Thursday

September 29, 2016
Total # Posts: 36,058

**Math**

40 : 60 : 120 : 140 = 4 : 6 : 12 : 14 = 2 : 3 : 6 : 7

*August 26, 2016*

**value**

from what you have: Logx + logy=4 logx +2logy=3 log(xy) = log(x^4 y^2) = 3 so : log(xy) = log(x^4 y^2) x^4 y^2 = xy x^3 y = 1 y = 1/x^3 , of course x > 0 in logx + logy = 3 logx + log(1/x^3) = 3 log(x(1/x^3)) = 3 log (1/x^2) = 3 1/x^2 = 10^3 = 1000 1000x^2 = 1 x^2 = 1/1000 ...

*August 26, 2016*

**maths reiny help!!**

I just copied my previous solution and changed the numbers: Suppose that the cost of each of the original books was $x per book So the cost was 80x He got a 15% discount, so the cost was (.85)80x = 68x but for 68x he actually got 90 books so the cost of each book was only 68x/...

*August 26, 2016*

**algebra**

width ---- w length ---- w+6 width*length = area w(w+6) = 72 w^2 + 6w - 72 = 0 (w-6)(w+12) = 0 w = 6 or w = a negative the width is 6 cm with only a few nice choices you could have easily checked each one in your head e.g. for the first one: is 10 times 16 equal to 72 ? NO etc

*August 26, 2016*

**Math**

cows --- x chickesn --- y x+y = 12 ** 4x + 2y = 28 or 2x + y = 14 *** subtract ** from *** x = 2 then y = 10 2 cows and 10 chicks

*August 26, 2016*

**math**

2 workers takes 15 hours to make 3 fireplaces 2 workers takes 5 hours to make 1 fireplace 2 workers takes 20 hours to make 4 fireplaces 1 worker takes 40 hours to make 4 fireplaces 5 workers takes 8 hours to make 4 fireplaces or it takes 30 work-hours to make 3 fireplaces it ...

*August 26, 2016*

**Maths**

let Katie's present age be k let Melanie's present age be m Five years ago: Katie ---- k - 5 Melanie -- m-5 k-5 = 10(m-5) k - 10m = -45 ** 2nd condition: Katie's age in 15 years = 3(Melanies age in 11 years) k + 15 = 3(m + 11) k+15 = 3m + 33 k - 3m = 18 *** ...

*August 25, 2016*

**MAth**

I did this for you yesterday http://www.jiskha.com/display.cgi?id=1472041460 Why are you repeating it? btw, it should say "How many complete revolutions are needed?"

*August 25, 2016*

**Math help**

recall that cot^2 x +1 = csc^2 x so ∫(cot^2 x-csc^2 x)^2dx = ∫(cot^2 x-(cot^2 + 1)^2dx = ∫ -1 dx take over

*August 25, 2016*

**MATHS**

what is 1 - .8(.7) ?

*August 25, 2016*

**Math**

add 246 to both sides

*August 24, 2016*

**Math**

correct

*August 24, 2016*

**Math**

Since a constant multiplier is not usually written behind a binomial, I suspect you meant: (x+1)^2 = 9 then x+1 = ±√9 = ±3 x+1 = 3 ----> x = 2 or x+1 = -3 ---> x = -4

*August 24, 2016*

**MAV school**

x/4 + (120-x)/5 = 28 times 20 , the LCD 5x + 4(120-x) = 560 5x + 480 - 4x = 560 x = 80 so we split them up as 80 and 40 , with the 80 being divided by 4 and the 40 divided by 5 check: 80/4 + 40/5 = 20+8 = 28

*August 24, 2016*

**MAth**

Circumference of barrel = 56π cm number of rotations = 2944/(56π) = appr 16.7

*August 24, 2016*

**MATHS PLZZ HELP PLZZ SOMEONE KINDA BEG YOU**

Suppose that the cost of each of the origininal bools was $x per book So the cost was 50x He got a 10% discount, so the cost was (.9)50x = 45x but for 45x he actually got 60 books so the cost of each book was only 45x/60 = 3x/4 As a percentage: (3x/4) / x = 3/4 or 75% which ...

*August 24, 2016*

**math**

The assumption would be that he would be randomly guessing at the answer. Since 12/15 = .8, why did you not include the probability of getting 12 correct out of the 15 ? Try adding that to your other cases. For b) wouldn't getting 20 out of 25 correct yield 80% ? Same for ...

*August 24, 2016*

**Math**

clearly I have a typo in the 3rd last line, should be = 2^2011 (-√3/2 + (1/2) i )

*August 24, 2016*

**Math**

let's use De Moivre's Theorem let z = √3 - 1 sketching it in the Argand plane will give you |r| = 2, and tanØ = -1/√3 Ø = 330° or 11π/6 z = 2(cos 330° - i sin 330°) z^2011 = 2^2011(cos (663630°) - i sin(663630°) ) ...

*August 24, 2016*

**Math**

By "a complete sketch" they very likely want a right-angled triangle. since tanØ = opposite/adjacent = 3/4 and the angle is in the third quadrant y = -3 and x = -4 r^2 = 9 + 16 = 25 r = 5 sin Ø = -4/5 cos(Ø + 180) = cosØcos180 - sinØ...

*August 23, 2016*

**Maths**

circumference of wheel = πd = .98π metres number of rotations = 1540 m/.98π m = 531.898.. = appr 532 rotations how did you get 500?

*August 23, 2016*

**Maths**

I will assume that you meant: (cosecθ-cotθ)^2=(1-cosθ)÷(1+cosθ) or else the identity is not true. LS = (1/sinØ - cosØ/sinØ)2 = (1-cosØ)^2 / sin^2 Ø = (1 - cosØ)(1-cosØ)/( (1 - cosØ)(1 + cos&...

*August 23, 2016*

**math**

What is 1.74 / 0.29 ?

*August 23, 2016*

**Math**

width or breadth ----- x cm length --------------- 3x - 2 solve for x, and sub back into my definitions 2x + 2(3x-2) = 60

*August 23, 2016*

**statistics**

number of "not reds" is 20 so prob(not red) 20/26 = 10/13 or prob(red) = 6/26 = 3/13 prob(not red) = 1 - 3/13 = 10/13

*August 23, 2016*

**math**

(3^-3)x = 4 (1/3^3)x = 4 (1/27)x = 4 x = 108

*August 23, 2016*

**Correction - Maxwell**

How did you get your answer? It is not correct Felicia's present age .... f Tom's present age ........ t 3f = t+4 ** f+3 + t+3 = 30 f+t = 24 t = 24 - f *** sub *** into ** 3f = 24-f + 4 4f = 28 f = 7 then t = 24-7 =17 Felicia is now 7 and Tom is now 17 check: three ...

*August 23, 2016*

**Math**

If exterior angle is 50°, then each interior angle is 130° let the number of sides be n , where n is a whole number sum of interior angles = 180(n-2) each interior angle is 180(n-2)/n 180(n-2)/n = 130 180n - 360 = 130n 50n = 360 n = 7.2 , silly answer, so nope, not ...

*August 22, 2016*

**Math**

slope of a line is the tangent of the angle that the line makes with the horizontal, so slope = rise/run = 225/1000 = 9/40 so the hypotenuse of the corresponding triangle is √(40^2 + 9^2) = √1681 cosine (angle) = 40/√1681 = 40/41

*August 22, 2016*

**Math**

unit digit of original number ---- x tens digit of original number ---- x+5 original number = 10(x+5) + x = 11x + 50 number reversed = 10x + (x+5) = 11x + 5 11x+50 + 11x + 5 = 99 22x = 44 x = 2 the original number was 72 check: 72 + 27 = 99 , my answer is correct

*August 22, 2016*

**Math**

well, |-9| = 9 so you have -9/9 = -1

*August 21, 2016*

**Math**

you got it 7 - √11

*August 21, 2016*

**Algebra**

I assume you meant: |t-2| = -1 since by definition |anything| is never negative, there is no solution.

*August 21, 2016*

**math**

Ok, who is stopping you ?

*August 21, 2016*

**math**

each of the other equal sides ---- x cm x^2 + x^2 = 98^2 2x^2 = 9604 x^2 = 4802 x = √4802 = 49√2 cm

*August 21, 2016*

**theory of probability**

What you have is the total number of ways to place the caps Let's actually list them, there are only 6 I will write them as a pair of digits, where the first number is the bottle and the second digit is the cap 11 22 33 ----> all correct 11 23 32 ----> 1 right, 2 ...

*August 21, 2016*

**Maths Percentage**

(1.25x)(r) = x 1.25r = 1 r = 1/1.25 = .8 = 80% So it must be reduced by 20% check: suppose the original was $100 after the increase it would be 125 after a reduction of 20% is would be .8(125) = 100

*August 21, 2016*

**Math**

2000(1+i)^2 = 24200 (1+i)^2 = 1.21 take √ of both sides, etc

*August 21, 2016*

**please help with this trigonometric identity!**

I am sure that you meant: (cos 'a' - cos 'b') / (sin 'a' + sin 'b') + (sin 'a' - sin 'b') / (cos 'a' + cos 'b') = 0 the LCD is (sina + sinb)(cosa + cosb) LS = ( (cosa - cosb)(cosa + cosb) + sina - sinb)(sina - ...

*August 19, 2016*

**Maths Algebra**

3(5x-7)-2(9x-11)=4(8x-13)-17 15x - 21 - 18x + 22 = 32x - 52 - 17 -35x = -70 x = 2 check: LS = 3(10-7) - 2(18-11) = 9 - 14 = -5 RS = 4(16-13) - 17 = 12 - 17 = -5 my answer is correct

*August 19, 2016*

**Maths Squares and Square roots**

The sum cannot be found without some kind of addition somewhere, but .... look at the last one: add the first and last ---> 22 add the 2nd and 2nd last ---> 22 add the 3rd and 3rd last ----> 22 how such pairs of 22 can you find? If you have an odd number of terms, do ...

*August 19, 2016*

**Maths Triangles**

Too messy to type here. That proof should be in most textbooks, if not, Google it. https://search.yahoo.com/search?fr=spigot-nt-gcmac&ei=utf-8&ilc=12&type=692858&p=proof%20:%20sum%20of%20angles%20in%20a%20triangle%20equals%20180

*August 19, 2016*

**Maths Quadrilaterals**

Once you have proven that the sum of the angles in a triangle is 180° ..... in your quad, draw in any diagonal to create two triangles. So ......

*August 19, 2016*

**Maths Time and Work**

Poorly worded. By "rates of working" , do you mean the amount of work done, or the time taken to do the same job.

*August 19, 2016*

**Maths Unitary Method**

The key word in the first part is "or" men's rate = 875/5 = .. women's rate = 875/7 = ... then 10(men's rate) + 7(women's rate) = ... (politically incorrect question)

*August 19, 2016*

**Maths Percentage**

what is 54000/1.1 ?

*August 19, 2016*

**Maths Compound Interest**

count = 512000(1.025)^2 = .....

*August 19, 2016*

**Maths Compound Interest**

When is 1000(1.10)^n = 1331 ? 1.1^n = 1.331 take log of both sides, and use log rules n log 1.1 = log 1.331 n = log 1.331/log 1.1 = .... you do the button pushing

*August 19, 2016*

**geometry**

Well, you know that that the area of a triangle = (1/2)bh, where b is the base and h is the height but you are told that h = 3b , so area = (1/2)(b)(3b) 27 = (1/2)(3b^2) times 2 54 = 3b^2 b^2 = 18 b = √18 or 3√2 ft base = 3√2 ft and the height is 9√2 ft...

*August 19, 2016*

**Correction - Maths**

I obviously got x = 360 So there are 360 marbles, I have no idea where I got the 510 from, and then I copied it again at the end. Time for my third cup of coffee.

*August 19, 2016*

**Maths**

let the total be x (2/5)x = r , also b+54 = (2/5)x b = 2x/5 - 54 = (2x - 270)/5 b : y = 5 : 7 5y = 7b y = (7/5)b y = 7(2x-270)/25 so 2x/5 + (2x-270)/5 + 7(2x-270)/25 = x times 25 10x + 10x - 1350 + 14x - 1890 = 25x -9x = -3240 x = 360 we have 510 marbles check: red = (2/5)(360...

*August 19, 2016*

**math**

I had done this for you. http://www.jiskha.com/display.cgi?id=1471418592

*August 17, 2016*

**Analytic Geometry**

Since you know the vertex, your equation must be x = a(y-0)^2 + 0 , if the axis of symmetry is horizontal x = ay^2 but (3,5) lies on it, so 3 = a(25) a = 3/25 x = (3/25)y^2 or 25x = 3y^2

*August 17, 2016*

**Maths**

cos(A+B) = cosAcosB - sinAsinB apply it to your question

*August 17, 2016*

**Math**

log3 9^4 = 4 log3 9 = 4(2) = 8 or , just think it through 9^4 = 3^8 so log3 3^8 must be 8

*August 17, 2016*

**math**

first number --- x 2nd number ---- 1/x x + 1/x = 3 x^2 + 1 = 3x x^2 - 3x + 1 = 0 using competing the square: x^2 - 3x + 9/4 = -1 + 9/4 (x + 3/2)^2 = 5/4 x + 3/2 = ± √5/2 x = -3/2 ± √5/2 x = (-3 + √5)/2 or x = (-3 - √5)/2

*August 17, 2016*

**Math**

assuming that "a" is the base - log a x^6 y^7 = -(loga x^6 + loga y^7) = -(6loga x + 7loga y) = -6loga x - 7loga y none of your choices are correct, unless there is a typo with that minus sign

*August 17, 2016*

**Math3c**

Just use the definitions of an AP and translate the English to Math. "the sum of the first three terms" = a + a+d + a+2d = 3a + 3d "the sum of the next four terms" = a+3d + a+4d + a+5d = 3a + 12d given: "the sum of the first three terms is one half the...

*August 17, 2016*

**Pre Cal**

Show me your expansion, and I will check it. Did you remember that i^2 = -1 ?

*August 17, 2016*

**Pre Cal**

take a look at this question I did several years ago http://www.jiskha.com/display.cgi?id=1315862859

*August 17, 2016*

**Calculus**

I will assume you mean: y = x^3 + 3x^2 , notice how we show exponents here x^3 + 3x^2 = 0 x^2(x + 3) = 0 finish it up

*August 17, 2016*

**math**

wherever you see y, replace it with 2 and evaluate

*August 17, 2016*

**Algebra**

1. let his actual speed by x km/hr time to do his 40 km trip = 40/x let his supposed speed be x+1 km/h time taken = 40/(x+1) 40/x - 40(x+1) = 2 times x(x+1) , the LCD 40(x+1) - 40x = 2x^2 + 2x 2x^2 + 2x - 40 = 0 x^2 + x - 20 = 0 (x+5)(x-4) = 0 x = 4 or a negative he went at 4 ...

*August 17, 2016*

**Math**

clearly, (f + g)(x) = 5x - 3 which is linear, thus the domain is the set of all real numbers.

*August 17, 2016*

**Math**

For P(a,b) and Q(c,d) the midpoint M is ( (a+c)/2 , (b+d)/2 ) apply this to your problem

*August 17, 2016*

**math**

cost price of cheaper chocolates = 1.50/10 = .15 each cost of expensive chocolates = .20 let the number of each type of chocolates be x cost price = .15x + .2x = .35x selling price = 4/20 = .2 each return on sale = 2x(.2) = .4x .4x - .35x = 10 .05x = 10 x = 200 he bought 200 ...

*August 17, 2016*

**math**

Hard to understand your notation. I will assume you mean: 4.5 kg at 600 per kg ----> 2700 2 kg at 1200 per kg -----> 2400 3 kg at 1500 per kg -----> 4500 total = 9600 leaving 10000-9600 = 400

*August 17, 2016*

**math**

did you mean "Roman numeral" ? 1959 ----> MCMLIX http://www.rapidtables.com/convert/number/roman-numerals-converter.htm

*August 17, 2016*

**physics question**

Look at this question answered by Damon over 5 years ago, just change the numbers to fit your question. http://www.jiskha.com/display.cgi?id=1296412513

*August 17, 2016*

**Pre-calc**

6csc Ø - 5 = 1 csc Ø = 6/6 = 1 then sin Ø = 1 consider the sine curve and it is clear that Ø = π/2 or ±2π + π/2 or ±4π + π/2 ... for the given interval, Ø = π/2 general solution: Ø = π/2...

*August 16, 2016*

**Math**

The first question can be answered in 2 ways for each of those, the 2nd question can be answered in 2 ways, so 2^2 or 4 so far ... number of ways = 2^5 = 32

*August 16, 2016*

**Calculus**

by simple inspection, and knowing the rules of derivatives for sine and cosine .... no need for substitution. ∫sin(x)cos^2(x)dx = (-1/3) cos^3 x + c

*August 16, 2016*

**math algebra**

I assume you meant: 10, 2, 2/5, 2/25 clearly a = 10 , r = 1/5 you should know your formulas. term(n) = ar^(n-1) term(7) = 10(1/5)^6 = 10/15625 = 2/3125

*August 16, 2016*

**algebra**

Just did this. Why are you changing names and repeating the question ?

*August 16, 2016*

**math**

let the unit digit be x and the tens digit by y then the original number is 10y + x and the number reversed is 10x + y 10x + y - (10y + x) = 18 9x - 9y = 18 x - y = 2 but we also know that xy = 24 it should be obvious that the two number are 6 and 4. Since reversing the ...

*August 16, 2016*

**Math**

According to the wording of the question, your answer is correct Now -- 5 at end of month 1 = 5(2) = 10 at end of month 2 = 5(2^2) = 5(4) = 20 at end of month 3 = 5(2^3) = 5(8) = 40 ... at end of month 8 = 5(2^8) = 5(256) = 1280

*August 16, 2016*

**Math**

recall that area of triangle = (1/2) base x height 36 = (1/2)(base)(9) multiply both sides by 2 72 = 9base base = 72/9 = 8

*August 16, 2016*

**Algebra**

how about this way: using (ab)^n = (a^n)(b^n) (4x^-1)^-1 = (4^-1)(x^-1)^-1 = (1/4)(x^1) = (1/4)x or = x/4 #2 (x^3+3x^2+3x+1)^(-2/3) = 1/(x^3+3x^2+3x+1)^(2/3) notice I assumed your exponent was -2/3, the way you typed it, the exponent would have been -2 , with 3 a divisor ( (x^...

*August 16, 2016*

**mathematical method**

First of all let's expand this (2-i)(1+3i)(3+4i) = (2-i)(3 + 13i + 12i^2) = (2-i)(13i - 9) , remember that i^2 = -1 = 26i - 18 - 13i^2 + 9i = -5 + 35i magnitude = √(25 + 1225) = √1250 = 25√2

*August 16, 2016*

**math**

Their share of the profit should be proportional to the amount of their investment Total investment = 13000 Alex's share is 8000/13000 = 8/13 Ali's share is 5/13 So 5/8 = 2000/x , assuming Ali and Ally are the same person 5x = 16000 x = 3200 check: 2000 : 3200 = 5 : 8

*August 16, 2016*

**Math**

The distance between them is decreasing at a rate of 50 mph, (17+13) So in the last minute the distance to be covered is (1/60)(50) miles ----> recall, distance = rate x time = 5/6 of a mile

*August 15, 2016*

**math**

Don't become obsessed with formulas, just think it through. you want the distance around 1/2 of a circle = (1/2)(2π(30)) = 30π Then you must add the diameter, which would be 60 cm total = 30π + 60 which looks like πr + 2r

*August 15, 2016*

**Help on PreCalc**

As usual, make a sketch of a right-angled triangle and using Pythagoras, r^2 = 8^2 + 15^2 = 289 r = 17 π<α<3π/2 ----> α is in quadrant III sin α = -15/17 and cos α = -8/17 recall cos 2A = 1 - 2sin^2 A thus: cos α = 1 - 2sin^2 (α...

*August 15, 2016*

**Maths**

"1/3 of boys and 1/4 of girls." is not a complete sentence. What about the 1/3 of boys and 1/4 of girls ?

*August 15, 2016*

**Pre-calc**

tan2θ=7/11 ; π<2θ<3π/2 so 2Ø is in quadrant III and Ø is in quadrant II construct a right-angled triangle, with angle 2Ø, opposite side as 7, and adjacent side as 11 the hypotenuse is √170. Remember 2Ø is in ...

*August 13, 2016*

**Pre-calc**

As Steve and Damon pointed out to you earlier, sin(α−β) = sinαcosβ - cosαsinβ given: tanα=5/7 and sinα<0 , so by the CAST rule α must be in quadrant III since tanα = 5/7, by Pythagoras, the hypotenuse of our triangle ...

*August 13, 2016*

**Algebra**

So go ahead and simplify the expression that Steve gave you.

*August 12, 2016*

**math**

let the size of the cut-out be a square of side x inches base = (8-2x) by (11.75 - 2x) and the height is x x(8-2x)(11.75-2x) = 63.75 x(94 - 39.5x + 4x^2) = 63.75 94x - 39.5x^2 + 4x^3 - 63.75 = 0 don't know what method you know to solve a cubic, I ran it through Wolfram and...

*August 11, 2016*

**Calc**

let the angle between the two equal sides be Ø area = (1/2)(L)(L)sinØ , (you should know that formula) d(area)/dØ = (1/2)L^2 (-cosØ) , where L is a constant for a max of area (1/2)L^2(-cosØ) = 0 cosØ = 0 but of course cos 90° =0 ...

*August 11, 2016*

**Algebra**

Assuming that each way is 400 miles, (even though in Rome they wouldn't know what miles are, and would be using km.) let speed of plane in still air be x mph let speed of wind be y mph going with the wind: 5(x+y) = 400 ---> x + y = 80 going against the wind: 10(x-y) = ...

*August 11, 2016*

**precal**

x2 - 6x + 5y = -34 5y = -x^2 + 6x - 34 = -1(x^2 - 6x + 9 - 9) -34 = -(x-3)^2 + 9 - 34 y = (-1/5)(x - 3)^2 - 25/5 y = (-1/5)(x-3)^2 - 5 lots of algebraic typing ahead, so I will let you watch 4 great videos dealing with this topic by the remarkable Mr. Khan https://www....

*August 11, 2016*

**Maths**

roots of 4x^2-16x+15=0 are a and b, (for alpha and beta) by the properties of roots of a quadratic a+b = -(-16/4) = 4 ab = 15/4 new roots: a/b and b/a sum of new roots = a/b + b/a = (a^2 + b^2)/(ab) now a^2 + b^2 = (a+b)^2 - 2ab = 4^2 - 2(15/4) = 17/2 so sum of new roots = (17...

*August 11, 2016*

**Math**

My money is on Henry's solution

*August 11, 2016*

**Pre-calc**

That's not what you had originally. Glad you changed it, now my solution should make sense to you.

*August 11, 2016*

**Pre-calc**

The wording of your question makes no sense to me. Do you want csc(5π/6) as found on the unit circle? We have an ordered pair associated with (5π/6) , not csc(5π/6) I strongly suggest you print out one of the many unit circle diagrams available. Here is one of ...

*August 11, 2016*

**correction - Math**

easier way (and correct answer) : let the cost of a tie be $x cost of a shirt = $(x+50) 4x + 7(x+50) = 746 4x + 7x + 350 = 746 11x = 396 x = 36 Each tie costs $36, (and a shirt costs $86) expensive tastes!

*August 11, 2016*

**Math**

8 men mow 4 identical greens in 20 minutes 2 men mow 1 identical green in 20 minutes 6 men mow 1 identical green in 60 minutes

*August 11, 2016*

**Math**

2400 hectares of canola in 12 days using 4 machines 600 hectares of canola in 12 days using 1 machine 3600 hectares of canola in 12 days using 6 machines or time is directly proportional with the acreage and inversely with the number of machines T = k (A/M) given: 12 = k(2400/...

*August 11, 2016*

**Maths**

I don't see a quadrilateral bounded by only 3 sides.

*August 10, 2016*

**algebra**

Just translate the English to Math: let the height be x ft "the width is 3 times longer than the height" ---> width = 3x "the length is 9 times longer than the height" -----> length = 9x Now use the given to form your equation x(3x)(9x) = 64 27x^3 = ...

*August 10, 2016*