# Posts by Reiny

Total # Posts: 38,753

**Pre-Algebra**

simple case of Pythagoras h^2 + 16^2 = 20^2 solve for h

**math**

amount invested at 3% --- x intereste at that = .03x amount invested at 5% ---- 16000 - x interest at that = .05(16000-x) they are equal, so solve .03x = .05(16000 - x) 3x = 5(16000-x) carry on

**MATHS**

The width of the pathway is the unknown, let it be x m so make a sketch and you will see that the length of the whole thing is 120 + 2x and the width is 50+2x area of the whole thing = (120+2x)(50+2x) = 4x^2 + 340x + 6000 If the garden area is 6000, and the pathway is also ...

**Advanced maths**

a = 9 term(n) = a + (n-1)d = 105 (n-1)d = 105 - a = 105-9 = 96 sum(n) = (n/2)(2a + (n-1)d) = 741 (n/2)(18 + 96) = 741 n/2 = 6.5 n = 13 (n-1)d = 96 12d = 96 d = 8 the terms are 9, 17, 25, ..

**Maths**

Suppose we have n objects. In how many ways can I take all of them of course the answer to that is 1 way. but from the theory of combinations it would be n!/( (n-n)(n!) ) = n!/(0!n!) = 1/0! but we know that has to be 1 1/0! = 1, this can only be true if we define 0! = 1 That ...

**Calculus**

thanks for catching that, of course when you add 1 to -2 you get -1, not -3 - sometimes the simple things mess us up! Ok, then I should have had: ln (y-1) = -1/x + c and plugging in (1,2) ln 1 = (-1/1) = c c = 1, you had that. so we get to ln (y-1) = -1/x + 1 or (x-1)/x now ...

**Calculus**

dy/dx = (y-1)/(x^2) dy = (y-1)/(x^2) dx dy/(y-1) = x^-2 dx the next step is where you went wrong, ln (y-1) = (-1/3)x^-3 + c check by taking the derivative. given: the point (1,2) lies on it, so ln (2-1) = (-1/3)(1^3) + c 0 = -1/3 + c c = 1/3 ln (y-1) = (-1/3)x^-3 + 1/3 = ( -1/...

**correction - Statistics**

C(13,4)/C(52/4) = 715/270725 = 11/4165 or appr .002641 Nonetheless' second answer is not correct, should be (13/52)(12/51)(11/50)(10/49) which comes out to the same as my answer above "drawing" cards usually means that you are holding the cards in your hand, ...

**math**

how about the two points (0,0,3) and (3,3,0) ? a line containing those two point has direction [3,3,-3] or [1,1,-1] if reduced let's take the dot product of [1,1,-1] and [2,3,5] = 2 + 3 - 5 = 0 so if the dot product is 0, then the vectors are perpendicular. By now you ...

**math**

amount = 8000(1.04)^8 + 6000(1.04)^2 = ...

**algebra**

If you meant: (a+b)^3 - 8 then your answer is correct

**Maths**

The time taken is inversely proportional to the speed t = k/v if t = 10, v = 6 10 = k/6 k = 60 when v = 8 t = 60/8 = 7.5 minutes

**Maths - trigonometry**

secØ sin(36+Ø) = 0 secØ = 0 or sin(36°+Ø) = 0 secØ can never be zero, secØ?1 OR secØ ? -1 so: sin(36°+Ø) = 0 36+Ø = 0° or 180° or 360° or -180° ... then Ø = -36° , Ø = 144&...

**algebra**

I hope you mean: (v^2+6v+8)/(v^2+v-12) ÷ ((v+2)/(2v-6) ) = (v+2)(v+4)/((v+4)(v-3) * (2(v-3)/(v+2) = 2(v+2)(v+4)(v-3) / ( (v+4)(v-3)(v+2) ) = 2 , where v ? -4,-2, 3

**algebra**

correct, the division was exact with no remainder. the answer is 8x^2 + 20x + 24 synthetic division confirms it: 3 | 8 - 4 - 36 - 72 ........ 24 .. 60 .. 72 .... 8..20 .. 24 ... 0 the 8, 20, 24 represents 8x^2 + 20x + 24 the 0 shows no remainder.

**MATH**

Why don't you try it with two different functions, e.g. f(x) = x+2 , g(x) = 2x - 1 let y = f(x) + g(x) = x+2 + 2x - 1 = 3x + 1 is this a straight line ? so what do you think about a) ??? ... c) let y = f(x) * g(x) = (x+2)(2x-1) = 2x^2 + 3x - 2 Is a quadratic a straight ...

**math**

Do you have a typo? did you mean: Suppose x can be expressed as a function of y by x = 5y ? 3 ?? If so, then a) x + 3= 5y y = (x+3)/5 b) since all I did was to re-arrange the equation, I don't have two equations, it is the same equation. Of course all properties such as ...

**Trignometry**

just set it equal to 10 10 = 12+2.83sin((2?)/365(t-800) -2 = 2.83sin((2?)/365(t-800) -2/2.83 = sin((2?)/365(t-800) -.706713... = sin((2?)/365(t-800) using my calculator set to radians, taking the inverse sine of +.706713, I get a reference angle of .78484 radians but for the ...

**Math PLEASE HELP!!!!!!!!!!!!!!!**

let the distance be x miles let the normal speed by y mph time at normal speed = x/y but x/y = 4 x = 4y time at slower speed = x/(y-6) x/(y-6) = 4.5 4.5y - 27 = x 4.5y - 27 = 4y .5y = 27 y = 54 , x = 4(54) = 216 He lives 216 miles from work. normal speed is 54 mph. check: time...

**Mathematics**

age of each of the twins --- x mother's age = x+33 In 3 years from now: age of each of the twins = x+3 mother's age = x+36 x+36= 2(x+3 + x+3) solve for x, and sub into my definitions

**Math**

a) You will have to find the average time, which involves adding the 7 times and then dividing by 7 Too bad that "we" have not gone metric with units of time, so you will have to convert each of the times to a decimal number in terms of hours, (unless you use the D&...

**Pre calc**

cos(?) ? sin(?) = 1 , I will assume Ø from 0 to 2? cosØ = 1+sinØ square both sides cos^2 Ø = 1 + 2sinØ + sin^2 Ø 1 - sin^2 Ø = 1 + 2sinØ + sin^2 Ø 2sin^2 Ø + 2sinØ = 0 2sinØ(sinØ + 1) = ...

**algebra**

60 cm = .6 m one rotation = .6? m 80 km/h = 80,000 m/60 min = 400/3 m/min number of rotations/min = (400/3) / (.6?) = 70.7 rotations in a minute or 70.7/60 rotations per minute = 1.1789 rotations per second but 1 rotation = 2? radians, so the angular velocity = 2?(1.1789..) ...

**Maths**

I did this on Thursday http://www.jiskha.com/display.cgi?id=1492110004

**math**

p = k (q^2)(1/r) when p=36,q=3,r=4 so: 36 = k(9)(1/4) k = 36(4)/9 = 16 p = 16q^2/r when p=200, r=2 200 = 16q^2 /2 q^2 = 400/16 q = 20/4 = 5

**Math --- Oob**

The only difficulty here is that they use different unit of speed. we need 144 km/h to m/s 144 km/h = 144000 m / 3600 seconds = 400 m/s let the distance from p to q be x m time for first leg of trip = x/60 s time for 2nd leg = x/400 s avg speed = total distance over total time...

**Math please help me**

n! is a special mathematical operator. n! = 1x2x3x4x...x(n-1)x n e.g. 4! = 1x2x3x4 = 24 6! = 1x2x3x4x5x6 = 720 the n must be a whole number, and by special definiton 0!=1 This operator is used primarily in the calculations of permutations, combinations, and in statistics.

**algebra 2**

x + x+1 + x+2 = 90 solve for x sub into x+2

**Maths**

Well, a cylinder has volume ? r^2 h a cone has volume (1/3)? r^2 h So the cone would have a volume of (1/3)(12) cm^3 or 4 cm^3

**Math**

Just set up a ratio: (2/3) / 4 = x/9 4x = 9(2/3) = 6 x = 3/2 cups

**Math Double Check Me Please**

Betta Fish, your were right in #2, so there was no need to say anything about it. I only corrected your mistake in #1

**Math Double Check Me Please**

#1 I get s^2 = 6^2 + 8^2 = 100 s = 10

**Calculus**

dy/dx=150yx^14 divide both sides by y (dy/dx) / y = 150x^14 ln(y) = 10 x^15 + c but (0,6) lies on it, so ln 6 = 10(0) + c c = ln 6 ln y = 10x^15 + ln 6 is one such equation

**Linear algebra**

You have to be more precise in your notation, you probably meant: x k+2 = 3x k+1 + 10x k that is: x 0 = 1 = 5^0 x 1 = 5 = 5^1 x 2 = 3(5) + 10(1) = 25 = 25(1) = 5^2 x 3 = 3(25) + 10(5) = 125 = 25(5) = 5^3 x 4 = 3(125) + 10(25) = 625 = 25(25) = 5^4 x5 = 3(625) + 10(125...

**Maths**

i = .06/4 = .015 n = ? 200000(1.015)^n = 24000 1.015^n = 1.2 take log of both sides log (1.015^n) = log 1.2 n log 1.015 = log 1.2 n = log 1.2/log 1.015 = 12.25 quarter years = appr 3 years and 3 weeks

**Trig**

the way you typed it: 1+tan^2x/tan^2x = 1 + 1 = 2 what you probably meant: (1+tan^2x)/tan^2x = sec^2 x / tan^2 x = (1/cos^2 x) / (sin^2 x/cos^2 x) = 1/sin^2 x or = csc^2 x

**Calculus**

Bob: what is your question ? YTLG: what question are you answering ?

**Calculus**

f(x) = 9/x^3 -10/x^7 = 9x^-3 - 10x^-7 If F'(x) = f(x) then F(x) = (9/-4)x^-4 - (10/-8)x^-8 + c = (-9/4)(1/x^4) + (5/4)(1/x^8) + c You have F(1) = ), since the ) is on the same key as 0, I will assume you meant: F(1) = 0 0 = -9/4 + 5/4 + c c = 1 F(x) = (-9/4)(1/x^4) + (5/4...

**Calculus**

Follow the same steps I used in your other post of this type of problem.

**Trig**

Under a dilation of -3, the point (5,-3) would be (-15,9) Where is that point located?

**Math**

q ' (x) = 2x^3 + 2bx + 32 q '' (x) = 6x^2 + 2b both are equal to zero, so 6x^2 + 2b = 0 2b = -6x^2 b = -3x^2 and 2x^3 + 2bx + 32 = 0 2x^3 + 2(-3x^2)(x) + 32 = 0 -4x^3 = -32 x^3 = 8 x = 2 then b = -3(4) = -12 check: q(x) = (1/2)x^4 - 12x^2 + 32x - 5 q ' (x) = 2x...

**Pre calc**

done many times before. Look at Related Questions below, here is one of them http://www.jiskha.com/display.cgi?id=1491961364

**Math**

Jane ---- x Fred ---- 2x+3 x + 2x+3 < 36 3x < 33 x < 11 Looks like Jane is less than 11 years old. testing: let Jane be 10 then Fred is 23 , their sum is < 36

**value**

x + x^2 < 12 x^2 + x - 12 < 0 (x+4)(x-3) < 0 So where is the corresponding parabola below the x-axis ?? The intercepts are -4 and 3, so x+x^2 < 12 is true for -4 < x < 3, that is, all the numbers between -4 and 3 But you want only non-negative x's , so...

**Maxima**

I assume Maxima is some application which I don't have, so by the "good ol' fashioned way" ... 5 = ?(6*9.8(sin x-0.2 cos x)) square both sides 25 = 6*9.8(sinx - .2cosx) .42517.. = sinx - .2cosx .2cosx = sinx - .42517 square again: .04cos^2 x = sin^2 x - ....

**MATH**

I have a feeling that your definition of a#b contains a typo. I have suspicions about that second equal sign. Since the + and the = are on the same key on your keyboard, I suspect it should be + a#b=a^b-2ab + b^b(-a)^b+b^b 4#(-3) = 4^(-3) - 2(4)(-3) + (-3)^(-3) (-4)^(-3) + (-3...

**Pre calc**

start with : cos(?) = 5/13, ? in Quadrant IV you should recognize the 5-12-13 right-angled triangle and since cosØ = adjacent/hypotenuse x = 5, r = 13 , y = -12, since Ø is in IV and sinØ = -12/13 also tan(?) = ??15 = -?15/1 = y/x and ? is in II, y = ?15...

**Maths**

Make a sketch , complete the triangle draw a horizontal from the top of the man to the tower, then tanØ = 18.5/15 Ø = appr 50.96°

**Physics (Attempt 3 for help)**

look at the Related Questions from last Friday http://www.jiskha.com/display.cgi?id=1491587591

**Math**

16:15 or 4:14 pm in the US

**math**

prob(a 6) = 1/6 prob( purple) = 1/6 prob(as stated) = (1/6)(1/6) = 1/36

**Math**

Let that number of years be x Ethan --- 40+x son ------ 12+x 40+x = 5(12+x) 40+x = 60 + 5x -4x = 20 x = -5 it happened 5 years ago check: 5 yrs ago, Ethan was 35, son was 7 and 35 is 5 times 7

**math**

sum(8) = (8/2)(2a + 7d) = 60 2a + 7d = 15 sum(50) = (50/2)(2a + 49d) = 880 2a + 49d = 35.2 subtract them: 42d = 20.2 d = 202/420 = 101/210 2a + 7(101/210) = 15 2a = 349/30 a = 349/60 term(43) = a + 42d = 349/60 + 42(101/210 = 1561/60

**Math**

sum(5) = (5/2)(2a + 4d) = 30 2a + 4d = 12 a + 2d = 6 a = 6-2d so we can assign any value to d e.g. d = 7 then a = 6-14 = -8 one possible sequence is: -8 , -1, 6, 13, 20 (their sum is 30) let d = 3 a = 6-6 = 0 terms are: 0, 3, 6, 9, 12 (their sum is 30) your turn.

**math**

amount to be mortgaged = .9(290000) = 261,000 i = .10/12 = .008333... (keep as is in calculator memory) n = 30(12) = 360 payment = p p( 1 - 1.008333..^-360)/.008333 = 261000 I get p = $2290.46 I will do the "outstanding balance" after 5 years, you do the other two ...

**Math probability**

My Venn consists of two intersecting circles within a rectangle, rectangle is 30 from your data, I let the intersection of M and T be x Then the part of only M is 17-x, and the part of only T is 10-x n((TUM)')=5 --> The part outside the two circles but within the ...

**math**

Just consider the possible sums, then arrange the digits: 4+0+0 = 4 ---> 400 3+1+0 = 4 ---> 310 301 130 103 2+2+0 = 4 ---> 220 202 1+1+2 = 4 ---> 112 121 211

**math algebra three system equation**

A preliminary glance at the coefficients tells you that the y's would be the easiest to eliminate. As a matter of fact, you can do it in your head: add the first two equations: 5x + 8z = 73 , #4 mentally double the 2nd and add to the third: 11x + 16z = 151 , #5 double #4...

**please help, Word problem**

3h + 5d = 25 6h + 4d = 29 ----> 3h + 2d = 14.50 subtract this from the first: 3d = 10.50 d = 3.50 sub back into first to get h, the price of a hotdog.

**algebra**

adults ---- a children --- 288 - a solve for a: 9a + 2.5(288-a) = 1760

**Algebraic word problem**

The sum of their ages add up to 98 years --> a+b+c=98 Double Alex’s age and add to Ben’s gives 84 years 2a + b = 84 The sum of three times Alex’s age and twice Casey’s age is 163 ---> 3a + 2c = 163 form 2a+b = 84 ---> b = 84-2a I would now plug ...

**Math intermediate algebra**

shortest side --- x middle size ----- y largest side ----- z first equation is obvious: x+y+z = 33 , #1 second equation: "The sum of the length of the longest side and twice the length of the shortest side is 31 inches" ---> z + 2x = 31 , #2 third equation: "...

**Word problem**

you can use two variables: number of nickels --- x number of dimes ---- y x+y = 22 5x + 10y = 175 --> divide by 5 x + 2y = 35 subtract them: y = 13 sub back into x+y = 22 ----> y = 9 or, using one variable: let the number of nickels be x then the number of dimes = 22-x ...

**Trig**

Hard to figure out what you are doing. 2 cos^2 x-cos x = 0 cosx(2cosx - 1) = 0 cosx = 0 or cosx = 1/2 if cosx = 0, x = ?/2 or x = 3?/2 if cosx = 1/2 x = ?/3 or x = 2? - ?/3 = 5?/3 so you have 4 answers: ?/2, 3?/2, ?/3, and 5?/3 (in degrees: 90°, 270°, 60°, 300°...

**MATH HELP PLS**

Are the entries in the Venn diagram given or were they your calculations? When you say: There are 11 in the Band section , does that mean "band only" ? Same question for "17 in the Choir section"

**Math**

sum of 5: 14, 23, 32, 41 ----- 4 cases: prob(5 with 2 dice) = 4/36 = 1/9 number of times for 108 rolls = (1/9)(108) = 12

**Calc**

Vector equation of what ? A line, a plane ?? What does R(0) mean ? Fix your typos and repost so it makes sense.

**College Algebra**

let x be the amount of 30% gold then 50-x is the amount of 80% gold solve for x: .3x + .8(50-x) = .68(50)

**algebra**

Did you notice all the y values are perfect squares when x=1 , y = (1 + 8)^2 when x=2, y = (2+8)^2 when x=3, y = (3+8)^2 ... mmmhhhh?

**Algebra**

straight lines are usually written in the form y = mx + b, e.g. : y = 5x - 9 yours looks nothing like that furthermore, points are shown in the form (-7,4) repost so we know what you mean

**Math**

#5, can't see the graphs, but should have a y-intercept of 3, leaning to the right with a slope of 3 6. slope = (-10 -(-5))/(-9 - (-2)) = -5/-7 = 5/7

**math**

assuming simple interest: I = PRT 200 = P(.05)(4) P = 200/(.05(4)) = 1000

**algebra**

earning: x spending: y savings: x-y part of salary which is saving = (x-y)/x

**Maths**

number is the whole class ---- x number of boys = x-18 or number of boys = (1/4)x x/4 = x-18 times 4 x = 4x - 72 -3x=-72 x = 24 state your conclusion

**Differential Equation**

y=x^2+4x dy/dx = 2x + 4 checking in (xdy/dx)=x^2+y LS = x(2x+4) = 2x^2 + 4x RS = x^2 + x^2 + 4x = 2x^2 + 4x = LS Yes, it is

**algebra**

let the 3 numbers in AP be a-d, a, and a+d a-d + a + a-d = 33 3a = 33 a = 11 after the changes, the new numbers are: a-d + 2, a+1, and a+d+6 or 13-d , 12, and 17+d which are now is GP, so 12/(13-d) = (17+d)/12 144 = 221 - 4d - d^2 d^2 + 4d - 77 = 0 (d + 11)(d-7) = 0 d = -11 or...

**Basic Numeracy and statistics (math)**

Your given equation does not match your given data. If the initial velocity is 800 m/sec, then the equation would be h = -16t^2 + 800t , when shot from ground level. follow "Nonetheless' " suggestion and find the x-intercept 0 = 16t^2 + 800t 16t(t - 50) = 0 take ...

**Maths IX**

volume of the 5 cm sphere = (4/3)?(5^3) = (500/3)? cm^3 volume of shell = (4/3)?(10^3) - (4/3)?(8^3) = (1952/3)? since the mass is a function of the volume, [ (1952/3)?] / [(500/3)?] = x/6.25 1952/500 = x/6.28 500x = 12200 x = 24.4 kg check my arithmetic

**Math - Probability**

of the 26 letters, 5 are vowels prob (3 vowels of 3) = (5/26)(5/26)(5/26) = appr .0071 or .01 to the nearest hundredth

**Math**

I will do the last one, you do the other two G(t)=650e^(0.055t) , tells me the continuous rate is 5.5% with a different base: G(t) = 650(1+r)t pick t = 5, (we can choose anything) in the first: g(5) = 650 e^(.055(5)) = 650 e^(.275) = 855.7449 in the 2nd: 855.7449 = 650(1+r)^5 ...

**Maths**

How many .... what ??? I assume you are asking for the rate of increase of the depth. for the of length 25 m, the depth increases by 2 m so the depth increases 1 m per 12.5 m of length notice the width has nothing to do with it.

**Math**

Well, the first 4 represents 400 the 4 in the unit position represents 4 what is 400/4 ??

**Algebra**

assume an equation of the kind, C = a e^(kt), where C is the consumption, a is the intital amount , t is the number of years since 1945, and k is a constant. given: when t = 0, C = 40, 40 = a e(k(0)) a = 40 so we have: C = 40 e^(kt) given : when t = 25 (1970), C = 27.4 27.4 = ...

**Math**

simply C(h) = 5h + 10

**Math**

I assume you want to find the equivalent equation with e as its base, so you want .5 = e^(80r) ln .5 = 80r lne, but ln e = 1 r = ln.5/80 = -.0086643 or P(initial)(1/2)^(t/80) = Pinitial(e)^(rt) (1/2)^(t/80) = e^(rt) take ln of both sides (t/80) (ln .5) = rt divide by t (ln .5...

**Trigonometry**

or even simpler: draw a median from the right-angle to the hypotenuse. proof: let the triangle be A(0,0), B(b,0) and C(0,c) let AD be the median. midpoint of BC = ( (b/2 , c/2) AD = ?(b^2/4 + c^2/4) BD = ?(b - b/2)^2 + (c/2-0)^2 ) = CD = ?( b^2/4 + c^2/4) = AD

**geometry**

Assuming you made a sketch. Let the angle bisector of ?ACD meet BD at E let the diagonals intersect at F In a rhombus the diagonals right-bisect each other. So, in triangle CEF, angle F = 90 angle E = 64, thus angle FCE = 26° which makes angle BCD = 104° and of course...

**Proof by contradiction**

looks like both Damon and I have a typo in mine: from 4x^2 - 4x + 1 < 0 (2x - 1)^2 < 0 the conclusion is still the same in Damon's from (4x^2+1)/4x <1 NOTE-parentheses VITAL and multiply both sides by 4 x you would get: 4x^2 + 1 < 4x <---- which is the same ...

**Proof by contradiction**

Some strange math taking place here. first of all, the way you typed it ... 4x^2+1/4x <1 , if you multiply by 4x you would get 16x^4 + 1 < 4x According to your result, I suspect that your question was: (4x^2+1)/(4x) < 1 then 4x^2 + 1 < 4x+1 4x^2 - 4x + 1 < 0 (2x...

**Maths**

16y³+16y² +4y = 4y(4y^2 + 4y + 1) = 4y(2y + 1)^2

**Vidya mandir rajgoli**

Not enough information. We need an angle. Is it a right-angled triangle? Then use Pythagoras

**Linear equations**

the first as is : 60x + 10y = -16 divide 2nd by 10: -5x - 10y = 5 add them 55x = -11 x = -11/55 = -1/5 plug back into -5x - 10y = 5 -5(-1/5) - 10y = 5 1 - 10y = 5 -10y = 4 y = -2/5

**Math**

let the base of the first triangle be b let the height of the first triangle be h area of first triangle = (1/2)bh If the sides are tripled the new triangle is similar to the first one, and the height will also be tripled new base = 3b new height = 3h new area = (1/2)(3b)(3h...

**Math**

c < -1 means that you want all numbers to left of -1, but not -1 itself. This is shown with an arrow to the left of -1 with an open circle around the -1 if the circle is closed or solid, then it would be c ? -1, the -1 would be included so the correct choice is the first one

**Math**

Draw a straight line 6 units long. Subdivide each unit into 5 parts. Count the parts, there will be 30 of them , since 6 ÷ (1/5) = 6 * (5/1) = 30

**Geometry**

Find the area of the first pizza: A = ?r^2 = ?(6^2) = 36? find the area of the smaller pizza take the difference in the two areas

**Pre-Algebra**

x+y=97 x-y=19 add them up: 2x = 116 x = 58 sub that into the first equation to find y

**Math**

cylinders are easy: Consider a can of height h, and radius r Visualize taking off both lids of a tin can, you would have 2 circles. Now cut the "sleeve" along the height then fold it flat, and you would have a rectangle of length 2?r and height h So the surface area...

**Math**

Following the order of operation the way you typed it, and assuming O is the same as 0 1.9(.16) = .25x x = 1.9(1.6)/.25 = 12.16 if you meant: 1.9=0.25/(0.16x) 1.9(.16x) = .25 3.04x = .25 x = .25/3.04 = 25/304

**math**

small typo in Steve's answer: last line should be S30 = 30/2 (2k + 29(-k/3)) = 15(-23k/3) = -115k