Monday

February 20, 2017
Total # Posts: 37,717

**Math**

amount taken out as loan = 25 - .2(25) = 20 or just take .8(25) = 20 amount owing after 8 years = 20(1.025)^8 = 24.368 gh cedis

*November 18, 2016*

**Math**

1 7/10 = 17/10 "as many" suggests multiplication e.g. bill eats 3 times as many donuts as Bob if Bob eats 4 donuts, then Bill would eat 3*4 or 12 donuts so Elizabeth has (17/10) as many as Rosalie. let Rosalie's number of plants be x then: (17/10)x = 51 ----> ...

*November 18, 2016*

**Math**

time for first trip = d/x time for return = d/y total time = (d/x + d/y) = (dy + dx)/(xy) = d(x+y)/(xy) total distance = 2d average speed = 2d/( d(x+y)/(xy) ) = 2xy/(x+y) = 50 xy/(x+y) = 25 xy = 25x + 25y 25y - xy = 25x y(25 - x) = -25x y = 25x/(x-25) e.g. let x = 50, then y...

*November 18, 2016*

**math**

horizontal path = 15(2.5) = 37.5 units^2 vertical path = 9(2.5) = 22.5 units^2 total = 60 units^2 BUT, we counted the intersection of the paths twice, so we have to subtract 2.5(2.5) or 6.25 units^2 leaving us with 63.75 units^2

*November 18, 2016*

**Geometry**

So what is (3/2)(4.8) ? Just add up your 4 sides, remember they come in equal pairs.

*November 18, 2016*

**Order MATH!**

I suggest you change them all to decimals, and then it is easy to see.

*November 18, 2016*

**Pre-calculus**

correction for #1, should say: (1+cosx)/(1-cosx) = (secx + 1)/(secx - 1) RS = (1/cosx + 1)/(1/cosx - 1) = (1/cosx + 1)/(1/cosx - 1) * cosx/cox = (1+ cosx)/(1 - cosx) = LS Well, that was easy. #2, hint: change everything to sines and cosines expand and simplify the LS #3, use ...

*November 18, 2016*

**Maths**

So in 60 minutes he can type 3200 words. How many words can he type in 1 minute? Then how many in 15 minutes ?

*November 18, 2016*

**additional maths (maths)**

so you just want the max of d(t) find the derivative, set it equal to zero, and solve that for t Once you have the value of t which gives you the maximum, plug it back into d(t) to actually find that distance. Very straight-forward.

*November 18, 2016*

**Maths**

The missing angle ? = 45° by the sine law: a/sin35 = 40/sin100 a = 40sin35/sin100 = appr 23.3 c/sin45 = 40/sin100 c = 40sin45/sin100 = appr 28.7 area = (1/2)(ab)sin45 = appr 329.5 units^2

*November 18, 2016*

**maths**

so he gave away 60%, leaving him with 40% .4x = 9600 solve for x

*November 18, 2016*

**Math (Differentials)**

our f(x) = x^(1/3) , and f ' (x) = (1/3)x^(-2/3) = 1/(3(x)^(2/3) ) I will go with your x = 27 , dx = -2 f(x + dx) is appr = f(x) + f ' (x) (dx) f(25) = f(27) + (1/3)(27)^(-2/3) = 3 + (1/27)(-2) = 3 - .0741 = 2.926 you simply added the part at the end instead of ...

*November 18, 2016*

**algebra 2**

Your calculations are correct (sum of roots = 2+3i + 2-3i = 4 product of roots = (2+3i)(2-3i) = 4-(-9) = 13 ) It said to write the quadratic equation, which is x^2 - 4x + 13 = 0 you had y = x^2 - 4x + 13 , which is the quadratic function.

*November 17, 2016*

**Math**

I will place the parabola as opening to the right, with its vertex at (0,0) so the equation is y^2 = 4px, where (p,0) is the focus but (6,16) lies on it 16^2 = 4p(6) p = 256/24 = 32/3 So it should be placed at (32/3 , 0)

*November 17, 2016*

**Geometry**

original area = base x height = bh new area = .7b x 1.2h = .84bh so there is a 16% decrease in the area

*November 17, 2016*

**Calculus: Centers of Mass**

A quick calculation shows that the line intersects the parabola at (2,2) in the first quadrant lots of work ahead of us: first you must find the area of the region, it has to be done in two parts: from x=0 to x=2 under the curve, then from x=2 to x=4 under the straight line ...

*November 17, 2016*

**correction - Difficult Math**

I misread "Thirty of the cards from his cousin are National League players" as one third of the cards from his cousin are NL players

*November 17, 2016*

**Difficult Math**

total collection ---- x from dad --- x/4 from uncle --- x/5 ---> (.2)x = (2/10)x = x/5 from brother --- x/2 leaving : x -x/4 - x/5 - x/2 = x/20 so from cousin = x/20 so (1/3)(x/20) = 30 x = 1800 Steve has 1800 cards check: from dad = 1800/4 = 450 from uncle = .2(1800) = 360...

*November 17, 2016*

**Math**

999,999,999,999 = appr 1,000,000,000,000 = 10^12 ( you would be off by $1 on 1 Trillion dollars) 100,000,000,000,000 = 10^14 so 100,000,000,000,000 times 999,999,999,999 = 10^12 * 10^14 = 10^26 that would be 100 septillion.

*November 17, 2016*

**Math**

In arithmetic "of" means multiplication, so 1/10 of 2(10)+4(1)+6(1/10)+7(1/100)+8(1/1000) = (1/10)(20) + 4 + .6 + .07 + .008 = 2+4+.6+.07+.008 = 6.678 http://www.wolframalpha.com/input/?i=evaluate+1%2F10+*+2(10)%2B4(1)%2B6(1%2F10)%2B7(1%2F100)%2B8(1%2F1000) if you ...

*November 17, 2016*

**Algebra**

Help with what? You have given us two different circles. What do you want to do? They do intersect. Here is a picture of your problem http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%2B6y%2B5%3D0+,+x%5E2%2By%5E2-2x-8%3D0

*November 17, 2016*

**Maths**

no XYYYY , where X is the vowel, Y can be anything else number of ways = (2)(4!) = 48 e.g. E(BGIN) - one of the 24 ways to arrange BGIN I(GBEN) - one of the 24 ways to arrange GBEN

*November 17, 2016*

**Maths**

That result is like adding 3/10 + 14/20 + 24/30 = 41/60 Wow, just adding the numerators and the denominators ! Unfortunately Math doesn't work like that 3/10 + 14/20 + 24/30 = 18/60 + 42/60 + 48/60 = 108/60 for 3 tests so average = (108÷3)/60 = 36/60 = 60% By simply...

*November 17, 2016*

**calc**

no, for the 2xy term you have to use the product rule 2y dy/dx + (2x)(dy/dx) + 2y(1) - 3x^2 = 0 keep all the dy/dx terms on the left, everybody else goes to the right 2y dy/dx + 2x dy/dx = 3x^2 - 2y factor out the dy/dx dy/dx (2y + 2x) = (3x^2 - 2y) divide dy/dx = (3x^2 - 2y...

*November 17, 2016*

**math**

The best way to do this is to actually sketch it. I am sure it will make perfect sense to you after you draw it. Remember that y =-2 is a horizontal line 2 units below the x-axis

*November 17, 2016*

**math**

profit = revenue - cost = 12x - .01x^2 - 8^x - 7 d(profit)/dx = 12 - .02x - (8^x)(ln8) = 0 for a max of profit 12 - .02x = ln8 (8^x) if x = 0, LS = 12 , RS = ln8 or appr 2.08 if x = 1, LS = 11.98 , RS = appr 16 so there is a solution between 0 and 1 This question does not make...

*November 17, 2016*

**Math**

Strange wording. "What fraction" of what should the shorter side be increased? Since the sides are stated in a ratio, they could be 4 cm by 5 cm, 40 miles by 50 miles, 8 ft by 10 ft, etc In each case the shorter side would be increased by 1/4 of its original length. ...

*November 17, 2016*

**math**

you are simply solving the quadratic 187 = -16t^2 + 45t + 364 16t^2 - 45t - 177 = 0 solve by using the formula, one of the answers will probably be negative. Reject it.

*November 17, 2016*

**Maths**

I will assume the 2nd direction is 125° The angle between the two directions is 90° so AC = ?(120^2 + 200^2) = 233.238 km or Suppose we did not see that 90° ,we could simply use vectors AC = (120cos35,120sin35) + (200cos125,200sin125) = (98.298.., 68.829..) + (-114...

*November 17, 2016*

**Maths**

As an illustration of your problem, place 3 identical coins, e.g. 3 quarters in such a way that they are tangent to each other. Sketching a triangle around them results in an equilateral triangle, we want the perimeter of that triangle. Let's concentrate on one of these ...

*November 17, 2016*

**Algebra**

place the vertex at (0,0) and the focus at (8,0) The directrix will be x = -8 let P(x,y) be any point By definition: ?( (x-8)^2 + y^2) = x+8 square both sides x^2 - 16x + 64 + y^2 = x^2 + 16x + 64 y^2 = 32x so at the point where the dish is 10 ft wide, y = 5 25 = 32x x = 25/32

*November 16, 2016*

**Math**

10,000(1.04)^n = 15000 1.04^n = 1.5 take logs of both sides log 1.04^n = log 1.5 n log 1.04 = log 1.5 n = log 1.5/log1.04 = 10.338.. 10 years will not be enough , so she makes 15,000 or more in the 11 th year for the second question you have an arithmetic sequence with a = ...

*November 16, 2016*

**6 grade math**

no need for guessing, just reverse the steps: the first thing we did was multiply by 2, then subtract 27 to get 407 So everything done in reverse: ( 407+27) divide by 2 = 434 ÷ 2 = 217

*November 16, 2016*

**Algebra**

x e^.06t = 70000 x = 70000/e^(.06(19)) = 22,387.33

*November 16, 2016*

**Statistics**

prob(exactly one boy) = C(7,1)xC(5,4)/C(12,5) = 7(5)/792 = 35/792 prob(exactly 2 boys) = C(7,2)xC(5,3)/792 = 21(10)/792 = 35/132 at least one boy = 1 - prob(all girls) = 1 - 1/792 =791/792

*November 16, 2016*

**Math**

you second equation is x-2055 = .25y , what's with the G ? but y = x x-2055 = .25x .75x = 2055 x = 2740

*November 16, 2016*

**Math**

Did you mean, find cos t ? if so, cos t = 5/?29

*November 16, 2016*

**mathematics**

Did you mean x+y=1 x-y=3 ?? if so, add them to get 2x=4 x=2 now subtract them 2y = -2 y = -1

*November 16, 2016*

**math**

Just translate from English to Math larger number --- x smaller number --- y x-y = 15---> x = y + 15 3x = 8y 3(y+15) = 8y 3y + 45 = 8y 45 = 5y y = 9 , then x = 9+15 = 24 state your conclusion

*November 16, 2016*

**math**

speed of train ---- t km/h speed of car ----- c km/h 120/t + 480/c = 8 15/t + 60/c = 1 times tc tc = 15c + 60t 200/t + 400/c = 25/3 times tc (25/3)tc = 200c + 400t tc = (3/25)(200c + 400t) = 24c + 48t 24c + 48 = 15c + 60t 9c = 12t c = 4t/3 sub into 15/t + 60/c = 1 15/t + 60/(...

*November 16, 2016*

**math**

boys rate = 1/b men's rate = 1/m job done by 2 men and 5 boys in 4 days = 4(2/b + 5/m) = 8/b + 20/m job done by 4 men and 4 boys in 3 days = 3(4/m + 4/b) = 12/m + 12/b 8/b + 20/m = 12/m + 12/b 8/m = 4/b 8b = 4m m = 2b or b = m/2 The man's rate is twice the boy's ...

*November 16, 2016*

**TRIANGLE MATH HELP!!!**

Obviously.

*November 16, 2016*

**TRIANGLE MATH HELP!!!**

clearly 47:29:104 ? 46:30:104, but close and 4 : 6 : 8 ? 5.6 : 8 : 11 because: 5.6/4 = 1.4 8/6 = 1.333... 1.375 which answer matches my conclusion

*November 16, 2016*

**Math Help!!!**

6/202.5 = x/52.5 202.5x = 6(52.5) 202.5x = 315 x = 315/202.5 = 3150/2025 = 14/9 or 1 5/9 or 1.5555.... take your pick 1.555... rounded to one decimal is 1.6

*November 16, 2016*

**Math Help!!!**

set up a simple ratio and solve for x 6/202.5 = x/52.5

*November 16, 2016*

**Calculus**

hint: What is the derivative of secx ??

*November 16, 2016*

**Ravindra bharathi school Maths**

Did you mean 1 m , 23 cm? which is 123 cm adding 21 cm gives her 144 cm (tall 10 year old girl, did I mis-read your question?)

*November 16, 2016*

**Algebra**

Retype after correcting the English.

*November 16, 2016*

**math**

one number --- 2x , (avoiding fractions) the other ----- x + 5 (2x)^2- (x+5)^2 = 17 4x^2 - x^2 - 10x -25 - 17 = 0 3x^2 - 10x - 42 = 0 x = (10 ± ?604)/6 = (5 ± ?151)/3 2x = .... x+5 = ... it works, I checked on my calculator

*November 16, 2016*

**Maths**

If I read this correctly, we would get: 1, 4, 5, 10, 20, 40, 80, ... in effect, each term is twice its previous term from the 4th term on Where does the number 2016 come in? clearly not in this sequence. suppose my term start with 1, 2 , then we get 1,2, 3, 6, 12, 24, , again ...

*November 16, 2016*

**Math**

6n = 8p or n = 4p/3 n = p+3.5 4p/3 = p + 3.5 times 3 4p = 3p + 10.5 p = 10.5

*November 16, 2016*

**Maths**

new length = 1.2(50) or 60 m new area = 2340 new width = 2340/60 = 39 increase in width = 9 m

*November 16, 2016*

**math**

I did the previous one for you. Do be successful in this topic you simply MUST know how to do this type of trivial question. They don't come any easier than this one. Show me the steps you would take to solve this problem.

*November 15, 2016*

**math**

number of ways to get 3 tens and 2 kings = C(4,3) * C(4,2) = 24 prob(of your event) = 24/C(52,5) = 24/2598960 = 1/108290

*November 15, 2016*

**math. PLEASE HELP.**

Following your description I got sin 29° = opp/hyp = 4.6/c csin29 = 4.6 c = 4.6/sin29 = 9.48826.. or appr 9.5 I don't know how you got 2.5

*November 15, 2016*

**disagree - math**

Batting "order" implies that the order they play is important, so 13 P 9 = 13*12*11*10*9*8*7*6*5 = ....

*November 15, 2016*

**Math**

dividing by: 2's leaving one remainder: 3 5 7 9 11 13 15 ... odd numbers 3's leaving one remainder: 4 7 10 13 16 19 22 25 28 ... common difference 3 So far: 7 13 19 25 31 37 43 49 .... (common difference is 6) 4's leaving one remainder: 5 9 13 17 21 25 29 33 37 41 ...

*November 15, 2016*

**Algebra**

The only condition your equation states is that y = 3 That is, there is no condition on x, so the x can be anything. e.g. (4,3), (1,3), (506,3), (12.34, 3), (?,3), .... the result is a horizontal line 3 units above the x-axis, that is, the y = 3

*November 15, 2016*

**Geometry**

What makes you say it is (9,5) ???

*November 15, 2016*

**Algebra2**

correct

*November 15, 2016*

**Pre-cal**

sec x = 2csc x 1/cosx = 2/sinx sinx = 2cosx sinx/cosx = 2 tanx = 2 yes, I would use tan^-1 (2), but make sure your calculator is set to radians, (DRG key) Also remember that the tangent is positive in quads I and III tan^-1 (2) = appr 1.107 x = 1.107 or x = ?+1.107= appr 4.249

*November 15, 2016*

**math**

so in 7 years ? amount = 3000(1.05)^7 = ....

*November 15, 2016*

**Algebra**

2a = 4 a = 2 e = c/a c/2 = 3/2 c = 3 in a hyperbola: a^2 + b^2 = c^2 4 + b^2 = 9 b^2 = 5 a^2 = 4 centre is (-2,3) (x+2)^2 /4 - (y-3)^2 /5 = 1

*November 15, 2016*

**Algebra**

g(x) = x^2 - 2 g(-2) = (-2)^2 - 2 = 4-2 = 2

*November 15, 2016*

**Maths**

smaller angle --- x larger angle --- x+20 x + x+20 + 90 = 180 2x = 70 x = 35 the angles are 35° , 55° and 90°

*November 15, 2016*

**Trigonometry**

taking your data: y = (4/7)sin (x + 3?) + 1 when x = ?/2 y = (4/7)sin(?/2+3?) = 1 = (4/7)sin (7?/2) + 1 = (4/7)(-1) + 1 = 3/7

*November 15, 2016*

**MATH 123**

1((1/2)^(t/5730) = .55 (.5)^(t/5730 = .55 take log of both sides log (.5)^(t/5730 = log .55 (t/5730) log .5 = log .55 t/5730 = log .55/log .5 t = 5730(log .55/log .5) = appr 4942 years

*November 15, 2016*

**math**

x + y ? 20 9x + 12y ? 200 whatever graph they give you, there should be one with the region below x+y = 20 shaded in AND the region above 9x + 12y = 200 shaded in. It should look something like this: http://www.wolframalpha.com/input/?i=plot+x+%2B+y+%3D+20+,+9x+%2B+12y+%3D+200...

*November 15, 2016*

**math**

When you have a function such as P(x) = 2(x-3)(x-4) you could also write it as y = 2(x-3)(x-4) So when they speak of the zeros of the function, they are really describing the x's that make y = 0 that is: 2(x-3)(x-4) = 0 Now think about the answer of 0 after a ...

*November 15, 2016*

**maths**

fog = f(g(x)) = f(2x-3) = (2x-3)^2 + 3(2x-3) + 1 = 4x^2 - 12x + 9 + 6x - 9 + 1 = 4x^2 - 6x + 1 now do gog in the same way

*November 15, 2016*

**Math**

A : B = 5:11 = 10 : 22 = ... = 10x : 22x A : B : C = 2:3:15 = 10:15:75 = ... = 10x:15x:75x in solution X we have 10x/(22x) of A so amount of A in 400 L ofX is (10/22)(400) = appr 181.8 L in solution Y amount of C in 400 L = 75x/(100x)(400) = 300 L

*November 15, 2016*

**maths**

qD(9) = 8000/(81+1) = appr 97.56 qD(8.5) = 8000(72.25+1) = appr 109.22 So, what do you think?

*November 15, 2016*

**algebra**

just translate .... four times a number --- 4x fourteen times its reciprocal --- 17(1/x) or 17/x the sum of ---> + is 15 ----> = 15 so: 4x + 17/x = 15 How easy was that?

*November 15, 2016*

**Algebra**

woman's rate ---- 1/x man's rate ----- 1/(x-5) , where x > 5 combined rate = 1/x + 1/(x-5) = (x-5 +x)/(x(x-5)) = (2x-5)/(x^2 - 5x) (2x-5)/(x^2 - 5x) = 1/6 x^2 - 5x = 12x - 30 x^2 - 17x + 30 = 0 (x-15)(x-2) = 0 x = 15 or x =2 , but x > 5 x = 15 The woman can do ...

*November 15, 2016*

**Math**

1-(-2)^2*(-1)^3 = 1 - 4(-1) = 1 + 4 = 5

*November 15, 2016*

**maths**

Make your sketch. Method 1, complete the parallelogram and find the diagonal x^2 = 5^2 + 3^2 - 2(5)(3)cos 150° = 59.9807... x = appr 7.74 (exact value: x^2 = 34 + 30?3/2 = 34 + 15?3 x = ?(34 + 15?3) ) method 2 place vector P along the horizontal so vector P = (5,0) vector ...

*November 15, 2016*

**Algebra**

same thing e.g. (1/2)(12) = 6 12/2 = 6 as to your question, mom's age ---- x Rowena's age -- x/2 8 years ago: mom ---- x-8 Rowena -- x/2 - 8 x/2 - 8 = (1/3)(x-8) times 6, the LCD 3x - 48 = 2(x-8) 3x - 48 = 2x - 16 x = 32 Mom is 32, Rowena is 16 check: 8 years ago, the ...

*November 15, 2016*

**math**

Arggghhhh!

*November 15, 2016*

**Maths**

How about this approach? A:B = 2:3 or 6:9 B:C = 9:5 ---> notice the value of B is the same so A:B:C = 6:9:5 or 6x:9x:5x 6x+9x+5x = 400 20x = 400 x = 20 so A got 6(20) = 120 B got 9(20) = 180 C got 5(20) = 100

*November 15, 2016*

**Math**

I am going to assume you meant (2x-7)/4 - (x-6)/7 = 0 then (2x-7)/4 = (x-6)/7 multiply both sides by 28, the LCD 7(2x-7) = 4(x-6) 14x - 49 = 4x - 24 10x = 25 x = 25/10 = 5/2 or 2.5 or 2 1/2

*November 14, 2016*

**Math**

50x^4 / (12x) = 25x^3 /6 or (25/6)x^3

*November 14, 2016*

**thomas middle such**

it is less than 300 --> 1xx or 2xx the hundreds digit is 3 less than the ones digit ---1x4 or 2x5 the tens digit is 5 more than the hundreds digit ---> 164 or 274 the sum if the digits is 11 ----> 164

*November 14, 2016*

**algebra**

original: width --- x length --- 5x , (it said so) new dimensions: length = 5x - 3 width = x+10 perimeter = 2* width + 2*length = 2(x+10) + 2(5x-3) = 374 2x + 20 + 10x - 6 = 374 12x = 360 x = 30 So the original rectangle had a width of 30 m and a length of 150 m

*November 14, 2016*

**algebra**

4b/2 + 3 = 11 + b 2b + 3 = 11 + b, since 4/2 = 2 2b - b = 11-3 b = 8 or 4b/2 + 3 = 11 + b multiply every term by 2 4b + 6 = 22 + 2b 4b - 2b = 22 - 6 2b = 16 divide both sides by 2 b = 8

*November 14, 2016*

**math**

the effective distance: 16 km east and 8 km north ---> right-angled triangle hint: Pythagoras

*November 14, 2016*

**math**

Poorly worded question. Are we to assume that some questions were skipped, and no reward or penalty for skipped questions? I will assume that. rights ---- x wrongs --- y skipped -- 40-x-y) 5x - 3y + 0(40-x-y) = 70 5x - 3y = 72 y = (5x-70)/3 , clearly 14 ? x ? 40 , x+y ? 40 ...

*November 14, 2016*

**Math**

Now: Benny ---- x years Apple ---- 38-x 6 years ago: Benny ---- x-7 Apple ----- 38-x - 7 = 31-x 31-x = 3(x-7) solve for x, and sub into my definitions

*November 14, 2016*

**Maths**

let the perpendicular height be 4x let the slant height be 5x (4x)^2 + 6^2 = (5x^2 16x^2 + 36 = 25x^2 carry on, of course you would reject the negative value of x after taking the square root at the end.

*November 14, 2016*

**Maths**

Think of the 5 kids standing in a row, and in each row changing positions 1 ---> 3 2 ---> 5 3 ---> 1 4 ---> 2 5 ---> 4 At the start,,,: 1 2 3 4 5 ---> A B C D E after 1 round: 3 4 1 5 2 ---> C D A E B after 2 round: 1 5 3 2 4 ---> A E C B D after 3 ...

*November 14, 2016*

**math**

depends where you want the water spout to be. It would make sense to have the spout at the origin. Then the zeros of the function would be (0,0) and (8,0) and the vertex would be at (4,6) height = a(x - 4)^2 + 6 but (0,0) lies on it, thus: 0 = a(0-4)^2 + 6 16a = -6 a = -3/8 ...

*November 14, 2016*

**Aljebra**

original number in first box --- x original number in 2nd box --- 123-x after shift: first box ----- x-10 2nd box --- 123-x + 10 = 133-x 133-x = 2(x-10) solve for x

*November 13, 2016*

**Math**

3?(x - 1) + 6 when x = 26 = 3?25 + 6 = ....

*November 13, 2016*

**pre algebra**

adult tickets ---- x children tickets --- 2x + 15 solve for x: 12x + 5(2x+15) = 1920

*November 13, 2016*

**pre algebra**

follow the same method and steps I just showed you in your other posts. The two questions are of the same structure.

*November 13, 2016*

**intermediate maths**

granddaughter's age---- x James' age --------- 6x 2 years from now: granddaughter's age --- x+2 James' age ---------- 6x + 2 6x+2 = 5(x+2) solve for x

*November 13, 2016*

**Algebra**

speed of slower rider --- x km/h speed of faster rider ---- 2x km/h distance gone by slower = 3(x) = 3x distance gone by faster = 3(2x) = 6x 3x + 6x = 90 9x = 90 x = 10 rate of slower rider = 10 km/h rate of faster rider = 2(10) = 20 km/h

*November 13, 2016*

**Calculus**

let the point of contact be P(a,b) let A be (1,7) slope of AP = (b-7)/(a-1) the closest point would be where the tangent at P is perpendicular to AP 2y dy/dx = 1 dy/dx = 1/(2y) so at P, the slope of the tangent is 1/(2b) so (b-7)/(a-1) = -2b b-7 = -2ab + 2b -b = -2ab + 7 2ab...

*November 13, 2016*

**math**

In a parallelogram Abcd angle add ??? side an ???? e ????? x+y ???? wow!

*November 13, 2016*

**Math**

Just follow the definition: a*b means 3a^2+b 3*1 means 3(3^2) + 1 = .....

*November 13, 2016*

**Math**

number correct --- x , 0 ? x ? 20 number wrong ---- y number skipped ---- 20-x-y 5x - y + 0 = 72 y = 5x - 72 y ? 0 if x = 14, y = -2 , not possible if x = 15 , y = 3 , skipped = 2 if x = 16, y = 8 , not possible , x+y>20 so he got 16 right, 8 wrong, and skipped 2 check: 5(...

*November 13, 2016*