Saturday

January 31, 2015

January 31, 2015

Total # Posts: 28,807

**College Algebra and Trigonometry**

Wow, 20 sheets of paper ? Since you titled your post "College Algebra & Trig" I will assume you know that both cos(π/4) and sin(π/4) = √2/2 so x = (√2/2)u - (√2/2)v and y = (√2/2)u + (√2/2)v In 5x^2 - 6xy + 5y^2 we will need...
*January 25, 2015*

**maths**

please retype we use x^2 for x squared, x^3 for x cubed etc What does ..... mean ? If you mean division, then use / for the division sign and place brackets in the correct positions
*January 25, 2015*

**Math**

The way I read it .... y = (x-8)^2 - 6 is the result if the parabola y = (x-1)^2 + 14 has been moved 7 units to the right and 20 units down, so the point (-3,30) went along for the ride, so (-3,30) ---> (4,10) check: old vertex = (1,14) new vertex = (8,-6) ---> 7 to the ...
*January 25, 2015*

**math**

let's assume you mean 2x^2 + 8x +3 = 0 since it does not factor, let's use the formula x = (-8 ± √40)/4 = (-8 ± 2√10)/4 = (-4 ± √10)/2
*January 24, 2015*

**math**

Suppose I change the question to ... "If 15 pencils cost 3 dollars, how many pencils can be bought for 90 cents?" I am sure you could do that question. Now simply replace the numbers you used with the p, d, and c and use the same operations in the same order.
*January 24, 2015*

**Math**

I think we must assume that the tower is in relatively flat plane. I don't know how well you can sketch 3-D diagrams, but mine has two right-angled triangles. One showing the first fire, has a base angle of 8° and a height of 50, so the distance of the fire from is: 50...
*January 24, 2015*

**Math**

#1 "How tall was the tree originally if the piece they chopped down was 7feet tall" ??? 7 ft tall ? #2 , x^2 = 5^2 + 3^2 = 34 x = √34 = appr 5.83 ft or 6 ft to the nearest foot
*January 24, 2015*

**Math**

I would "solve" the equation this way: 3 cot^2 x -1 = 0 cot^2 x = 1/3 tan^2 x = 3 tan x = ±√3 so x is in any of the 4 quadrants, x = 60° , 180°-60° , 180°+60° , 360°-60° = 60° , 120° , 240° or 300° in radians...
*January 24, 2015*

**Math**

A triple of numbers such as 5, 12, 13 is called a Pythagorean triple, because the satisfy the Pythagorean equation. The simplest such triple is 3, 4, 5 (3^2 + 4^2 = 5^2) and 5, 12, 13 is the next simple one. Of course any multiple of that triple would also work, e.g. 3 x (3, 4...
*January 24, 2015*

**combination probability**

Ok Let's assume that all the marbles are distinguishable , that is, I can tell any red apart from the other reds, etc Now lets "choose" 2 reds and 2 whites = C(18,2)*C(16,2) = 18360 Remember in those the order does not matter, and we can tell reds apart and ...
*January 24, 2015*

**combination probability**

Are you looking for the probability of drawing 2 reds and 2 whites when drawing any 4 marbles ? you could have 4!/(2!2!) ways or 6 ways for it to happen: RRWW WWRR RWWR RWRW WRWR WRRW prob of (RWRW) = (6/18)*(7/17)*(5/16)*(6/15) = (6*7*5*6)/73440 prob(WRRW) = (7/18)*(6/17)(*(5...
*January 24, 2015*

**Geometry ques**

We will need the equation of the tangent. y = tanx y' = sec^2 x when x = π/4 , tan π/4 = 1 so at the point (π/4,1) the slope is sec^2 (π/4) = 2 so equation is y = 2x + b at (π/4,1) 1 = 2(π/4) + b b = 1 - π/2 = (2-π)/2 tangent ...
*January 24, 2015*

**Paarabola Ques**

It has to be perpendicular to the tangent.
*January 24, 2015*

**Probability Ques**

what is whist?
*January 24, 2015*

**Algebra**

prove: (1 + 2 + 4 + . . . + 2n) + 1 = 2n+1 testing: if n = 1 , LS = (1) + 1 = 2 RS = 2(1) + 1 = 3 FAIL if n=2 , LS = (1 + 2) + 1 = 4 RS = 2(2) + 1 = 5 , FAIL again Hard to prove something which is not true check your spelling or the wording of the question. I don't know ...
*January 24, 2015*

**Add maths form 4**

done: http://www.jiskha.com/display.cgi?id=1422068863
*January 23, 2015*

**math**

Much Ado About Nothing. two ordered pairs (1950 , 2555360972) and (2000 , 6079006982) slope = (6079006982 - 2555360972)/(2000-1950) = 70472920.2 ---> m for N(t)= mt+b using the first point: 2555360972 = 70472920.2(1950) + b b = -1.348668 x 10^11 so we have N(t) = 70472920....
*January 23, 2015*

**Add maths**

recall that for ax^2 + bx + c = 0 , the sum of the roots = -b/a product of the roots = c/a we are given that the roots are r and 3r so from your equation of x^2 - 2qx + 2q+4 = 0 a = 1, b = -2q, c = 2q+4 r+3r = 2q/1 4r = 2q q = 2r r(3r) = 2q+4 3r^2 = 2(2r) + 4 3r^2 - 4r - 4 = 0...
*January 23, 2015*

**Math (factors and products)**

integral values are integer numbers, so k cannot be a fraction possible factors that end in +12: (x+1)(x+12) (x-1)(x-12) (x+2)(x+6) (x-2)(x-6)--> x^2 - 8x + 12 , so k = -8 (x+3)(x+4) (x-3)(x-4) I expanded one of them, to show one value of k You do the others
*January 23, 2015*

**math**

So we are looking for the between 3181+53 and 3181-53 or between 3234 and 3128 . best webpage for this stuff: http://davidmlane.com/hyperstat/z_table.html enter 3181 for mean enter 526 for sd click on between: enter 3128 and 3234 to get .0803
*January 23, 2015*

**algebra**

f(x)+g(x) = -5x - 4 + 6x - 7 = .....
*January 23, 2015*

**Algebra**

take out a common factor, then use grouping ... 3x^3 + 9x^2 - 3x - 9 = 3(x^3 + 3x^2 - x - 3) = 3( x^2(x + 3) - (x + 3) = 3(x+3)(x^2 - 1) = 3(x+3)(x-1)(x+1)
*January 23, 2015*

**algebra**

testing for 3 terms, (n=3) 1²/1 + (1²+2²)/2 + (1²+2²+3²)/3 = 1 + 5/2 + 14/3 = 49/6 for n = 3 a) --> (3/36)(36+45+17) = 49/6 b) --> (3/6)((4)(2) = 4 , noway! c) --> (9+9+29) = 47 , noway! suspicious it could be a) test for n = 2 sum(2) = 1...
*January 23, 2015*

**algebra**

try it yourselves, using the method I showed in your two other posts of this type
*January 23, 2015*

**algebra**

let's see if we find a pattern sum(1) = 4 sum(2) = 4+6 = 10 sum(3) = 4 + 6 + 9 = 19 sum(4) = 19+13 = 32 using a) the corresponding answers would be 4 10 19 32 mmmmhhh , looking good using b) the terms are -11/3 .... noway using c) the terms are 24 ... forget it! could it ...
*January 23, 2015*

**Math**

agree
*January 23, 2015*

**Math**

clarify if you meant it the way you typed it, or if you meant 4(1^(x/2) )^x remember that 1^anything = 1 so the way you typed it, it would simply become y = 4(1/2)^x if you meant: y = 4(1^(x/2) )^x , then we have y = 4(1)^x or simply y = 4
*January 23, 2015*

**maths**

if collinear, then their slopes must be equal (d-1)/-k = (1-1)/(1-k) = (1-d)/(1) (1-d)/k = 0/(1-k) = (1-d)/1 from the middle ratio we know that the slope = 0 and thus all numerators are 0 so 1 - d = 0 d = 1 similarly if the first and the last are equal, (1-d)/k = (1-d)/1 , ...
*January 23, 2015*

**maths**

recall that for any quadrataic in general form the sum of the roots is -b/a and the product of the roots is c/a let the roots be r and 3r so -b/a = 4r ---- b = -4ar and c/a = 3r^2 ---- c = 3ar^2 I will assume your b2/ac is supposed to be b^2/(ac) then b^2/(ac) = (16 a^2 r^2)/(...
*January 23, 2015*

**algebra**

Now = time(0) = 2 = 2^1 time(1) = 4 = 2^2 time(2) = 8 = 2^3 ... time(n) = 2^(n+1) then 2^(n+1) = 10million log both sides and use rules of logs (n+1)log2 = log 10million n+1 = log 10million/lon2 = 7/log2 = 23.25.. n = 22.25 after 23 months there will be more than 30 million
*January 23, 2015*

**Math**

It asks for miles per gallons or miles / gallons So which numbers go where?
*January 22, 2015*

**ignore my babble - Antiderivatives**

Just go with Steve's reply, ignore mine I read that -3 as an extra term
*January 22, 2015*

**Antiderivatives**

If you differentiate your answers, you certainly don't get back the original f(x), so you are clearly wrong your problem is the middle term -4x^-3 for simple single terms like this, here is how I go about it to integrate I write down the given term: -4x^-3 I then raise the...
*January 22, 2015*

**Math**

Maybe some culinary experts could enlighten me, but ... if you "double" the recipe, wouldn't you just double all the ingredients ?? Anyway, taking the wording at face value, you would need 1.3(1.5) cups of water or 1.95 cups of water
*January 22, 2015*

**math: ratios**

a) Kieran has 9 parts and Simon has 2 parts, so together they have 11 parts, So the ratio of Kieran's parts to the whole = 9parts : 11parts = 9 : 11 b) Kieran/total = 9parts/11parts = 9/11 c) Simon/total = 2/11 (notice 2/11 + 9/11 = 11/11 or the whole total) d) 9x -2x = 28...
*January 22, 2015*

**Math please, please help**

All your numbers can be changed to nice decimals 3/4 = .75 , 2 3/4 = 2.75 3 7/8 = 3.875 map1: .75 inch ---> 30 miles 1 inch -----> 30/.75 = 40 2.75 inches--> 40(2.75) or 110 miles map2: .5 inches -----> 10 miles 1 inches ------> 10/.5 = 20 miles 3.875 --------&...
*January 22, 2015*

**math**

Looking at your other post, I will assume that we are again talking about "simple interest" (in reality simple interest would not be used for any length of time greater than one year. As a matter of fact the method used above would result in a rate much higher than 6...
*January 22, 2015*

**Quadratics**

ummmh, y = 3(x+2)^2 + 5
*January 22, 2015*

**Math-polynomials**

correct expand to show that your are correct.
*January 22, 2015*

**math**

suppose we just define n to be an even number (that way I don't have to worry about the 2n idea) then the 4 consecutive even number are n , n+2, n+4, and n+6 (n+2)^2 = n(n+6) n^2 + 4n + 4 = n^2 + 6n 4 = 2n n = 2 so the 4 numbers are 2 , 4, 6, and 8
*January 22, 2015*

**Math**

term(7) = a+6d term(4) = a+3d a+6d - (a+3d) = 15 a+6d-a-3d=15 3d=15 d = 5
*January 22, 2015*

**maths**

#1: a+6d=3 #2: a+11d=-3 subtract them -5d = 6 d = -6/5 back into a+6d=3 a + 6(-6/5) = 3 a = 3 + 36/5 = 51/5 first three terms are: 51/5 , 9 , 29/5
*January 22, 2015*

**7th grade math**

First one is correct For the second, yes, you could have just subtracted the two. They actually gave you more information than was needed. Obtaining the same answer confirms that your answer is correct. The second question would have been nice had it been worded this way: If ...
*January 22, 2015*

**algebra**

4000(1.04)^n = 4800 1.04^n = 1.2 take log of both sides and use log rules n log1.04 = log 1.2 n = log 1.2/log 1.04 = appr 4.65 years
*January 22, 2015*

**Math**

correct --- x wrong ---- y , both x and y must be whole numbers x+y+2 = 20 x+y = 18 , #! 5x - 3y - 2 = 72 5x - 3y = 74 , #2 #1 times 3 --> 3x+3y=54 #2 as is -----> 5x - 3y = 74 add them 8x = 128 x = 16 back in #1 16+y=18 y = 2 a) he got 16 right, and 2 wrong, skipping 2 ...
*January 22, 2015*

**Math**

side of base of cuboid ---- x x^2 = 44 let the height be h x^2 h = 378.4 h = 378.4/44 = 8.6
*January 22, 2015*

**math**

I would pick b)
*January 22, 2015*

**Math**

#1, the key terms in each answer is the power term pick any two increasing values of x e.g. x = 2, y = 7^2 - 2 = 47 x = 3 , y = 7^3 - 2 = 341 Is there any reason for this pattern NOT to continue, so the function is INCREASING You will see the same for c) and d) Now look at b) ...
*January 22, 2015*

**math**

A good way is to take two pieces of graph paper and cut both of them into 8by8 square pieces It is easy to see that there is 1 large 8x8 square on a chessboard Now use one of the 2 pieces and cut it down to a 7x7 square template. Try placing this template on the 8x8 sheet (...
*January 22, 2015*

**probability**

The three mustaches can be used in 4 different ways, that is we could use any of the 3 of them or we could none at all in the same way the eyebrows can be used in 3 ways, the noses in 5 ways, and the set of ears in 2 ways. so the number of different makeups is 4x3x5x2 = 120 ...
*January 22, 2015*

**. 8th grade math**

2 nitro react with 3 hydro to make 2 ammo ratio: 2 : 3 : 2 we want : x : 42 : 28 2(14) : 3(14) : 2(14) so x = 28 28 molecules of nitrogen are needed check: ratio of 28:42:28 = 2:3:2
*January 21, 2015*

**Math**

#1, none are increasing http://www.wolframalpha.com/input/?i=plot+y+%3D+-2%5Ex+%2C+y+%3D+2+%281%2F2%5Ex%29+%2C+y+%3D+3+%284%5E-x%29+%2C+y+%3D+-4+%282%5Ex%29 2. for y-intercept , let x = 0 4(2^0) - 2 = 4(1) - 2 = 2 3. as x ---> +big 3^x get big , so the whole expression ...
*January 21, 2015*

**math**

simplify the situation. Suppose I compare the number 3 with the number 12 Would you agree that 12 is 4 times the number 3 ? What did I do with 12 and 3 to get 4 ? Did I subtract them? no way Did I divide them ? yeahhh so area of Canada = 1 x 10^7 and area of Mexico= 2 x 10^6 ...
*January 21, 2015*

**Math**

I would use elimination. 4x + 4y + 2z = -10 ----- 1st times 2 3x + 4y + 2z = 0 ----- #2 as is subtract them x = -10 ------ that was lucky 3x + 4y + 2z = 0 --- #2 x + 3y + 2z = 1 ----#3 subtract them 2x + y = -1 sub x = -10 into that -20 + y = -1 y = 19 back into #1 2x+2y+z = -...
*January 21, 2015*

**Math**

yes
*January 21, 2015*

**math**

arc length = rØ , where Ø is the angle in radians = 36(12) = 432 cm so in 1 second the wheel covers 432 cm so to cover 100 m or 10000cm would take 10000/432 or 23.15 seconds
*January 21, 2015*

**Math**

There are 9 things to choose from and we choose 2 of them There are C(9,2) such choices or 36 choices, which must match the number of children
*January 21, 2015*

**Precalc/Trig**

make a sketch and place (2,-3) into the fourth quadrant. Complete the right-angled triangle the hypotenuse will be √13 , x - 2, y = -3 let the angle be Ø tanØ = -3/2 Ø = 2π - .98279.. = 5.3 so one point is (√13, 5.3) which is what you have...
*January 21, 2015*

**Math**

find the vertex to find the maximum height let 0 = 15 + 110t - 16t^2 and solve for t to get the time it hits the ground. One of your answers will be negative, you will ignore that one
*January 21, 2015*

**math**

since area = lw x^2 + x - 12 = (x+4)( ......) clearly ( ..... ) must be (x - 3) check: expand (x-3)(x+4)
*January 21, 2015*

**Math**

Is there a question? Also, which is it, 35402.06 or 35403.06 ?
*January 21, 2015*

**Algebra please help**

mmh, let her try x = 3 and to really confuse her, let her try x =
*January 21, 2015*

**12 Math**

f(1) = 2 + 5 - 1 - 3 + 1 = 4 f(3) = 162 + 135 - 9 - 9 + 1 = 280 for between the points (1,4) and (3,280) slope = (280-4)/(3-1) = 138 f'(x) = 8x^3 + 15x^2 - 2x - 3 f ' (1) = 8+15 - 2 - 3 = 18 at (1,4) the real slope is 18 f ' (3) = 216 + 135 - 6 - 3 = 342 at (3,280...
*January 21, 2015*

**math**

Re-wording your problem: find the vertex of the parabola h = -4.9t^2 + 16t + .5 the t of the vertex is -16/(2(-4.9)) = 80/49 the h = -4.9(80/49) + 16(80/49) + .5 = appr 13.56 m
*January 21, 2015*

**Math**

Since the shapes are similar, the ratio of their corresponding sides must be the same so.... new side/24 = newbase/oldbase newside/24 = 11/16 newside = 11(24)/16 = 16.5 mm check: newside/oldside = 16.5/24 =.6875 newbase/oldbase = 11/16 = .6875 we're good!
*January 21, 2015*

**algebra**

What is your rule ?
*January 21, 2015*

**algebra**

(6v^2 + 7vd - 3d^2) - (9v^2 - 5vd + 19d^2) = 6v^2 + 7vd - 3d^2 - 9v^2 + 5vd - 19d^2 = ... easy from there
*January 21, 2015*

**algebra**

In this case there is no need for the brackets. Now just add up the "like" terms
*January 21, 2015*

**math**

let the string be 1 unit of length shorter piece --- x longer piece ---- 1-x ratio of string to smaller part = 1/x ratio of smaller part to larger part = x/(1-x) 1/x = 6(x/(1-x) 1/x = 6x/(1-x) 6x^1 = 1 - x 6x^2 + x - 1 = 0 (3x - 1)(2x + 1) = 0 x = 1/3 or x = -1/2, the last ...
*January 21, 2015*

**Math**

Well, first you would add up the fruits. You will have to convert all the fractions to improper fractions, get a common denominator, and simplify to one fraction. Then multiply that by 1/5
*January 20, 2015*

**Algebra**

pounds of cheaper --- x pounds of higher price -- 40-x solve for x 4.93x + 5.85(40-x) = 5.62(40)
*January 20, 2015*

**extra note - Algebra**

I should not have called y = mx + b the "general form" y = mx + b is called the slope y-intercept form general form would be: 2x - 7y + 19 = 0 some texts call 2x-7y=-19 the standard form
*January 20, 2015*

**Algebra**

yes, there are several methods first you need the slope slope = (5-3)/(8-1) = 2/7 general form: y = mx + b, where m is the slope and b is the y-intercept y = (2/7)x + b but the point (1,3) is on it, so 3 = (2/7)(1) + b multiply by 7 to get rid of fractions 21 = 2 + 7b 7b = 19 ...
*January 20, 2015*

**Math**

.6 (some number) = 24 .6(some number)/.6 = 24/.6 some number = 40 or more in standard form .6x = 24 x = 24/.6 = 40 1.8x = 80 x = 80/1.8 = 44.44.. (the 4 repeats) or x = 400/9 check: (180/100)(400/9) = 80
*January 20, 2015*

**Pre-Calc**

What a silly silly question, anyway.... -.107x^2 + 5.68x - 48.5 = 26 -.107x^2 + 5.68x - 74.5 = 0 times 1000 to get rid of all those decimals 107x^2 - 5680x + 74500 = 0 use the quadratic formula and reject any answer that falls outside the given domain (I did get a valid answer)
*January 20, 2015*

**Equation7**

correct
*January 20, 2015*

**Equation7**

Did you sub c = -13 back in to see if it works ?? I bet it won't, since I see a blatant error in your 2nd last line Hint: don't you think that little c should be changed to 5c/5 ? Don't you need a common denominator to subtract ?
*January 20, 2015*

**Algebra**

from your x + 8 = -15 x = -15-8 x = -23 then y = 3x-8 = 3(-23) - 8 = -77 check: in #1 3x - y = 3(-23) -(-77) = -69 + 77 = 8 , check! in #2: 4x - y = 4(-23) - (-77) = -92 + 77 = -15 , check! x = -23 , y = -77
*January 20, 2015*

**Math**

Why not sub x = 1.5 into the left side and then into the right side. Did you get the same result? If so, then you were correct, if not ....
*January 20, 2015*

**Algebra**

Ok, but what about d) ????? y = 2x + 3 for (1,5) 5 = 2(1) + 3 5 = 2+3 5 = 5 your a) y = -2x + 7 5 = -2(1) + 7 5 = -2+7 5 = 5 that works too, so (1,5) lies on two different lines and (1.5) must be the intersection of y = 2x+3 and y = -2x +7
*January 20, 2015*

**Algebra**

a) , c), and d) have a slope of 2 b) doesn't even have an x term Now which equation does (1,5) fit into ??? put x = 1 into each right side of the equation and see if you get a y value of 5
*January 20, 2015*

**Math**

So you have 6 + 12 + 18 + ... + 996 this is an AS where a = 6, d = 6 so 996 = 6 + (n-1)(6) 996 = 6 + 6n - 6 6n = 996 n = 166 , you are right so far sum(166) = 83(first + last) = 83(6 + 996) = 83166 , you had that too or using the more standard sum formula S(n) = (n/2)(2a + (n-...
*January 20, 2015*

**Math**

do 2.25 ÷ 0.0075
*January 20, 2015*

**Math**

What do you mean you changed the fractions to 4x-3x=28-6 ? HOW ? That doesn't even make any sense -1/4x+6=2/3x+28 multiply each term by 12 , the LCD (-1/4x)(12) + 6(12) = (2/3x)(12) + 28(12) -3x + 72 = 8x + 336 -11x = 264 x = - 24
*January 20, 2015*

**Math**

x = 22 doesn't even come to satisfying the equation. How did you get that ?
*January 20, 2015*

**Math**

N(M or E) = N(M) + N(E) - N( M and E) + other 50 = 21 + 32 - 7 + other other = 4 or If you know Venn diagrams, this is a real easy one to set up
*January 20, 2015*

**Math**

divide 16.5 by 10.5 16.5/10.5 = appr 1.57 times
*January 20, 2015*

**Math**

perfectly set up for using substitution: in the 2nd: 4x - 2(3x+2) = -8 4x - 6x - 4 = -8 -2x = -4 x = 2 , then y = 3(2) + 2 = 8 but, anyway... line them up in a better way: #1: 3x - y = -2 #2: 4x - 2y = -8 double the first: 6x - 2y = -4 subtract the 2nd: 2x = 4 x = 2 sub back ...
*January 20, 2015*

**math**

number of pictures it can hold --- x (1/4)x + 375 = (2/3)x times 12 3x + 4500 = 8x 5x = 4500 x = 900 so originally we had (1/4)900 = 225 pictures
*January 20, 2015*

**Math**

number who play clarinet --- x number who play flute ----- 2x , (notice how I avoided fractions?) 2x + x + 8 = 44 3x = 36 x = 12 So 12 play clarinet, 24 play flute and 8 play oboe
*January 20, 2015*

**Pre calc**

ok, you fixed your earlier typo. Did you make a sketch? I completed the parallogram and am looking at a triangle with sides 30 and 15 and the angle between them as 102° by the cosine law: R^2 = 30^2 + 15^2 - 2(30)(15)cos102 = 1312.102... R = appr 36.22 mph by sine law: sin...
*January 20, 2015*

**MATH**

first line them up properly #1: -x + 2y = 6 #2: x - 6y = -18 add them: -4y = -12 y = 3 in #1: -x + 6 = 6 -x = 0 x = 0 why did you not sub your values back in to see if you are correct ?
*January 20, 2015*

**Pre calc**

"The water current is 15 mph with a direction of 22 mph." ---> makes no sense to me
*January 20, 2015*

**math**

Mmmmhhh, as a Canadian, I always thought that the US had 50 states, but anyway .... You must have data for the whole country, but I will give you the hints for the 10 sets of data you show. I will not do the arithmetic for you. To get the mean, just add them up and divide by ...
*January 20, 2015*

**trigonometry**

One more clue. Since all 6 trig functions can be defined in terms of sin and cos, I often change everything to sines and cosines, unless I see an obvious definition such as 1 + cot^2 Ø = csc^2 Ø in #1
*January 20, 2015*

**trigonometry**

Most of these appear to be based on the Pythagorean identity sin^2 x + cos^2 x = 1 , and its variations e.g. if I divide the above by sin^2 x , I get 1 + cot^2 x = csc^2 x and that is what I see in the LS of #1 Use LS for left side and RS for right side, work each side ...
*January 20, 2015*

**Math Help**

cosx - cosx/(1-tanx) = sinxcosx/(sinx - cosx) LS = cosx - cosx/(1 - sinx/cosx) = cosx - cosx/( (cosx - sinx)/cosx ) = cosx - cosx(cosx)/(cosx - sinx) = cosx + cos^2 x/(sinx - cosx) = (sinxcosx - cos^2 x + cos^2 x)/(sinx - cosx) = sinxcosx/(sinx - cosx) = RS
*January 20, 2015*

**Math Help**

If you have a typo in #1 and you meant: cot^2y(sec^2 y-1)=1 , then LS = cot^2 y (tan^2 y) = 1 = RS recall that : tanx = sinx/cosx and cotx = cosx/sinx so tanxcotx = (sinx/cosx)(cosx/sinx) = 1 The first substitution is one of the basic Pythagorean identities derived from sin^2 ...
*January 20, 2015*

**Math**

nice triangle, with sides 20,20 and the contained angle between them as 3° could just use cosine law: x^2 = 20^2+20^2-2(20)(20)cos3° = 1.09637.. x = √1.09... = appr 1.047 miles or since you have an isosceles triangle, draw and altitude to get a right-angled ...
*January 20, 2015*

**math**

Assuming the second purchase was in 500 g packages .... (typo) The shopkeeper bought 30(1000) + 20(500) or 40000g , or 40 kg He/she divided this into 40000/125 smaller packets or 320 packets of 125 g each
*January 20, 2015*

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