# Posts by Reiny

Total # Posts: 38,315

**Math**

Damon did this for you on Saturday. What part of his solution did you not like ?? http://www.jiskha.com/display.cgi?id=1483831115

**Pre-Calculus**

radius ---- x height ---- x+5 V = ? r^2 h = ?(x^2)(x+5) , but x = d/2 = ?(d^2/4)(d/2 + 5) = ?( d^3/8 + d^2/4) or = (1/8)?(d^3 + 2d^2) or = (1/8)? d^2(d + 2) or ....

**Pre-Calculus**

make a sketch to see that V = x(11-2x)(8.5 - 2x) = x(93.5 - 39x - 4x^2) = 93.5x - 39x^2 - 4x^3 dV/dx = 93.5 - 78x - 12x^2 = 0 for a max of V solve for x

**Math- Sequences and Series**

n = 1 , S(1) = 1 - 4 = -3 n= 2, S(2) = 4 - 8 = -4 n = 3, S(3) = 9 - 12 = -3 n = 4, S(4) = 16 - 16 = 0 term(1) = -3 term(2) = sum(2) - sum(1) = -4-(-3) = -1 term(3) = sum(3) - sum(2) = -3 -(-4) = 1 term(4) = sum(4) - sum(3) = 0 -(-3) = 3 so the first 4 terms are -3, -1, 1, 3 ...

**Math**

sum(10) = a(r^10 - 1)/(r-1) 699050 = a(4^10 - 1)/3 2097150 = a(1048575) a = 2

**Math**

H(x)= -3x^2+24x-46 = -3(x^2 - 8x + ....) - 46 = -3(x^2 - 8x + 16) - 46 + 48 = -3(x - 4)^2 + 2 vertex is (4, 2) or for f(x) = ax^2 + bx + c the x of the vertex is -b/(2a) for H(x)= -3x^2+24x-46 x of the vertex is -24/-6 = 4 H(4) = -48 + 96 - 46 = 2 vertex is (4,2)

**Math**

What is the method you were taught for this procedure, since there are several ways to do this?

**Math**

a@b = 3a + 2b u@v = 3u + 2v = 20 v@u = 3v + 2u = 20 add them: 5u + 5v = 40 u + v = 8 then 2u@3v = 6u + 6v = 6(u+v) = 6(20) = 120

**math**

Let the number of boys be 3x let the number of girls be 4x ( notice 3x : 4x = 3 : 4 ) given : 4x = 200 x = 50 So we have 150 boys and 200 girls, for a total of 350. ( notice 150:200 = 3:4 , as required)

**MATHS**

yes, join the centroid to each of the vertices

**Math(simple interest)**

amount invested at 7.5% ---- x amount invested at 9% ----- 2x amount invested at 8% = 10000-2x-x = 10000 - 3x .08(10000-3x) + .09(2x) + .075x = 845 times 1000 80(10000-3x) + 90(2x) + 75x = 845000 now it is easy, just solve for x, then back-substitute into my definitions

**Math**

prob(picking a red, then a green) = (5/11)(2/10) = 1/11 Working in the prob that he will also eat it needs more information. e.g. How hungry is he? Will he eat it now, or later, etc

**math**

Too many unknowns here. Is this compound interest or simple interest? Are the instalment payments made monthly or ? Since it will take more than a year to pay it with monthly instalments, I will assume compound interest. i = .10/12 = .00833... then 500(1 - 1.008333...^-n)/....

**Algebra 1**

everything factors nicely. Things are already partially factored giving you clues as what the other factors will be (X^2 - 9)(7x + 21) / (x- 3)(x^2 + 6x + 9) = (x+3)(x-3)(7)(x+3) / ( (x-3)(x+3)(x+3) = 7 , x ? ± 3

**Algebra**

look back at your previous post where I answered this. How did your name change from Clarise to Clary?

**Math**

cost of hat ---- x cost of shoes ---- x+9 x + 2(x+9) = 60 solve for x

**Math**

Did you make a sketch? You did not state where the right angle is, I will assume it is at L In triangle JMK, we have bisected angles of 60° and 30°, so angle JMK = (180 - 30 - 15)° = 135°

**Math**

1.5 hens can lay 1.5 eggs in 1.5 days 3 hens can lay 3 eggs in 1.5 days 3 hens can lay 12 eggs in 6 days double the hens would double the number of eggs without changing the time multiplying the the time would multiply the eggs without changing the number of hens

**Algebra 1**

?6 + ?54 + ?150 = ?6 + ?9?6 + ?25?6 = ?6 + 3?6 + 5?6 = 9?6

**Math**

number of large tables ---- x number of smaller tables = 19-x 6x + 4(19-x) = 90 solve for x

**Math**

The five friends received 7 marbles each, so that accounts for 35 marbles. Including the 12 he kept for himself, the brother received 47 marbles from Natalie. But that was only 1/3 of what she had , so she had 3(47) or 141 marbles to begin with.

**Algebra 8th**

a(1)=17 a(n+1)=a(n)-3 a(2) = a(1) - 3 = 17-3 = 14 a(3) = a(2) - 3 = 14-3 = 11 decreases by 3 each time, ? - 3 = 17 looks like a(n) = -3n+ 20 a(1) =20. a(n+1)=1/2*a(n) a(2) = (1/2) a(1) = 10 a(3) = (1/2) a(2) = 5 so 20, 10, 5 <---- a GS with a = 20 r = 1/2 t(n) = ar^(n-1) t(...

**Math**

weight of each melon ---- x kg 8x + 1.25 = 19.25 solve for x

**Math**

doesn't matter what the first roll is, but there are 6 ways to match it so prob(of your case) = 1/6

**math**

number of books ---- x number of pens ----- y number of pencils --- 30-x-y (we know x and y must be whole numbers) 30x + 24y + 6(30-x-y) = 300 30x + 24y + 180 - 6x - 6y = 300 24x + 18y = 120 4x + 3y = 20 y = (20 - 4x)/3 try x = 1 , 2, 3, or 4 for y to be a whole number, x has ...

**math**

h/53 = tan 61° solve for h

**Math**

let the smaller be x then the larger is x+4 x^2 + (x+4)^2 = 520 x^2 + x^2 + 8x + 16 = 520 2x^2 + 8x - 504 x^2 + 4x - 252 = 0 (x+18)(x-14) = 0 x = -18 or x = 14 2 cases: if x = -18 , the smaller is -18, the larger is -14 if x = 14, then the larger is 18

**pre cal**

recall sinØ = y/r from the given: r^2 = 4^2 + (-8)^2 = 80 r = ?80 = 4?5 since (4,-8) is in quad IV , and in IV the sine is negative, sinØ = -8/4?5 = -2/?5 or -2?5/5

**algebra story problems**

when is 16t^2 = 16 ?? same question about 4 years ago? http://www.jiskha.com/display.cgi?id=1375384643

**Business Math**

when is 4000(1.031)^n = 12000 ? 1.031^n = 3 take log of both sides, and use log rules n log 1.031 = log 3 n = log3/log1.031 = appr 35.99 So it would take 36 half-years or 18 years check: 4000(1.031)^36 = 12005.27 , not bad

**Math**

you are both welcome

**Math**

When you multiply or divide an inequation by a negative number the inequality sign must be reversed. e.g. -5 < 4 is a true statement, but when I multiply be -1, the statement 5 < -4 would be false but 5 > -4 makes it true, so ..... -5p > -55 divide both sides by -5...

**plz sequence sir steve reiny bob damon i need u**

Here is my attempt: a,b, and c are in AS, so b-a = c-b c = 2b-a a, c, b are in GS, so c/a = b/c c^2 = ab (2b-a)^2 = ab 4b^2 - 4ab + a^2 = ab 4b^2 - 5ab + a^2 = 0 (b-a)(4b - a) = 0 b = a or b = a/4 but the numbers are supposed to be distinct, so can only go with b = a/4 also c^...

**seven lakes junior high school Math**

Visualize it. make a sketch of the x-y plane and grid on a piece of paper. Now fold it so that quadrant II falls on quadrant III. Does the crease fall along the horzontal (x-axis) or the vertical (y-axis) ??

**Calculus**

I agree with Damon's answer I followed your steps and found and error around the third last step ok at : dh/dt = -12 / (81*pi) , but then .... dh/dt = -4/(27?) ----> you had -4/(9?) = -.04716 you can also simplify your steps: from v = (1/12) * pi * h^3 why not just ...

**math**

If you meant the angle is 30°, then tan30° = h/10 h = 10tan30° = ...

**Grade 6, percentage**

original amount ---- $x amount spent on transport = .12x amount left = .88x he spends 1/4 of that on food leaving him with (3/4)(.88x) = .66x gives $1320 to parents, leaving him with .66x - 1320 actual cost of bike = .8(825) = 660 Assuming he spent all of his leftover money on...

**math**

other side = x hypotenuse = ?(x^2 + 12^2) x + ?(x^2 + 144) = 18 ?(x^2 + 144) = 18-x square both sides: x^2 + 144 = 324 - 36x + x^2 36x = 324-144 x = 5 your triangle is 5 by 12 with a hypotenuse of 13 check: is 5+13 = 18? YUP is 5^2 + 12^2 = 13^2 ? , YUP you should recognize ...

**Algebra**

correct There are some minor flaws in your presentation x+y=6300(-11) should have been -11(x+y)=6300(-11) to get -11x -11y = -69300 0.11x+ 0.08y=597(100) should have said 100(0.11x+ 0.08y)=597(100) to get 11x + 8y = 59700 The way you have it, the left side is not equal to the ...

**Grade 6, percentage**

fix this typo: "he gave 1320% to his parents"

**math**

Q={x|x is an integer and -4<x<-2} = {-3} How many integers lie between -4 and -2 ?

**Grade 6, percentage**

number who took the bus ---- x "there were 360 more pupils who walked than those who took buses" --> number who walked = x+360 (x+360) : x = 65% : 35% = 13 : 7 (x+360)/x = 13/7 13x = 7x + 2520 6x = 2520 x = 420 so 420 took the bus, and 780 walked total number of ...

**calculus**

I don't see the problem with this limit question other than your notation. I will assume you meant: lim 4^(2x -1) , as x ---> 0 Since you don't want to use substitution, which is always my first step, you could look at the graph of y = 4^(2x-1) and observe what it ...

**value**

Make your vector diagram. You should have a triangle with sides 200 and 100 and the contained angle of 135°. The third side is your resultant velocity, call it x by the cosine law: x^2 = 200^2 + 100^2 - 2(200)(100)cos 135° continue let me know what you get

**math**

I will assume that in each case, the first ball drawn is not returned. prob(2 blue) = (12/35)(11/34) = .. prob(2 yellow) = you do it prob(red, then yellow) = (14/35)(9/34) = ... prob(red, then yellow) = your turn again

**Pre calc**

the slope-yintercept form is y = mx +b so why not plug in your given data ?

**Math**

Since the new line is parallel to x+3y=5 it differs only in the constant: x+3y=c plug in (-1,4) to find c and you are done

**Maths**

let the amount he spent on food, utilities, socializing and savings be 2x , 7x, 3x, and 4x respectively 2x = 2500 solve for x, then sub back into my definitions add them all up to get the total expenses. divide this by .8 to get his total earnings.

**am I right ? or no?**

You did not show your answers, how can we check ?

**Trig**

make sketches of each triangle for sinx = 4/5 sin^2 + cos^2 x = 1 16/25 + cos^2 x = 1 cos^2 x = 9/25 cos x = 3/5, in quadrant I siny = 5/13 using your triangle and Pythagoras cosy = -12/13 , since we are in quadrant II sin(x+y) = sinxcosy + cosxsiny = (4/5)(-12/13) + (3/5)(5/...

**Algebra 2**

T)r) = 100 (1.1)^r plug in r = 8 and calculate

**algebra**

but the integers are consecutive, so smaller number --- x next integer ---- x+1 x + x+1 ? 9x - 5(x+1) 2x + 1 ? 4x - 5 2x ? -6 x ? -3 Also consider Steve's other possibility .

**Maths**

but Mike, you said that the two sides are equal, so the triangle is isosceles, and the angles would be (180 - 1/60)/2 ° = 89.99166.. ° each or your top angle is 1 minute of angle the base angles would be (10800 - 1)/2 minutes of angle = 5399.5 minutes = 89.99166.. °...

**Maths**

compare your answer of 14,730,933,173.9 with mine: 1.4725 x 10^10 they are the same answer correct to 4 significant digits.

**Maths**

Looks like you are doing some astronomical type of calculation. Make an exaggerated diagram of an isosceles triangle with a vertex angle of 1/60° or 1 minute of angle and mark each of the equal sides as 50,620,..... I am tempted to state your side as 5.0621 x 10^13 , or ...

**math**

number of metres of fencing = 3200/1.6 = 2000 m so each side of the square is 2000/4 or 500 m and its area is 500^2 m^2 cost of "reaping" = 500^2 /100 * 1.2 = 3000 rupees

**math**

a = 16 ar^4 = 9 sub in a = 16 16r^4 = 9 4r = ± 3 r = ± 3/4 7th term = ar^6 = 16(±3/4) = 16(729/4096) = 729/256

**Math**

length of BC = ?( (5-1)^2 + (1-3)^2) = ?(16+4) = ?20 = 2?5 since BM = (1/2)BC BM = ?5

**Statistics**

number of two-digit numbers: 10, 11, ... , 99, ----> 90 of them (1 - 9 are missing) smaller than 20: 10,11, ... , 19 ----> 10 of them prob( < 20) = 10/90 = 1/9 use the same type of analysis for the two other parts, let me know what you get.

**Maths**

solve: 4x - 23 = (1/3)(54)

**Maths**

looks like your standard: x = my + b case1: y = 2 when x = 15 15 = 2m + b ** case2: y = 4 when x = 27 27 = 4m + b *** subtract ** from *** 12 = 2m m=6 from ** 15 = 12+b ---> b=3 x = 6y + 3 when y = 7 x = 42+3 = 45

**Math**

new length = 1.15(8) = ... new width = ....

**maths**

original dimensions ---- w by l original area = wl new width = 9w/10 new length = L L(9w/10) = lw L = lw/(9w/10) = (10/9)l = 1.111.. so the length would have to increase, not be reduced, as your question stated. The increase is 10/9 of the original or appr 11.1% check: if wl ...

**Maths**

(4/3) ? r^3 = 250?/3 4?r^3 = 250? r^3 = 250/4 or 500/8 r = 500^(1/3) / 2 SA = 4? r^2 = 4? (500)^(2/3) / 8 = (1/2)(500)^(2/3) ?

**Algerbra**

The two areas of similar objects are proportional to the square of their corresponding sides. The two volumes of similar objects are proportional to the cubes of their corresponding sides. sides of model^2 : sides of statue^2 = 6 : 253.5 side of model : side of statue = ?6 : ?...

**Maths**

looks like your base is x-2 and the height is x, so (1/2)(x)(x-2) = 2.5 x(x-2) = 5 x^2 - 2x - 5 = 0 solve for x and take it from there

**Mathmatics**

Just re-arrange it .... 3x^2 - x^3 + 3 = 0 -x^3 = -3x^2 - 3 x^3 = 3x^2 + 3 divide both sides by x^2 x = 3 + 3/x^2 let x = 3.2 RS = 3+ 3/10.24 = 3.29296875 sub that into the RS RS = 3 + 3/(3.2929...)^2 = 3.276659... new RS = 3.279420685 new RS = 3.278950402 new RS = 3.279030424...

**Maths**

your sequence has a = 7, d = 6 term(n) = a+(n-1)d = 7 + 6(n-1) = 7 + 6n - 6 = 6n + 1 term(n+1) = a + (n-2)d = 7 + 6(n-2) = 7 + 6n - 12 = 6n - 5 (6n+1)^2 - (6n-5)^2 = 36n^2 + 12n + 1 - (36n^2 - 60n + 25) = 72n - 24 = 24(3n - 1) which is clearly a multiple of 24 (anything ...

**Math**

make a sketch and use a simple ratio: h/55 = 8/11 solve for h

**Math**

f (g(x) ) = (1 + g(x) )/(1 - g(x) ) = (1 + x/(1-x) / (1 - x/(1-x) ) multiply top and bottom by (1-x) = (1 - x + x) / (1 - x - x) = 1/(1 - 2x) check: let x = 2 g(2) = 2/(1-2) = -2 f(g(2)) = f(-2) = (1-2)/(1+2) = -1/3 in mine f(g(2)) = 1/(1-4) = -1/3 it is "highly likely&...

**geometry**

Follow similar steps I used in your previous post. Make sure you use the definition of supplement of an angle.

**geometry**

let the angle be x then its complement is 90-x 90-x = x + 18 -2x = -72 x = 36 check: the angle is 36° and its complement is 54° which is 18° more than 36°

**Geometry**

first transformation: (x,y) ---> (x+5,y) (-3,-3) ----> (2,-3) second transformation: reflection in y = 1 (x,y) ---> (x, 2-y) (2,-3) ----> (2, 5) A' is (2,5)

**Kudos for Steve**

What a splendid observation ! Ignore my gibberish, it must contain an error somewhere anyhow.

**maths**

tanx - ?3 + tan2x + ?3tanx tan2x = 0 tanx - ?3 + tan 2x(1 + ?3tanx) = 0 recall tan 2x = 2tanx/(1 - tan^2 x) tanx - ?3 + 2tanx/(1 - tan^2 x)(1 + ?3tanx) = 0 times (1 - tan^2 x) tanx - tan^3 x - ?3 + ?3tan^2 x + 2tanx(1 + ?3tanx) = 0 let tanx = y for easier typing y - y^3 - ?3...

**algebra**

Can you think of 2 numbers which have a sum of 11 and when multiplied give a product of -42 ? how about -3 and +14 ? Now form the factors

**algebra**

Steve answered this same question for you over a week ago http://www.jiskha.com/display.cgi?id=1482520904

**math**

looks like you defined the larger as x and the smaller as y so x - y = 26 is correct then.... "one number is three times the other " ---> x = 3y now sub that into the first equation: x - y = 26 3y - y = 26 2y = 26 y = 13 then x = 3y = 3(13) = 39

**Algebra**

Why not follow the same steps I showed you for the questions similar to this one. Let me know how you make out.

**Math :)**

It helps to make a sketch in this case, I assume you did that (-2,-1) ---reflect in y=-5 ---> (-2,-9) notice the midpoint of these points lies on y = -5 (-2,-9) ---reflect in x = 1)---> (4,-9) again, notice the midpoint of these two points lies on the line x = 1

**trigonomentry**

looks like your equation to solve is incomplete.

**Math**

Just like in trigonometry, a counterclockwise rotation is considered positive.

**Algebra**

Start with what I gave you here: http://www.jiskha.com/display.cgi?id=1483383485 Pick any two points on y = ?x e.g. (9,3) and some other point find the equation of the straight line passing through two points, and you are done

**math**

"the fifth term of an arithmetic progression is 19" ----> a+4d = 19 " the fourteenth term is 55" ----> a+13d=55 subtract the two equations: 9d = 36 d = 4 in a+13d = 55 a + 13(4) = 55 a = 3

**Algebra**

try y = ?x and y = (1/4)x + 1 see: http://www.wolframalpha.com/input/?i=y+%3D+%E2%88%9Ax+,+y+%3D+(1%2F4)x+%2B+1

**Math**

15 metres is 1500 cm. So what is 1500/75 ? This is a silly question. The snowball would have hit the ground long before it traveled 15 m due to gravity. The speed of 75 cm/s is way too slow.

**Math**

What a sucker you would be to play this game! the expected winnings on one play is 15 cents. You are playing this 30 times, so your can expect to win $4.50 , but you spent $30 to play those games.

**@ R**

Why did you repost this question ?? Just noticed that Steve answered it for you several days ago http://www.jiskha.com/display.cgi?id=1483135842

**Math**

Assuming you meant: f(x)=?x^3 ?x^2 +16x+16 f ' (x) = -3x^2 - 2x + 16 f ''(x) = -6x - 2 If you are studying Calculus or Pre-Calculus, you MUST know how to do this. if f(x) = 0 ?x^3 ?x^2 +16x+16 = 0 x^3 + x^2 - 16x - 16 = 0 by grouping, x^2(x+1) - 16(x+1) = 0 (x+1)(x...

**Math**

No idea what a "tape diagram" is, but the question is easy to solve in the traditional way: number of adults ---- 45 number of students ---- 90 Just noticed that there is NO question in your post. If you want the return for the museum Return = 25(45) + 12(90) = $2205

**math C2 sequences and series**

8th term of AS = a+7d 4th term of AS = a+3d 2nd term of AS = a+d then, if they form the first three terms of a GS (a+3d)/(a+7d) = (a+d)/(a+3d) (a+3d)^2 = (a+7d)(a+d) a^2 + 6ad + 9d^2 = a^2 + 8ad + 7d^2 2d^2 - 2ad = 0 d(d-a) = 0 d = 0 or d = a but we are told that d ? 0 , so d...

**Math**

what is 100000(.95)^2 ?

**Math**

let the number be x 1/(x-4) = 2(1/x) solve for x

**Geometry**

Did you know that the slope of a line equals the tangent of the angle that the line makes with the x-axis ? so tan45° = 1 so we know the slope of the line is 1 (-5-5)/(a-4) = 1 a - 4 = -10 a = -6 Check with a quick sketch of the situation.

**math**

Even though with only 3 terms, 20 + 12 + 36/5 + .... seems to be the sum of an infinite series with a = 20 and r = .6 Sum(all terms) = a/(1-r) = 20/(1-.6) = 20/.4 = 50 btw, " ---tend as n" makes no sense.

**Math**

4d^2= (d+4)(-d+12) 4d^2 = -d^2 + 12d - 4d + 48 5d^2 - 8dd = 48 d^2 - (8/5)d = 48/5 d^2 - (8/5)d + 16/25 = 48/5 + 16/25 (d - 4/5)^2 = 256/25 d - 4/5 = ± 16/5 d = 4/5 + 16/5 OR d = 4/5 - 16/5 d = 4 or d = -12/5

**math**

Well, did you use your graph as instructed? What did you get?

**Math**

let the tens digit be x, and the unit digit be y So the number is 10x + y, the number reversed is 10y + x 10x+y - (10y+x) = 9 9x - 9y = 9 x - y = 1 or x = y+1 ** 2x = 7y-8 sub in ** 2(y+1) = 7y - 8 2y + 2 = 7y - 8 -5y = -10 y = 2 The number is 32 check: the number reversed is ...

**math(geometric series)**

2nd term is 3/2 --- ar = 3/2 sum of all terms is 8 a/(1-r) = 8 divide the first equation by the 2nd equation: (ar) / (a/(1-r)) = (3/2) / 8 r(1-r) = 3/16 r - r^2 = 3/16 3 = 16r - 16r^2 16r^2 - 16r + 3 = 0 (4r - 1)(4r - 3) = 0 r = 1/4 or r = 3/4 check for r = 1/4 a(1/4) = 3/2 a...

**math(A.P/G.P)**

Shall I assume that 2% p.a C.I means 2% per annum compounded instantaneously ? the amount = 55 e^.02t if 2005 ---> t = 0 then 2015 --- t = 10 amount = 55 e^(.02(10)) = 67.177 crores (is 1 crore equal to 10 million? I see one answer as 6700, but that would not match your ...