Sunday
July 5, 2015

Posts by Reiny


Total # Posts: 30,330

Maths
great so far: (a+2d)/a = (a+8d)/(a+2d) (a+2d)^2 = a(a+8d) a^2 + 4ad + 4d^2 = a^2 + 8ad 4d^2 = 4ad 4d = 4a a = d r = (a+2d)/a = (d + 2d)/d = 3d/d = 3 makes sense to me: looks like we can start with any value for a e.g let a = 5 then d = 5 and for the AS t1 = 5 t3 = 5+10 = 15 t9...
January 16, 2015

Math, Quadratic Functions, Max/Min Word Problems
let the two number be x and 72-x let P be their product P = x(72 - x) = -x^2 + 72x the x of the vertex is -72/-2 = 36 then P = 36(72-36) = l6^2 = 1296
January 16, 2015

algebra
look at the pattern: salary now =salary(0) = 3000 salary after 1 year = salary(1) = 300 + 3000 salary after 2 years = salary(2) = 2(300) + 3000 .... salary after n years = salary(n) = n(300) + 3000 A) salary(n) = 300n + 3000 so now just plug in whatever number of years for n B...
January 16, 2015

Math
What part of my answer to the same question you posted did you not like ?
January 15, 2015

word problems
use a simple ratio height of man /shadow of man = height of tower/shadow of tower. notice I set up "like things" in the same pattern (5 10/12) / (4 2/12) = height of tower/(8 9/12) (35/6) / (25/6) = tower/(35/4) tower = (35/4)(35/6) / (25/6) = 49/4 inches or 12 ft 3 ...
January 15, 2015

MATH
1 pile has 9 pictures 2 piles contain 18 pictures 3 piles contain 27 pictures If you can call the statement number of pictures = 9x3 an "equation", so be it. What is this p thing? To use a variable in such a problem as this is just plain nonsense.
January 15, 2015

maths
shorter of parallel sides --- longer of parallel sides --- x+7 (1/2)(x + x+7)(24) = 276 times 2 (2x+7)(24) = 552 divide by 24 2x+7 = 23 2x = 16 x = 8 parallel sides are 8 and 15
January 15, 2015

algebra factorisation
(x-y) is a common factor, so = (x-y)( 4(x-y)^2 - 1) now in the second bracket I see a difference of squares = (x-y)(2(x-y) + 1)(2(x-y) - 1) = (x-y)(2x - 2y +1)(2x - 2y -1)
January 15, 2015

Math
the third angle R can easily be found to be 52° then use the sine law. I will one side, then you do the other. PR/sin71 = 14.5/sin57° PR = 14.5sin71/sin57 = appr. 16.3
January 15, 2015

math
Have you not come across the slope-yintercept form of the equation?? if y = mx + b the slope is m and the y-intercept is b so match up your equation y = 3.9x - 4.2 with y = mx + b
January 15, 2015

Math
I will do the 2nd one, you do the others. given: cos 2x = 7/25 1 - 2sin^2 x = 7/25 2sin^2 x = 1-7/25 = 18/25 sin^2 x = 9/25 sinx = ± 3/25 sketch a right-angled triangle with height 3 and hypotenuse 25 then the adjacent side = √(625-9) = √616 if sinx = +3/25...
January 15, 2015

Math
sweaters --- x jeans ------ y x+y = 5 40x +20y = 160 or 2x + y = 8 subtract them: x = 3 then y = 2 Maria bought 3 sweaters and 2 jeans
January 15, 2015

MATH
So when they met, Carter had traveled for 3 hours and Max had traveled 2.5 hrs. let Max's speed be x mph Carter's distance = 150 miles Max's distance = 2.5x .60(150+2.5x) = 150 90 + 1.5x = 150 1.5x = 60 x = 40 a) distance between towns = 150 + 2.5(40) = 250 miles b...
January 15, 2015

MAth Igcse
mmmh, I just noticed that Steve answered this question for you earlier. Why are you reposting it ?
January 15, 2015

trigo
I assumed that by N 67°50' , you meant N 67°50' W I had a triangle with sides 85 and 39 and the angle between them as exactly 85° Using the cosine law I got your distance. Good job now look at the actual triangle. let the angle at the bottom be Ø so ...
January 15, 2015

math
volume of big tank = 10x8x4 or 320 inches^3 volume of a little tank = 3x3x3 or 27 inches^3 number of little tanks = 320/27 = 11.8.. you will need 12 tanks, the last one will be not quite full.
January 15, 2015

solid mensuration
arc = rØ , where Ø is in radians 28° = 28(π/180) radians = appr 112 = r (28(π/180)) r = 112(180)/(28π) = appr 229.2 m or 112 must be 28/360 of the circumference of the circle (28/360)(2πr) = 112 56πr = 112(360) r = 112(360)/(56π...
January 15, 2015

Math
#1. present value of loan = 320-20=300 payment = 34 n = 10 let the monthly rate be i 34( 1 - (1+i)^-10)/i = 300 There is no simple algebraic method to solve this type of equation. One method is interpolation, or if you know calculus, you could use Newton's Method. I will ...
January 14, 2015

Geometry
Not sure what you mean by "angle-side relationship" in triangles. The angles and sides are related by the Sine Law and the Cosine Law in trig If you are looking for something else, have some fun with this: http://www.mathopenref.com/trianglesideangle.html
January 14, 2015

Math
so the area of the table to be tiled is 4ft - 2(6inches) by 3ft - 2(6inches) = 3 ft by 2 ft. and that area is 6 ft^2
January 14, 2015

calculus
I will assume you meant f(x) = e^2 sinx e^2cosx = 0 then cosx = 0 , since e^2 is a constant x = π/2, 3π/2 (the graph of y = a cosx crosses the x-axis at π/2 , (90°) and 3π/2 , (270°) So there are two zeros for f ' (x)
January 14, 2015

Calculus
Go with Damon's solution, I somehow read the balloon as 3 ft instead of 5 ft above the boy correction: d^2 = (15t)^2 + (5+5t)^2 2d dd/dt + 2(15t)(15) + 2(5+5t)(5) dd/dt = (225t + 25 +25t)/d = (250t + 25)/d when t=3 d^2 = 45^2 + 20^2 = 2425 d = √2425 dd/dt = (250(3...
January 14, 2015

Calculus
make a sketch putting the boy somewhere on the road let the time passes since the boy was directly under the ballon be t seconds the the boy went 15t ft and the balloon is at a height of (3 + 5t) ft let the distance between them be d ft so we have a right-angled triangle with ...
January 14, 2015

Geometry
did that already got this far Join AC let AC = y in triangle ADC y^2 = 22^2 + 30^2 -2(22)(30)cos D = 1384 - 1320cosD in triangle BAC, let AB = a y^2 = a^2 + a^2 - 2(a)(a)cos (2x+34°) = 2a^2 - 2a^2 cos (2x+34) so now set 2a^2 - 2a^2 cos (2x+34) = 1384 - 1320cosD Was there ...
January 14, 2015

MATH!!!! AHHH!!!
No, you want a "system", which means you need two equations. My new system was: 11x + 7y = 13 and 6x + 4y = 8 The original 8x + 5y = 9 was replaced by the sum of the two original equations, and the original 3x + 2y = 4 was replaced by a multiple of that (I multiplied...
January 14, 2015

MATH!!!! AHHH!!!
A: let's add them as suggested: 11x + 7y = 13 multiply the 2nd by 2 6x + 4y = 8 Note: the system : 11x+7y = 13 and 6x + 4y = 8 is not unique, I could have done anything I wanted here. B. ok, let's solve the original system: #1 times 2: 16x + 10y = 18 #2 times 5: 15x + ...
January 14, 2015

Math
yes, d) is also correct
January 14, 2015

found it - Math
a) correct b) tickets -- cost 20 ----- 20(12.5) or 250 , that was given 32 ----- 32(12.5) or 400 36 ----- 36(12.5) or .... 40 ----- ........ c) y(12.5) + x(12.5) or
January 14, 2015

Arggghhh -Math
Looks like you double-posted this, and one of the monitors deleted one of them. And I had just answered the one that got deleted.
January 14, 2015

Algebra 1
Come on Will Surely you can do this one!
January 14, 2015

Algebra 1
Meg --- m Jill --- m-2 Beth = (1/2)(m) = m/2 or = (1/2)m other possibly: let Jill be x Meg --- x+2 Beth --- (x+2)/2 or = x/2 + 1 or = (1/2)x + 1 try it by letting Meg = y
January 14, 2015

Math
Gab --- x Fel --- x+6 Mom --- 2(x+6) = 2x + 12 aunt --- (2x+12) + 6 = 2x + 18
January 14, 2015

math
If I read your question correctly 3/5 : 3/8 ----> divide each term of the ratio by 3 = 1/5 : 1/8 ---> multiply each term of the ratio by 40 = 8 : 5 ----> divide each term of the ratio by 1 = 8/5 : 1 I don't get 3/8 : 1 either.
January 14, 2015

math
number of cases, not worrying about order: 2hops 1 hop 6 0 5 2 4 4 3 6 2 8 1 10 0 12 number of ways each of the above can be arranged e.g. the 5 double hops and 2 single hops could be dddddss sddddds etc 6 0 --- 1 5 2 -- 7!/(5!2!) = 21 4 4 -- 8!/(4!4!) = 70 3 6 -- 9!/(3!6!) = ...
January 14, 2015

Algebra- Middle
The question makes no sense. Equations do not have a numerical value. They should have asked Is the solution to 1/3(x-9) = 2x+7 greater than or less than the solution to 4/3(x+4) = -4x To say that one equation is greater than another equation makes absolutely no sense. As to ...
January 13, 2015

math
0 = -16t^2 + 250 16t^2 = 250 t^2 = 250/16 t = √250/4 = appr 3.95 or 4.0 sec to the nearest tenth
January 13, 2015

algebra
Quick mental calculation for you k = 20 LS = -10-40 = -50 RS = -2 - 16 = -18 nope, it is wrong. Now show me what steps you had, so I can help you.
January 13, 2015

calc
then a|1 0| |0 1| + b|1 0| |0 0| = |6 0| |0 5| hope this lines up .... so |a 0| |0 a| + |b 0| |0 0 | = |6 0| |0 5| only true if: a+b = 6 a+0+5 a = 5 , b = 1 makes it true yes, it can be expressed as a linear combination
January 13, 2015

math
slope of given line is 5 so the slope of the perpendicular line has to be -1/5 so it could only be B) or C) but (-10,3) satisfies only equation C) so C
January 13, 2015

Math
If by side unit, you mean "slant height" then the area of the cone = πrl, where l is the slant height, so Area = π(15)(28) = appr 1319
January 13, 2015

math
time at slower speed --- x hrs time at faster speed ---- 4-x hrs 54x + 60(4-x) = 225 solve for x, then evaluate 54x to find distance at slower speed
January 13, 2015

Math
not enough data
January 13, 2015

Algebra 2
confirm that you mean: (a−1)+a^2−b^21−ab+2(a−b)^(2b)
January 13, 2015

math
third part --- x other part --- x+5 each solve: x + x+5 + x+5 = 31
January 13, 2015

math
ummmmhh, On the first flip, it will land either heads or tails or an extremely low probability that it will land on its edge. Would you believe that they actually did an experiment at Harvard for that condition http://adsabs.harvard.edu/abs/1993PhRvE..48.2547M Using their ...
January 13, 2015

math
Well, we don't like it I just makes things confusing in answering questions.
January 13, 2015

math
http://www.jiskha.com/display.cgi?id=1421157183 Why do you keep switching names ?
January 13, 2015

math
complementary angles add up to 90 so if your angle is x its compliment would be 90-x twice its complement would be 2(90-x) "angle if it is 6 degree less than twice its complement" ---> x = 2(90-x) - 6 solve for x, then check if your answer satisfies the "...
January 13, 2015

math
not very likely! that would make the perimeter of the square alone equal to 512 wouldn't your equation have been 4x + 3(x-5) = 251 ?? I get x = 38 (which meets all the conditions)
January 13, 2015

math
I will set up your definitions let each side of the square be x then each side of the triangle is x-5 "the sum of the perimeters of the two figures is 251 cm" translate this into your equation, then solve for x Replace you x value in the definitions. let me know what...
January 13, 2015

math
width --- x length --- x+12 perimeter = 2xwidth + 2xlength 2x + 2(x+12) = 60 etc should be easy
January 13, 2015

math
short piece ---- x longer piece ---- 2x x + 2x = 34 take over
January 13, 2015

trigonometry
Did you make a sketch ? I filled in all your data , and you actually have redundant information we can simply take tan 39° = h/3 h = 3tan39 = 2.44 m
January 13, 2015

math,trigonometry
Write down the formula, then read it out loud
January 13, 2015

math
prob = (1/12)(1/7) = 1/84
January 13, 2015

algebra
1. No, she picks only one clip If we consider only the clips, there are 12 clips that are either blue or yellow, so the prob(blue or yellow) = 12/24 = 1/2 I have ignored the pushpins, since I assume she is able to distinguish between paper clips and pushpins when randomly ...
January 13, 2015

Algebra
You could have easily checked your answer by replacing them in the original question. here is what I did: 7c + 6o = 366 , I will work in cents 10c + 3o = 339 double the 2nd: 20c + 6o = 678 7c + 6o = 366 subtract them: 13c = 312 c = 24 back into 1st: 7c + 6o = 366 7(24) + 6o = ...
January 13, 2015

math
NOW: Martha --- x John ----- x+2 After 10 years: Marta ---- x+10 John ------x + 12 their sum 10 yrs from now = 2x + 22
January 12, 2015

propability
Since he puts the olives back, the second result is independent of the first prob(black,green) = (15/36)(21/36) = 35/144
January 12, 2015

math
women -- 3x men ---- 3x/2 children -- 9x men + children = 3x/2 + 9x = 3x/2 + 18x/2 = 21x/2
January 12, 2015

math
total coins ---- x foreign coins --- x/4 mexican coins -- (2/5)(x/4) = x/10 non-mexican foreign coins = (3/5)(x/4) = 3x/20 so 3/20 of the collection is non-Mexican foreign coins check: assume there are 60 coins so 1/4 are foreign or 15 of them 2/5 of those are Mexican or 6 are...
January 12, 2015

math
The logic of this question escapes me. Why would a "preferred" CD earning 1% have an advantage over a Standard CD that earns 2% anyway, so suppose he invests his $8000 at 2% he wants $2000 interest (to get to the 10,000 minimum ?? ) 2000 = 8000(.02)t t = 2000/(8000(....
January 12, 2015

algebra
for the first one, 5n - 3 = 447 5n = 450 n = 90 Yes, 447 is in the sequence and it is term(90) D) 14-3n = 447 -3n = 433 n = -433/3 , makes no sense, since n must be a natural number So, 447 cannot be a term in this sequence Do the others the same way
January 12, 2015

Math
jog : walk = 1/2 : 3/4 = 2 : 3 = 2/3 : 1 he jogs 2/3 mile for every mile he walks
January 12, 2015

Calculus
if f ' (x) > 0 , then the function is increasing if f ' (x) < 0 , then the function is decreasing so find the first derivative, and investigate it
January 12, 2015

Math
since the average of the 5 flight is 2 : 28 the total time was 5(2:28) = 10:140 = 12:20 first 4 flights: 2 : 10 3 : 20 1 : 15 2 : 40 ------ 8 : 85 = 9 : 25 last leg = 12:20 - 9:25 = 2 : 55 Too bad the world can't can convert to "metric time" It would make things ...
January 12, 2015

Geometry
Steve is right, I can't be bothered to find my error in all my mess.
January 12, 2015

Geometry
let the radius of circle R be r let the radius of circle W be w recall that arclength = rØ, where Ø is the angle in radians arc length on first circle = (π/2)r arc length of 2nd circle = (π/3)w but they are equal πr/2 = πw/3 r = 3w/2 area of ...
January 12, 2015

Math
yes
January 12, 2015

Calculus
yes, start with a = -5 v = -5t + c , where c is a constant given: when t = 0 , v = 25 25 = -5(0) + c c = 25 ,so v = -5t + 25 when car stops, v = 0 0 = -5t + 25 t = 5 it takes 5 seconds to stop
January 12, 2015

12 U Math
So I read it as: log2 x + log2(x+2) = 3 log2(x(x+2)) = 3 x(x+2) = 2^3 x^2 + 2x - 8 = 0 (x+4)(x-2) = 0 x = -4 OR x = 2 but in log x, x≥0 by definition x = 2
January 12, 2015

Algebra
no, they are perpendicular I one line has a slope of a/b then a perpendicular line has slope of -b/a , that is, one slope is the opposite reciprocal of the other. That is the case here: 3/2 vs -2/3
January 12, 2015

Algebra
slope of first line = 3/2 slope of 2nd line = -2/3 draw your conclusion based on what you must have learned about lines and their slopes
January 12, 2015

Maths Mechanics
So make sketch , on the y-axis mark off 300 From there draw a 45° angle line ( NW) and make it 40 units Joint the endpoint to the origin. That last line is your resultant I see a cosine law application Two sides of 300 and 40 with an angle of 135° between them
January 12, 2015

Algebra
a line parallel to y = 3x - 5 must look like y = 3x + b, that is, it can only differ in the constant, the slope stays the same. So we need to find that constant b. But we know that (3,1) lies on it, so in y = 3x + b 1 = 3(3) + b b = -8 new equation: y = 3x - 8
January 12, 2015

math
n + 20 = 80 , becomes n + 3 = ??? what did you do to 20 to bring it down to 20 ?? I bet you subtracted 17. So do the same thing to the right side. You said "I know whatever I do on one side I do on the other side " , but you didn't do it
January 12, 2015

Math
-2x^2+8x-6>0 2x^2 - 8x + 6 < 0 x^2 - 4x + 3 < 0 (x-3)(x-1) < 0 y = x^2 - 4x + 3 is a parabola opening upwards with x-intercepts at 3 and 1 so it is below the x-axis, ( < ) , for 1 < x < 3
January 12, 2015

Math
5^(4/3) = (5^4)^(1/3) = cuberoot (625) I would consider 5^(4/3) as simplified
January 12, 2015

Math
mmmh, "square root" always means index 1/2 "square" always means index 2
January 12, 2015

Math
I have no clue what you mean. Type it out in symbols instead of words To me "2square root 6 the same as square root 6" means 2√6 = √6
January 12, 2015

Math
Is 2√6 = √6 ??????? Are 2 apples the same as 1 apple ? Are 200 kg equal to 100 kg ? etc ? Don't you have a calculator?
January 12, 2015

Math
mmmmh, can you solve 25t - 80 = 60 ?
January 12, 2015

Algebra
children --- x adults -----9-x 210x + 315(9-x) = 2205 solve for x , should be straightforward. BTW, $315 for a trip to Hawaii? Time to update that Math textbook.
January 12, 2015

Math
ln (x^3) is indeed equal to 3ln x perhaps your calculator is reading your input as (ln x)^3 which of course is different verification by Wolfram: http://www.wolframalpha.com/input/?i=plot+y+%3D+log%28x%5E3%29+%2C+y+%3D+3log%28x%29 now change your input line from ln(x^3) to ln(...
January 12, 2015

Math
unless your ( bracket has a different meaning from the [ bracket, they are the same, both equal +9 or plain ol' 9
January 12, 2015

addmath A.P.
if in an AP, 2x+y - x = 9x-y - (2x+y) x + y = 7x - 2y 3y = 6x y = 2x also: x + 2x+y + 9x - y = 60 12x = 60 x = 5 , then y = 10 so the first term is x or 5 common difference = 2x+y - x = x+y = 15 term11 = a+10d = 5 +150 = 155 check: first 3 terms are: 5 , 20 , 35, ... is their ...
January 12, 2015

addmath
first condition: 3k - k = k+1 - 3k 4k = 1 k = 1/4, you had that so we have *, *, *, *, k , 3k, k+1 a+5d = 3k = 3/4 a + 4d = k = 1/4 subtract them d = 1/2 in a+4d = 1/4 a + 2 = 1/4 a = 1/4-2 = -7/4
January 12, 2015

Pre-Cal
let the radius of the circle be r let the side of the square be x 4x + 2πr = 360 2x + πr = 180 or x = (180- πr)/2 x^2 = πr^2 x = r√π (180 - πr)/2 = r√π 180 - πr = 2r√π 180 = 2r√π + πr r(2√&#...
January 12, 2015

trigo
in your sketch mark the top of the mountain as P and its base as Q Label AB = 562 and mark you angles In triangle ABP angle A = 22° 30' angle B = 180° - 30° 40 = 149° 20' angle C = 180 - A-B = 8° 10' by the Sine Law, you can find BP , which is ...
January 12, 2015

trigonometry
There are two different cases here, you don't say if they are on the same side of the plane, or opposite sides of the plane. (eg. both looking east , or one looking east the other looking west) I have them on opposite sides, horizontal distance from plane of #1 tan22.5 = ...
January 12, 2015

Please check my Calculus
All 3 are correct
January 12, 2015

alegbra 2
((x+h)^(-3)-x^(-3))/(h) = ( 1/(x^3 + 3x^2h + 3xh^2 + h^3) - 1/x^3) )/h common denominator at the top = ( (x^3 - x^3 - 3x^2h - 3xh^2 - h^3)/(x^3(x^3 + 3x^2h + 3xh^2 + h^3) )/h = ( -3x^2 - 3xh - h^2)/(x^3(x^3 + 3x^2h + 3xh^2 + h^3) ) checking: if I let h = 0 this reduces to -3x^...
January 12, 2015

Calculus
the top factors, so f(x) = (x+1)(x+3)(x+4)/(x+4) = x^2 + 4x + 3 , x ≠ -4 f ' (x) = 2x + 4 = 0 for a max/min 2x + 4 = 0 x = -2 Since the function is basically the parabola y = x^2 + 4x + 3 , with a hole at (-4,3) which opens up, x = -2 will produce a minimum f(-2) = 4...
January 11, 2015

Calculus
f ' (x) = 15x^4 - 15x^2 = 0 for a max/min 15x^2(x^2 - 1) = 0 x=0 or x=±1 to determine if these yield a max or a min look at the 2nd derivative f '' (x) = 60x^3 - 30x f "(0) = 0 , so x = 0 yields a point of inflection f "(1) = 60-30 > 0 , so x = ...
January 11, 2015

Reiny
Well Dustin, after teaching this stuff for about 35 years, it becomes part of your "permanent memory". I have been retired for 17 years and I try to keep my mind active doing this voluntary tutoring. I taught in Ontario, all grade levels and all math courses, but ...
January 11, 2015

math
Derek , how are you
January 11, 2015

derek --> steven ? math
why are you switching names
January 11, 2015

Geometry
why not use the value of π on you calculator I get r^2 = 41.730426.. r = 6.4599
January 11, 2015

Algebra 2
a + k = 240 5a + 3.5k = 1140 solve them
January 11, 2015

Algebra 2
any equation of the form y = k is a horizontal line any equation of the form x = c is a vertical line so from the point (2,3) x = 2
January 11, 2015

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