Thursday

February 26, 2015

February 26, 2015

Total # Posts: 29,207

**math**

one decilitre = (1/10) L or 100 ml so 5 dL = 500 ml or 1/2 L so we emptied 24 of those or 12 L were poured in leaving 38 more litres to be filled they come in 1/2 L packs, so we need 38/(1/2) or 76 more packets.
*January 20, 2015*

**math**

you have typos Is the first number 65160 ? How many in each packet ?
*January 20, 2015*

**Algebra**

this is a parabola in standard position with vertex (5,8) opening upwards so domain: reals range: reals, y ≥ 8
*January 19, 2015*

**Algebra**

I get q^(-2/3 + 1/3 - 4/3) = q^(-5/3) = 1/q(5/3)
*January 19, 2015*

**Math, Algebra**

no, you made an error in the first line should have been y-(-3)=(5/2)(x-(2)) y + 3 = (5/2)(x-2) ----> times 2 2y + 6 = 5(x-2) 2y + 6 = 5x - 10 16 = 5x - 2y or 5x - 2y = 16 OR 5x - 2y - 16 = 0 or from ----> y + 3 = (5/2)(x-2) y = (5/2)x - 5 - 3 y = (5/2)x - 8
*January 19, 2015*

**Math, Algebra**

given this kind of standard question, I must assume that you have learned how to find the equation. What part of the process do you not understand? Which method do you use? - the point-slope form ? - the y-intercept slope form? - ... ?
*January 19, 2015*

**Math**

slope of BC = (6-8)/(5+3) = -2/8 = -1/4 so y-4 = (-1/4)(x-1) y - 4 = (-1/4)x + 1/4 y = (-1/4)x + 17/4 or 4y - 16 = -x + 1 x + 4y = 17
*January 19, 2015*

**calculus**

Done when you posted it as Ben http://www.jiskha.com/display.cgi?id=1421722232 Don't switch names, it just causes confusion, and often duplication of replies.
*January 19, 2015*

**Calculus**

in general f(x) = f(x0) + f ' (x0)*(x-x0), where x0 is a value close to x and a value which we can calculate. let f(x) = x^(2/3) f ' (x) = (2/3)x^(-1/3) = 2/(3x^(1/3)) f(8) = 8^(2/3) = 4 f ' (8) = 2/(3(2)) = 1/3 f(8.2) = f(8) + f ' (8)*(8.2 - 8) = 4 + (1/3)(.2...
*January 19, 2015*

**MATHEMATICS**

What's to explain? You said that the speed was constant.
*January 19, 2015*

**calculus**

treat it as two ordered pairs of the type (t,c) given: (80,160) and (70, 120) slope = (160-120)/(80-70) = 40/10 = 4 so chirps = 4xtime + b using (80,160) 160 = 4(80) + b b = -160 chirps = 4(time) - 160 or 4(time) = chirps + 160 time = (1/4)chirps + 40 testing: if chirps = 120 ...
*January 19, 2015*

**correction - Math**

The last two replies from above are incorrect. It is the same logic as the handshake problem, as MathMate noted. You are basically looking for the number of subsets of 2 elements which is C(12,2) = 12!/(10!2!) = 66
*January 19, 2015*

**Math**

let's take an example and see what Wolfram says f(x) = (2x - 5)/(3x - 8) http://www.wolframalpha.com/input/?i=plot+y+%3D+%282x+-+5%29%2F%283x+-+8%29 Notice the vertical asymptote at x = 8/3 or x = d/c the x=intercept of 5/2 or b/a and the horizontal asymptote of y = 2/3 or...
*January 19, 2015*

**mathematics**

6^2 = 4^2 + 5^2 - 2(4)(5)cosØ cosØ = (16+25-36)/(40) = 1/8 Ø = 82.819.. 4^2 = 5^2 + 6^2 - 2(5)(6)cos A cosA = (25+36-16)/60 = 3/4 A = 41.4096.. and 2(41.4096..) = 82.81924... same as Ø or ... an actual "proof" from above: cos(smallest ...
*January 19, 2015*

**statistics**

I will read that as you want to get exactly 50% correct, if you mean at least 50% then it would be a long tedious calculation. prob of (10 of 20 correct) = C(20,10) (1/2)^10 (1/2)^10 = 184756 ( 1/2^20) = appr .1762
*January 19, 2015*

**algebra**

Did you make a sketch ? let the vertex in quadrant I be (x,y) then the vertex in quadratnt II is (-x,y) the base of our rectange = 2x and the height is y Area = xy = x(27 - x^2) = -x^3 + 27x d(area)/dx = 3x^2 - 27 = 0 for a max of area 3x^2 = 27 x^2 = 9 x = ±3 y = 27-9...
*January 19, 2015*

**math**

I don't like fractions and if I can avoid them , I will multiply each term by the LCD, in this case 15 15x + 9 + 4x = 15x - 35 4x = -44 x = -11 I have a strange feeling that you meant: (x+3)/5 + 4x/15 = (x-7)/3 again, times 15 3(x+3) + 4x = 5(x-7) 3x + 9 + 4x = 5x - 35 2x...
*January 19, 2015*

**math**

angle = (28/total) (360°) =
*January 19, 2015*

**ap calc**

F ' (x) = (2x+7)^(1/2) F(x) = (2/3)(1/2) (2x+7)^(3/2) + c F(1) = 7 7 = (2/3)(1/2)(9^(3/2)) + c 7 = (1/3)( 27) + c 7 = 9 + c c = -2 you finish it
*January 19, 2015*

**calc**

integrating f ' (x), we get f(x) = x^3 - x^2 + x + c, where c is a constant but the point (2,2) lies on f(x) , so 2 = 8 - 4 + 2 + c c = -4 f(x) = ...
*January 19, 2015*

**Algebra**

done, check back
*January 19, 2015*

**Math**

to move up or down just add or subtract the constant equal to the units moved so just to move it DOWN 3 would give us g(x) = x^2 - 3 to move horizontally replace each x with (x ± c) if you move it to the right, you need x - c if you move it to the left , you need x + c ...
*January 19, 2015*

**Algebra**

speed of plane without wind --- x mph speed of wind ------------- y mph time to fly into wind = 1037.5/(x-y) time to fly with the wind = 1037.5/(x+y) 1037.5/(x-y) - 1037.5(x+y) = 1.5 1037.5/(x-y) + 1037.5(x+y) = 7.5 add them 2075/(x-y) = 9 9x - 9y = 2075 .... #1 how about ...
*January 19, 2015*

**alegebra**

What grade level are you in This is a rather straighforward problem.
*January 19, 2015*

**alegebra**

amount of the 35% stuff --- x kg amount of the 65% stuff --- 20 - x kg .35x + .65(20-x) = .41(20) multiply by 100 35x + 65(20-x) = 820 35x + 1300 - 65x = 820 -30x = -480 x = 16 kg you state the conclusion
*January 19, 2015*

**Math**

1. LS = 1/tanØ + tanØ = (1+tan^2 Ø)/tanØ but 1+tan^2 Ø = sec^2 Ø, one of the basic identities in your repertoire = sec^2 Ø/tanØ = RS 2. for this one you must realize that secØcosØ = 1 LS = (secØ - 1...
*January 19, 2015*

**Calculus**

let the height of the shake level be h cm V= πr^2 h = 25πh dV/dt = 25π dh/dt -3.5 = 25π dh/dt dh/dt = -3.5/25π = appr -.04456.. cm^3/s
*January 19, 2015*

**grade 7 math**

hiking vs biking, is there a typo ? let the distance be d hiking time = d/5 car time = d/20 d/5 - d/20 = 6 times 20 4d - d = 120 3d = 120 d = 40 hiking time = 40/5 = 8 hrs check: hiking time = 40/5 = 8 car time = 40/20 = 2 which is a difference of 6 hours, answer is correct
*January 19, 2015*

**Math**

-2k - 2 > -16 + 5k -7k > -14 k < +2
*January 19, 2015*

**math**

80 boys need 60 loaves in 12 days 80 boys need 5 loaves in 1 days 80 boys need 90 loaves in 18 days 40 boys need 45 loaves in 12 days 120 boys need 135 loaves in 12 days
*January 19, 2015*

**maths**

lwh = V lw(16/√3) = 1296 lw = 81/√3 SA = 2lw + 2lh + 2hw the only value I know is lw, so you have missing information. If it is a square base.... the each side of the base is 27√3 and you can then find the SA
*January 19, 2015*

**Maths Vector Helpppp**

For easier typing I will use <...> to represent a vector and (.. ..)to represent a point. I can write the line l in parametric form x = 1-2t y = 5+t z = 2-t let P(x,y,z) be the point we are looking for on line l or P is (1-2t, 5+t, 2-t) vector AP = <1-2t-1, 5+t-2, 2-t...
*January 19, 2015*

**trigonometry**

One rotation is π(diameter) = 2π ft so in one minute it goes 70(2π) = 140π) ft in one hour it goes 60(140π) ft = 8400π ft/hr or appr 26389 ft/hr
*January 19, 2015*

**polynomial**

polynomial is (x+2)(x+1)(x-3) or (x+2)(x^2 - 2x - 3) = x^3 - 2x^2 - 3x + 2x^2 - 4x - 6 = x^3 - 7x - 6
*January 19, 2015*

**Math**

adults --- a students ---s a+s = 15000 or s = 15000-a 12.5a + 8.5s = 162000 times 2 25a + 17s = 324000 sub s = ... 25a + 17(15000-a) = 324000 25a - 17a =324000 - 255000 8a = 69000 a = 8625 s = 15000 - 8625 = 6375 so 8625 adults and 6375 students check: 8625(12.50) + 6375(8.50...
*January 18, 2015*

**Algebra 1a**

(xy)^-3/(x^-5y)^3 = (1/xy)^3 / ( (1/x^5) y)^3 = (1/x^3(1/y^3) / ( (1/x^15)(y^3) ) = (1/x^3)(1/y^3) (x^15)(1/y^3) = x^12 / y^6
*January 18, 2015*

**Math Homework Help**

The expression sec^2-y-1 makes no sense to me is it sec^2 (-y-1) ? #2 LS = cosx + sinx(sinx/cosx) = (cos^2 x + sin^2 x)/cosx = 1/cosx = sec x = RS
*January 18, 2015*

**Math**

I will assume that you mean (8 - i)/(2 + 3i) ....... the brackets are crucial here = (8 - i)/(2 + 3i) * (2-3i)/(2-3i_ = (16 - 24i - 2i + 3i^2)/(4 + 9) = (13 - 26i)/13 = 1 - 2i
*January 18, 2015*

**Algebra 1a**

remember that a^-x = 1/a^x now apply this along with your regular rules of powers.
*January 18, 2015*

**Mat 116 - Algebra**

Facing such a problem, you must have learned how to multiply powers with the same base Can you find it in your notes or textbook?
*January 18, 2015*

**Mat 116 - Algebra**

well, what does (2x)^3 mean ?
*January 18, 2015*

**MATHEMATICS**

you have to know the formula for the general term of an AS. term(n) = a + (n-1)d term5 = a+ 4d = 23 term12 = a + 11d = 72 subtract them 7d = 49 d = 7 sub into a+4d = 23 a + 28 = 23 a = -5 first three terms are -5 , 2, and 9
*January 18, 2015*

**Math**

Seems like a lot to do about nothing.... I made a sketch where OA is the vector of the boat in still water (ending up in quad II) and OB the current vector, ending up in quad IV I then completed the parallelogram ACBO. With some simple angle calculations, I found angle CAO = ...
*January 18, 2015*

**math**

distance of first leg = 4(50 ) = 200 km distance of 2nd leg = 3.5(60) = 210 km avg speed = total distance/total time = 410/7.5 = appr 54.7 km/h
*January 18, 2015*

**math**

solve the quadratic 6t^2 + 110t + 3000 = 6000 3t^2 + 55t - 1500 = 0 (t-15)(3t + 100) = 0 t = 15 or t is a negative, which would make no sense it will take 15 years
*January 18, 2015*

**Math**

to have an average of 10 games in 4 years, they must have a total of 40 games so far they have 8+17+6 = 31 so in the fourth year they need 9 games or (8+17+6+x)/4 = 10 31+x = 40 x = 9
*January 18, 2015*

**Algebra HELP!!**

f(1) = -1 + 8 + 2 = 9 f(4) = -16 + 32 + 2 = 18 avg rate of change = (18-9)/(4-1) = 3 ft/s this is a rate, you matches it up with A, which states a distance. You need a rate or speed, so it must be C
*January 18, 2015*

**Maths**

looks like an AS, with a = 13 , d = -2 tn + t(15-n) = a + (n-1)d + a + (14-n)d = a + nd - d + a + 14d - nd = 2a + 13d = 26 - 26 = 0
*January 18, 2015*

**addmath**

this simply becomes the arithmetic series 12 + 15 + 18 + .... + 999 where a = 12 , d = 3 so how many terms are there ? termn = a + (n-1)d 999 = 12 + (n-1)(3) 987 = 3m - 3 990 = 3n n =330 sum = (330/2)(24 + 329(3)) = 166815 or sum = (n/2)(first + last) = 165(12+999) = 166815
*January 18, 2015*

**Algebra**

I think she means (x^2 + x -12)/(x-3) = (x+4)(x-3)/(x-3) = x + 4 , x ≠3 (f/g)(x) = x+4 , x ≠ 3 domain: any real number, x≠3
*January 18, 2015*

**Mathematics**

I will assume you have learned how to use variables. Let the distance from A to the meeting point be x km then the distance from B to the meeting point is 120-x km time from point A = x/55 time from point B = (120-x)/45 but those two times must be equal, they both left at the ...
*January 18, 2015*

**algebra**

I will assume you meant h(t) = -20t^2 + 20t + 16 (Sam must be diving on some other planet than earth ) we need the vertex of this parabola the x of the vertex is -b/(2a) = -20/(-40) = 1/2 if x = 1/2 seconds h = -20(1/4) + 20(1/2) + 16 = 21 ft
*January 18, 2015*

**Calculus**

Just a note of caution. If this is a regular Calculus course, your questions will not become any easier than these. 1. V = (4/3)π r^3 dV/dt = 4πr^2 dr/dt for your given data dV/dt = 4π(64)(14) = 3584π inches^3/min SA = 4πr^2 dSA/dt = 8πr dr/dt ...
*January 18, 2015*

**matt-Hoiliding-KIng-M$A --- math**

I usually don't answer questions when students keep switching names, but I was curious. What is a hire purchase, not familiar with it. Is it just an instalment plan? Also, are these regular US or CND dollars ? The costs appear exorbitant.
*January 17, 2015*

**Trigonometry**

You should remember that two similar triangles have their corresponding angles equal, and their corresponding sides are in the same ratio So if, for example, you have 2 right angled triangles, one of sides 3-4-5 and the other 6-8-10 the angles would be the same so if we let ...
*January 17, 2015*

**Math**

since something like x^5 means (x)(x)(x)(x)(x) we can say that exponentiation is repeated multiplication.
*January 17, 2015*

**Geometry**

change in latitude = 41:15:50 - 32:47:39 = 8:28:11 = 8.47° circumference = 2π(4000) = 8000π use a ratio: distance/8000π = 8.47/360 distance = 8000π(8.47)/360 = appr 590 miles or using the fact that 1 nautical mile = 1 minute on a great circle 8:28:11 = ...
*January 17, 2015*

**calculus**

And just in case Damon's solution does not ring your bells, I did the second one, and Steve did the third one. Guess what, all the same way.
*January 17, 2015*

**Algebra 2**

I will do the one which potentially could have the most factors. (the highest exponent matches the maximum number of linear factors, so this one could have a maximum of 4, but could be less ) look at your first term, it is 1x^4, so any linear factor must look like (x ±...
*January 17, 2015*

**maths**

11002 = 1(2^3) + 1(2^2) + 0(2^1) + 0(2^0) = 8 + 4 + 0 + 0 = 12
*January 17, 2015*

**AP Calc (Limits)**

let's look at that bottom part √(x^2 - 12x + 36) = √(x-6)^2 = x-6 so you have f(x) = (x-6)(x+6)/x-6) = x+6 so as x --> 6 limit f(x) = 12
*January 17, 2015*

**Algebra 1**

correct
*January 17, 2015*

**Math**

(f(x)-f(a))/(x-a) = (1/x - 1/a)/(x-a) = ( (a - x)/(ax) )/(x-a) now (a-x)/(x-a) = -1 so .. = -1/(ax)
*January 16, 2015*

**Math**

(y - 4)^2 = 4 - x^2 y - 4 = ±√(4 - x^2) but we only want the top part, so y - 4 = +√(4 - x^2) y = √(4-x^2) + 4 Wolfram verification: http://www.wolframalpha.com/input/?i=plot+y+%3D+%E2%88%9A%284-x%5E2%29+%2B+4+from+-2+to+2
*January 16, 2015*

**Math**

Now I would have started by defining the radius as r and the height of the rectangular window as h ( avoiding a lot of fractions) Perimeter of half a circle = (1/2)(2πr) = πr the three sides of the rectangle = 2r + 2h so 2r + 2h + πr = 26 h = (26 - 2r - πr...
*January 16, 2015*

**another speed**

let the time be t hrs northbound went 280t miles southbound went 320t miles 280t + 320t = 1000 t = 1000/600 = 5/3 hr or 1 hr 40 min they are 1000 miles apart at 11:40 am
*January 16, 2015*

**Algebra 1**

agree
*January 16, 2015*

**math**

first of all we can get rid of our decimals by multiplying each term by 10 to get 24x + 29y + 64 = 0 for the x-intercept, let y = 0 mentally block out the y term to get 24x = -64 x = -64/24 = -8/3 for the y-intercept, let x = 0 mentally block out the x term to get 29y = -64 y...
*January 16, 2015*

**math**

(10/21)x + 12y - 3
*January 16, 2015*

**Calculus**

you must have meant: V = x^2 h dV/dt = x^2 dh/dt + 2xh dx/dt now just fill in the given data
*January 16, 2015*

**Mathematics**

a+d + a+5d = 4 2a + 6d = 4 or a + 3d = 2 a+2d = a+6d + 24 -4d = 24 d = -6 back in a+3d=2 a -18 = 2 a = 20 so term(n) = a + (n-1)(d) = 20 + (n-1)(-6) = 20 - 6n + 6 = 26 - 6n check: according to my formula term(2) = 26-12 = 14 term(6) = 26-6(6) = -10 , and their sum is 4 , ...
*January 16, 2015*

**math**

Did not even have to find the third side, just followed my usual routine.
*January 16, 2015*

**math**

From sinØ = 5/12 make a sketch and use Pythagoras to find the missing side x x^2 + 5^2 = 12^2 cos 2Ø = 1 - 2 sin^2 Ø = 1 - 2(5/12)^2 = 1 - 50/144 = 94/144 = 47/72
*January 16, 2015*

**Math**

If you are April, I did this for you http://www.jiskha.com/display.cgi?id=1421375385
*January 16, 2015*

**algebra**

The degree of a term is the sum of the exponents of its variables, e.g. for 7x^3 y^2 , the degree would be 5 the degree of a polynomial is the degree of the degree of the highest term . so I would say the degree of the polynomial is 5
*January 16, 2015*

**math**

#1, 2, and 3 are correct for #4, form your data I had the equation: y = 59 sin 2π(t - .25) + 149 so for t = .25 y = 59 sin 2π(0) + 149 = 149 great job!
*January 16, 2015*

**algebra**

72x^8 = (36)(2)x^8 or = (12)(6)(x^3)(x^5) or .... , your turn
*January 16, 2015*

**Maths**

great so far: (a+2d)/a = (a+8d)/(a+2d) (a+2d)^2 = a(a+8d) a^2 + 4ad + 4d^2 = a^2 + 8ad 4d^2 = 4ad 4d = 4a a = d r = (a+2d)/a = (d + 2d)/d = 3d/d = 3 makes sense to me: looks like we can start with any value for a e.g let a = 5 then d = 5 and for the AS t1 = 5 t3 = 5+10 = 15 t9...
*January 16, 2015*

**Math, Quadratic Functions, Max/Min Word Problems**

let the two number be x and 72-x let P be their product P = x(72 - x) = -x^2 + 72x the x of the vertex is -72/-2 = 36 then P = 36(72-36) = l6^2 = 1296
*January 16, 2015*

**algebra**

look at the pattern: salary now =salary(0) = 3000 salary after 1 year = salary(1) = 300 + 3000 salary after 2 years = salary(2) = 2(300) + 3000 .... salary after n years = salary(n) = n(300) + 3000 A) salary(n) = 300n + 3000 so now just plug in whatever number of years for n B...
*January 16, 2015*

**Math**

What part of my answer to the same question you posted did you not like ?
*January 15, 2015*

**word problems**

use a simple ratio height of man /shadow of man = height of tower/shadow of tower. notice I set up "like things" in the same pattern (5 10/12) / (4 2/12) = height of tower/(8 9/12) (35/6) / (25/6) = tower/(35/4) tower = (35/4)(35/6) / (25/6) = 49/4 inches or 12 ft 3 ...
*January 15, 2015*

**MATH**

1 pile has 9 pictures 2 piles contain 18 pictures 3 piles contain 27 pictures If you can call the statement number of pictures = 9x3 an "equation", so be it. What is this p thing? To use a variable in such a problem as this is just plain nonsense.
*January 15, 2015*

**maths**

shorter of parallel sides --- longer of parallel sides --- x+7 (1/2)(x + x+7)(24) = 276 times 2 (2x+7)(24) = 552 divide by 24 2x+7 = 23 2x = 16 x = 8 parallel sides are 8 and 15
*January 15, 2015*

**algebra factorisation**

(x-y) is a common factor, so = (x-y)( 4(x-y)^2 - 1) now in the second bracket I see a difference of squares = (x-y)(2(x-y) + 1)(2(x-y) - 1) = (x-y)(2x - 2y +1)(2x - 2y -1)
*January 15, 2015*

**Math**

the third angle R can easily be found to be 52° then use the sine law. I will one side, then you do the other. PR/sin71 = 14.5/sin57° PR = 14.5sin71/sin57 = appr. 16.3
*January 15, 2015*

**math**

Have you not come across the slope-yintercept form of the equation?? if y = mx + b the slope is m and the y-intercept is b so match up your equation y = 3.9x - 4.2 with y = mx + b
*January 15, 2015*

**Math**

I will do the 2nd one, you do the others. given: cos 2x = 7/25 1 - 2sin^2 x = 7/25 2sin^2 x = 1-7/25 = 18/25 sin^2 x = 9/25 sinx = ± 3/25 sketch a right-angled triangle with height 3 and hypotenuse 25 then the adjacent side = √(625-9) = √616 if sinx = +3/25...
*January 15, 2015*

**Math**

sweaters --- x jeans ------ y x+y = 5 40x +20y = 160 or 2x + y = 8 subtract them: x = 3 then y = 2 Maria bought 3 sweaters and 2 jeans
*January 15, 2015*

**MATH**

So when they met, Carter had traveled for 3 hours and Max had traveled 2.5 hrs. let Max's speed be x mph Carter's distance = 150 miles Max's distance = 2.5x .60(150+2.5x) = 150 90 + 1.5x = 150 1.5x = 60 x = 40 a) distance between towns = 150 + 2.5(40) = 250 miles b...
*January 15, 2015*

**MAth Igcse**

mmmh, I just noticed that Steve answered this question for you earlier. Why are you reposting it ?
*January 15, 2015*

**trigo**

I assumed that by N 67°50' , you meant N 67°50' W I had a triangle with sides 85 and 39 and the angle between them as exactly 85° Using the cosine law I got your distance. Good job now look at the actual triangle. let the angle at the bottom be Ø so ...
*January 15, 2015*

**math**

volume of big tank = 10x8x4 or 320 inches^3 volume of a little tank = 3x3x3 or 27 inches^3 number of little tanks = 320/27 = 11.8.. you will need 12 tanks, the last one will be not quite full.
*January 15, 2015*

**solid mensuration**

arc = rØ , where Ø is in radians 28° = 28(π/180) radians = appr 112 = r (28(π/180)) r = 112(180)/(28π) = appr 229.2 m or 112 must be 28/360 of the circumference of the circle (28/360)(2πr) = 112 56πr = 112(360) r = 112(360)/(56π...
*January 15, 2015*

**Math**

#1. present value of loan = 320-20=300 payment = 34 n = 10 let the monthly rate be i 34( 1 - (1+i)^-10)/i = 300 There is no simple algebraic method to solve this type of equation. One method is interpolation, or if you know calculus, you could use Newton's Method. I will ...
*January 14, 2015*

**Geometry**

Not sure what you mean by "angle-side relationship" in triangles. The angles and sides are related by the Sine Law and the Cosine Law in trig If you are looking for something else, have some fun with this: http://www.mathopenref.com/trianglesideangle.html
*January 14, 2015*

**Math**

so the area of the table to be tiled is 4ft - 2(6inches) by 3ft - 2(6inches) = 3 ft by 2 ft. and that area is 6 ft^2
*January 14, 2015*

**calculus**

I will assume you meant f(x) = e^2 sinx e^2cosx = 0 then cosx = 0 , since e^2 is a constant x = π/2, 3π/2 (the graph of y = a cosx crosses the x-axis at π/2 , (90°) and 3π/2 , (270°) So there are two zeros for f ' (x)
*January 14, 2015*

**Calculus**

Go with Damon's solution, I somehow read the balloon as 3 ft instead of 5 ft above the boy correction: d^2 = (15t)^2 + (5+5t)^2 2d dd/dt + 2(15t)(15) + 2(5+5t)(5) dd/dt = (225t + 25 +25t)/d = (250t + 25)/d when t=3 d^2 = 45^2 + 20^2 = 2425 d = √2425 dd/dt = (250(3...
*January 14, 2015*

**Calculus**

make a sketch putting the boy somewhere on the road let the time passes since the boy was directly under the ballon be t seconds the the boy went 15t ft and the balloon is at a height of (3 + 5t) ft let the distance between them be d ft so we have a right-angled triangle with ...
*January 14, 2015*

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