# Posts by Reiny

Total # Posts: 38,374

**precalculus**

There are several question of your type in the Related Questions section below

**precalculus**

Vague question. are you converting an equation or a point with rectangular coordinates?

**Maths**

For any number, there are 10 possible digits for the unit place, one of those is the 2. so prob(your event) = 1/10

**Algebra**

compare: http://www.jiskha.com/display.cgi?id=1480210517

**Algebra**

find the vertex of the parabola. The t of the vertex tells you when it reached the maximum height, the h tells you what that height is.

**Math**

equation: y = 100 (2)^(t/3.2) .. .. to get 450 bacteria 450 = 100 (2)^(x/3.2) 4.5 = 2^(x/3.2) take log of both sides and use log rules (x/3.2)log 2 = log 4.5 x/3.2 = log 4.5/log2 x = 6.944 hrs. or appr 7 hours

**precalculus**

How does this post differ from this one? http://www.jiskha.com/display.cgi?id=1480198638

**PreCalc**

let f(x) = 2x^3+x^2-8x+3 f(1) ? 0 f(-1) = -2+1+8+3 ? 0 f(3) ? 0 f(-3) ? 0 f(3/2) = 0 , yeahhhh, 2x-3 is a factor by long division, 2x^3+x^2-8x+3 = (2x-3)(x^2 + 2x -1) the quadratic has roots of x = -1 ± ?2 looking at the graph of y = 2x^3+x^2-8x+3 -1-?2 < x < -1+?...

**Algebra**

let the distance from Seattle to wilderness be x miles x/420 + x/300 = 6 times 2100 the LCM 5x + 7x = 12600 x = 1050 miles

**Trigonometry**

look at the cos^-1 (x/3) construct a triangle with base of x and hypotenuse of 3 by Pythagoras: r^2 = x^2 + y^2 3^2 = x^2 + y^2 y^2 = 9 - x^2 y = ?(9-x^2) so we want the tangent tan (cos^-1 x/3) = opposite/adjacent = ?(9-x^2)/3

**precalculus**

(3(cos(5pi/4)+i sin (5pi/4) ) )^8 = 3^8(cos 8(5?/4) + i sin 8(5?/4)) = 6561( cos 10? + i sin 10?) = 6561( 1 + i(0) ) = 6561 B (3-3i)^6 let z = 3-3i, so we want z^6 r = ?(9 + 9) = ?18 = 3?2 plot (3,-3) which is in IV, so Ø = 315° or 7?/4 z = 3?2(cos 7?/4 + i sin 7?/4...

**precalculus**

I checked the first 4, they were ok you seem to know what you are doing.

**Trigonometry**

a) isn't arcsin(sin(?)) the inverse of itself? so 13?/16 b) and c) same thing, except by definition arcsin( ..) will give you the smallest positive angle so arccos(cos(-?/18) = ?/18 d) arcsec(-?2) the angle Ø so that secØ = -?2 or cosØ = (-1/?2) &...

**precalculus**

a) ok b) (i-j)-(18i+27i) = -17i - 28j c) (5i-5j)-(30i+54j) --> you did 5u - 5v instead of 5u-v

**pre calculus**

250 pounds at 45° ---> (250cos45, 250sin45) 130 pounds at -60° ---> (130cos(-60), 130sin(-60) ) Resultant = (250cos45, 250sin45)+(130cos(-60), 130sin(-60) ) = (125?2, 125?2) + (65 , -65?3) = ( 125?2 + 65 , 125?2 - 65?3) = appr (241.7767 , 64.1934) maginitude...

**Discrete Math**

if you meant: x^1 + x^2 + x^3 + 2x^4 + x^5 = 68 there are none http://www.wolframalpha.com/input/?i=solve+x+%2B+x%5E2+%2B+x%5E3+%2B+2x%5E4+%2B+x%5E5+%3D+68

**pre calculus**

checking for right-angled triangle: is 100^2 = 55^2 + 85^2 ? NO so let's find the smallest angle by the cosine law: 55^2 = 100^2 + 85^2 - 2(100)(85)cosØ cosØ = 14200/17000 = .83529.. Ø = 33.35..° , (I stored it for accuracy on my calculator So area...

**pre calculus**

u=<0,-4>, v=<-2,-8> a) 2v+u = <-4,-16) + <0,-4) = <-4, -20> b) 5u - v = <0,-20> - <-2,-8) = <2, -12> c) do this one the same way

**Mathmatics help please**

clearly 25 and 15

**Maths help asap please**

3c-7 > 5c+4 3c - 5c > 4+7 -2c > 11 c < -11/2 or c < -5.5 so the smallest integer that is a solution is c = -6 check: if c = -6, -18 - 7 > -30+4 -25 > -36 , true! if c = -5 -15-7> -25+4 -22 > -21 , false

**Math**

subtract 2 from each part, and you are done -3<x+2<3 -3-2 < x+2-2 < 3-2 -5 < x < 1 ---> ( x lies between -5 and 1 )

**Math**

nothing wrong with that you could just use the trig-vector notation resultant = (10cos60,10sin60) + (20cos120,20sin120) + (30cos180,30sin180) + (40cos270,sin270) = (5, 5?3) + (-10, 10?3) + (-30, 0) + (0, -40) = ( -35, 5?3-40 )) your sketch will confirm that

**Trigonometry**

Both Steve and I both told you what was wrong with the wording of the question. http://www.jiskha.com/display.cgi?id=1480115359 Did you even look at the responses?

**Math**

(2 x 3)>2 - 5>2 is a false statement. you are basically saying: 6 > 2-5 > 2 6 > -3 > 2 the part 6 > -3 is true, but -3 > 2 is nonsense To ask "evaluate" the expression makes no sense Hey, wait a minute! Did you mean (2 x 3)^2 - 5^2 ?? then you...

**math**

You can't just drop the variable. 5(2x + 7) = 10x + 35 Now you can see that we can't add the 10 and 35 since they are "unlike" terms

**Math**

correct

**math**

The 14M, the 3M and the 1M are all expenses so what is 20 - (14+3+1) ?? I get 2 Million

**Calculus AB**

3y^3 + 2x^2 = 5 9y^2 dy/dx + 4x = 0 dy/dx = -4x/9y^2 when y = 1 , 3 + 2x^2 = 5 2x^2 = 2 x = ± 1 , but in quadrant 1, x = 1 dy/dx = -4(1)/9 = -4/9 equation of tangent: y-1 = (-4/9)(x-1) 9y-9 = -4x + 4 4x + 9y = 13 check: http://www.wolframalpha.com/input/?i=plot+3y%5E3+%...

**Trigonometry**

y = cos(3?/4 - x) already is a single function of x, namely the cosine function. I don't understand what else you want to do with it. We know: using cos(A-B) = cosAcosB + sinAsinB cos(3?/4 - x) = cos 3?/4 cosx + sin 3?/4 sin x = -?2/2 cosx + ?2/2sinx = ?2/2 (sinx - cosx...

**Math**

In the original number let the unit place by x then the tens place is 2x, (obviously x < 5) then the number in terms of its value is 10(2x) + x and the number reversed is 10x + 2x the difference between these two is 36, just translate this into Math. 10(2x) + x - (10x + 2x...

**Math**

clearly the 5 has to go in the unit position for the number to be odd At the front, what would be bigger, something 6 hundred or something 8 hundred?

**Mathematics**

let his sales be x .06x + 6000 = 10200 solve for x

**Maths**

330/x - 330/(x+5) = 1/2 That's ok, we end up with a quadratic. Multiply each term by 2x(x+5) 660(x+5) - 660x = x(x+5) 660x + 3300 - 660x = x^2 + 5x x^2 + 5x - 3300 = 0 (x-55)(x+60) = 0 x = 55 or x = -60, we would reject the -60 So your inward speed is 55 km/h, the return ...

**math**

90 = 2x3x3x5 since each pair of equal factors produces a perfect square, we have 3x3, a perfect square. So all we need is another 2 and another 5 How about 2x2x3x3x5x5 = 900 900 = 30^2 , so it is a perfect square, and it is divisible by 90

**math-factors and multiples**

both 40 and 32 divide by 8 both a^3 and a^2 divide by a^2 The GCF is 8a^2

**math**

It is 30a^2

**math**

5 ? m/-3 + 18 add m/3 to both sides 5 + m/3 ? 18 m/3 ? 13 m ? 39 or 5 ? m/-3 + 18 -13 ? m/-3 times -3 39 ? m m ? 39 , same as above

**math**

the slope of the 2nd is -2/16 = -1/8 which is the negative reciprocal of the slope of the first. Thus, the lines are perpendicular.

**math**

I assume we are factoring 25m^6-121m^4 = (5m^3 - 11m^2)(5m^3 + 11m^2)

**Calculus applications**

let the height be 100 cm^3 ?r^2 h = 100 h = 100/(?r^2) S = 2 circles + the sleeve = 2?r^2 + 2?rh = 2?r^2 + 2?r(100/(?r^2)) = 2?r^2 + 200/r you typed it wrong, it should have been 2?r^2 + 200 r^-1 dS/dr = 4?r - 200/r^2 = 0 for a min of S 4?r = 200/r^2 r^3 = 200/(4?) = 25/? r...

**Math**

Now: Marcus ---- x John ------ x+10 5 years from now: John's age = x+15 5 years ago: Marcus = x-5 3(x+15) = x-5 that would give you the silly answer of x = -25 checking now Marcus is -25 John is -15 5 years from now, John is -10 and 5 years ago Marcus was -30 sure enough 3...

**maths**

Without any restrictions, number of committees = C(10,4) = 210 include at least one woman ---> exclude cases of all 4 being men number of ways = 210 - C(5,4) = 205

**math**

now: daughter ---- x years Mary -------- 3x years 4 years ago: daughter : x-4 Mary : 3x-4 (x-4)(3x-4) = 40 3x^2 -16x + 16 = 40 3x^2 - 16x - 24 = 0 I was expecting it to factor, hoping for whole number solution, but .... x = (16 ± ?544)/6 = 6.55 or a negative check: if ...

**Math**

let the two numbers be 9x and 3x then 9x + 3x = 72 .. x = 6 sub into my definition to get the numbers.

**Math**

Find the midpoint of AB, then use your "distance between two points" formula to get CM .

**Maths**

let the numbers be x and x+1 solve: x + x+1 = 39

**math**

your first equation should have been 4x +5 = 37 instead of 4x(5) = 37 but then you miraculously switched it to the right one as you solved it. The answer is correct

**Further mathematics**

x^2 + y^2 = 5xy complet the square: x^2 + 2xy + y^2 = 7xy (x+y)^2 = 7xy take log of both sides 2log(x+y) = log 7 + logx + logy 2log(x+y) - log7 = logx + logy 2log(x+y) - 2log 7^(1/2) = logx + logy 2[ log(x+y) - log ?7] = logx + logy 2 log( (x+y)/?7 ) = logx + logx as required ...

**algebra~help me**

18^(4-4y)=54(?2)^(3y-2) take log of both sides (4-4y)log18 = lof54 + (1/2)(3y-2)log2 4log18 - 4ylog18 = log54 + (3y/2)log2 - log2 4log18 - log54 + log2 = y( (3/2)log2 + 4log18) 3.58972... = (5.4726...) y y = .655941

**Calculus**

so considering t = 0 to correspond with 2016 1000 = A 3^0 , but 3^0 = 1 A = 1000 b) y(5) = 1000 3^(4/3) = .... Use your calculator c) 100000 = 1000 3^(t/4) 1000 = 3^(t/4 take log of both sides log 1000 = log 3^(t/4) 3 = (t/4)log 3 t/4 = 3/log3 t = 12/log3 = appr 25.15 years iv...

**math**

Assuming the farm is a rectangle ... length --- x width = 39 2x + 2(39) = 187.2 find x once you have x, take x/39

**algebra**

How about you showing me some of your steps, now that I have done two very similar to this one for you ?

**algebra**

breath (width) ---- x length -----------x+12 2x + 2(x+12) = 144 carry on

**algebra**

smaller --- x larger --- y Now just translate into Math. 3(y - x) = y+3 3y - 3x = y+3 3x - 2y = -3 ** 3(y+x) = 8x + 2 3y + 3x = 8x + 2 5x - 3y = 2 *** solve ** and *** You should get two whole numbers.

**Differential calculus**

If expanded you would get a standard cubic Its x-intercept are (2,0), (-1,0) and (-3,0) http://www.wolframalpha.com/input/?i=plot+y%3D(x-2)(x%2B1)(x%2B3)

**maths**

let the two numbers be 5x and 7x "it's lam is 210" , I have no clue what that means.

**maths**

I will assume you meant the ninetieth term. If a and d are the first term and common difference respectively, then term(90) = 30 a + 89d = 30 a = 30-89d sum(17) = (17/2)(2a + 16d) = (17/2)(2(30-89d) + 16d) = (17/2)(60 - 162d)

**Math**

Did you make a sketch? 1) sin30° = h/15 h = 15sin30 = 15(1/2) = 7.5 m Very unsafe way to place a ladder, the angle should be > 76° at the ground 2) in reference to the 60° angle, the 13 m is the "adjacent" and you want the "opposite" side ...

**Statistics**

numer of ways = 15 x 14 x 12 = .... (assuming the order matters, and you have specified positions)

**Math**

correct (the jet stream does not just flow over the US )

**I dont know**

they can be any (x,y) such that x^2 + y^2 = 64 e.g. (2 , ?60), (?39 , 5) , (8,0), (8,0), (4?2 , 4?2) etc

**Algebra2**

but log8 2 = 1/3 so log8 (a/2) = log8 a - 1/3

**math**

equilateral ---> all sides are equal, so 3x+2 = 2y-x 4x + 2 = 2y 2x + 1 = y also 3x+2 = y + 3 3x+2 = 2x+1 + 3 x = 2 then y = 5 so each side is 3x+2 = 8 and the perimeter is 24

**Math**

9/(2x) = 15/12 "cross-multiply" 30x = 108 x = 108/30 = 18/5 or 3.6

**Math**

amount of peaches --- x lbs amount of melons ---- y lbs amount of apples ----- 100 - x - y lbs (assume both x and y are whole numbers) 10x + 3.5y + .5(100-x-y) = 100 double every term 20x + 7y + 100 - x - y = 200 19x + 6y = 100 x = (100 - 6y)/19 , clearly 0 < y < 6 by ...

**10th Grade Math**

To have a triangle, the sum of any two sides must be greater than the third side. look at C 5+10< 18 all the others form a triangle

**maths**

The volume of 2 similar objects is proportional to the cube of its linear sides 320/x = 8^3/6^3 512x = 69120 x = 69120/512 = 135 or the side ratio is 6/8 = 3/4 old volume = 8(l)(w) = 320 lw = 40 new volume = 6(3l/4)(3w/4) = 54/16 lw = (54/16)(40) = 135

**maths**

surface area of smaller = 4? r^2 surface area of larger = 4?(3r)^2 = 36?r^2 which is 9 times as great or the area of similar objects is proportional to the square of their linear dimension, so 1^2 : 3^2 = 1 : 9

**Algerbra**

so it will differ only in the constant let the equation be y = -4x + b but (-8,-4) lies on it, so -8 = -4(-8) + b solve for b and write the equation.

**Trigonometry**

tanØ = 4/1 = 4 Ø = 75.96 The angle should be 76° by ratio: 4/1 = 16/x x = 4

**Math**

number of adult tickets sold = 3x number of children tickets sold = 5x 5x = 3x + 180 take over.

**math**

LCD is 5b a/5 +4/b = ab/5b + 20/5b = (ab + 20)/(5b)

**Algebra**

slope of main street = (33-17)/(-22+2) = -4/5 so slope of Grimes Blvd = +5/4 y - 9 = (5/4)(x-80) y = (5/4)x - 100+ 9 y = (5/4)x - 91

**Math**

Follow the same steps I just showed you in your previous problem.

**Math**

number of girls ---- 7x number of boys ---- 5x "there are 8 more girls 10 boys" makes no sense are you saying, "there are 8 more girls than boys" ? which translated into math would be 7x = 5x+8 take it from here

**maths**

done, see below

**algebra**

number of nickels ---- x number of dimes ----- x+10 number of quarters = 37-(x + x+10) = 27 - 2x value of coins = 5x + 10(x+10) + 25(27-2x) = 5x + 10x + 100 + 675 - 50x = 775 - 35 x

**Math**

I don't know, you did not state the rate of interest.

**maths**

volume of wooden rod = ?(2^2)(6) = 24? volume which is submerged = 12? So the volume in the cylinder will change by that amount ?(4^2)h = 12? 16h = 12 h = 12/16 cm = 3/4 cm new depth = 4+3/4 cm = 19/4 cm or 4.75 cm

**maths**

" ... is placed in the tin or floats exactly half 2.what is the New depth of water " Retype in proper English so I can understand it.

**maths**

OK, even though have always been told that we can't add apples and oranges, ..... let the amount of apples be x lbs amount of oranges ----- (52 - x) lbs 5.25x + 3.8(52-x) = 4.25(52) 5.25x + 197.6 - 3.8x = 221 1.45x = 23.4 x = 16.1 lbs of apples and 35.9 lbs of oranges appr...

**math**

cost = 7.2(12) = 86.4 18 eggs = 1.5 dozen so you sold 10.5 dozen at 7.5 return = 10.5(7.5) = 78.75 loss = 86.4 - 78.75 = 7.65

**Maths**

Four times as much, or 32 kg Can you show me why that is so?

**maths**

volume of ball = (4/3)?(4.5)^3 So that is the change in volume in the cylinder once removed ?(6^2) h = (4/3)?(9/2)^3 36h = (4/3)(729/8) = 243/2 h = 243/72 = 27/8 the water will fall 27/8 cm or 3.375 cm check my arithmetic.

**Algebra 1**

The boat will be .15 miles from Ellen coming and going away. So 1 - 70t = .15 OR -1 + 70t = .15 t = .01214... hrs or t = .01642.. hrs t = .01214(3600) sec or t = .01642(3600) sec t = 43.7 sec OR t = 59.1 sec

**check - Math**

ok, the cat's were adopted, that means the count was reduced by 120, not increased. I read the question incorrectly number of cats after adoption = 2x - 120 make the simple change in the equation and solve

**Math**

number of cats ---- 2x number of dogs ----3x after adoption: number of cats = 2x + 120 (2x+120) : 3x = 3 : 7 (2x+120)/(3x) = 3/7 14x + 840 = 9x 5x = -840 x is a negative, which is not possible. notice 2:3 = .66.. and 3:7 = .42 , which is < 2/3 How can the ratio of cats : ...

**maths**

Area of a triangle = (1/2)(ab)sinØ where a and b are sides with Ø as the angle between them. Your data is perfectly suited for that formula

**found my error - Go with Steve - maths need help**

The second equation had addition, I read it as another subtraction.

**maths need help**

Log (a+3) (base 9) - log b(base 9)= c + (1/2) log9 (a+3) - log9 b = c+1/2 log9 ((a+3)/b) = c+1/2 ---> 9^(c+1/2) = (a+3)/b 3^(2c+1) = (a+3)/b ** log (a-3) (base 3) + log b (base 3)=c - 1 log3 (a-3)+ log3 b = c-1 log3 ( (a-3)/b )= c-1 --> 3^(c-1) = (a-3)/b *** divide ** by...

**Math**

let the roots of ax^2+bx+c=0 be m and n then m:n = r:1 m/n =r/1 m = rn sum of roots = m+n = rn + n = n(r+1) = -b/a ** product of roots = mn = n^2 r = c/a *** divide ** by *** (r+1)/nr = (-b/a) / (c/a) = -b/c rc + c = -bnr rc + bnr = -c r(c + bn) = -c r = -c/(c+bn) For acr^2+(...

**math**

A standard rotation is 2?. So whatever angle you have either adding or subracting multiples of 2? will yield a coterminal angle. e.g 8?/3 -----> think 480° 8?/2 - 2? = 2?/3 -----> think 120° 8?/3 + 2? = 14?/3 -----> think 840° 8?/3 - 4? = -4?/3 -----> ...

**calculus**

c(x)=3x^3 - 12x^2 +9000x c ' (x) = 9x^2 - 24x + 9000 = 0 for a max/min of c(x) 9x^2 - 24x + 9000 = 0 This equation has no real solution. c(0) = 0, for all values of x > 0, c(x) increases so our minimum cost is when we don't produce anything, (that actually makes ...

**Math**

If you are referring to your previous post, look at my reply to it.

**Math**

For any number to be divisible by 6, it must be divisible by both 2 and 3 To be divisible by 2, the unit digit must be even or zero, so that eliminates A - 5. To be divisible by 3, the sum of the digits must be a multiple of 3 (divisible by 3) Since we have a sum of 8 for the ...

**Algegra**

So let's just change Ax + By = C to the form y = mx + b Ax + By = C By = -Ax + C divide each term by B y = (-A/B)x + C/B So compare that to y = mx + b m = -A/B so I have just developed a quick way to find the slope of any equation in general form e.g. 7x + 9y = 17 has slpe...

**Math**

so with her new test, there will be 6 tests (sum of what you have so far + x)/6 = 69 solve for x

**maths**

original fraction --- x/y first new fraction: (x+1)/(y+1) = 2/3 3x + 3 = 2y + 2 3x - 2y = -1 ** second new fraction: (x-2)/(y-2) = 3/5 5x - 10 = 3y - 6 5x - 3y = 4 *** solve the two equations ** and ***

**mathematical methods for economics**

Did you try Venn diagrams? Start filling in from the intersection of all three circles. Put 50 in that intersection, then work your way outwards from there.

**Math, Surds**

let the length of each side be s s^2 = 60 s = ?60 = ?4*?15 = 2?15 each side is 2?15 m perimeter = 8?15 m