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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

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