay 3100(.85) or 2635 now choice B: pay 12 payments of 270 present value of the 12 payments at a monthly rate of i = 270( 1 - (1+i)^-12)/i= 2635 hard to solve, let Wolfram do it for us (I changed the i to x, since Wolfram thinks i = √-1 ) http://www....
March 26, 2014

math 2
let E(x,y) be your point use ratios ... for the x: (x-3)/(11-3) = 3/8 8x-24 = 24 8x = 48 x = 6 for the y: (y-4)/(3-4) = 3/8 8y - 32 = -3 8y = 29 y = 29/8 E is (6,29/8)
March 26, 2014

math
y - 6 = .5x - 3.5 y = .5x - 3.6 + 6 y = .5x + 2.5
March 26, 2014

math
slope of AB = 4/-2 = -2 so slope of new line = +1/2 new line: y-6 = (1/2)(x-7) expand and doctor it up any way you want.
March 26, 2014

argggh - Calculus
messed up in my expansion volume should have been 4x^3- 120x^2 + 800x and V' = 12x^2 - 240x + 800 = 0 3x^2 - 60x + 200=0 to get x = 4.23
March 26, 2014

Calculus
First things first: width --- s length ---- 2s 2s^2 = 800 s^2 = 400 s = 20 so the piece of metal is 20 by 40 let the side of the square to be cut out be x so the width is 20-2x the length is 40-2x the height is x Volume = x(20-2x)(40-2x) = 2x^3 - 120x^2 + 800x d(Volume)/dx = ...
March 26, 2014

Algreba
What about it ?
March 26, 2014

Calculus
you should have recalled that sin (-x) = -sinx so that sin(-.1) could not have been positive. did you mean -.1 ?
March 26, 2014

Math
slope of new line must be -2 so y =-2x + b plug in the given point (2,-7) -7 = -2(2) + b -3 = b y = -2x - 3
March 26, 2014

Calculus
yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5
March 26, 2014

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