Tuesday

August 30, 2016
Total # Posts: 35,601

**Calculus**

So at 2:00 pm the first ship would be 5 nautical miles directly south of the second ship. Let the time passes since 2:00 pm be t hours So the two ships form a right-angled triangle, with a horizontal side of 10t nmiles and a vertical of (5+5t) nmiles Let the distance between ...
*May 1, 2016*

**math**

Effectively, you have all the numbers form 100 to 999 , (can't start with 0 or else we have a 2 digit number) There would be 999-100 + 1 = 900 of them or using the standard permutation method choices for 1 digit = 9 choices for 2nd digit = 10 choices for 3rd digit = 10 ...
*May 1, 2016*

**Exponential Modeling**

what is 100(1.24)^5 ?
*April 30, 2016*

**Calculus**

My sketch shows the following: M is the man's position 16 m off shore A is the point on the shore perpendicular to M B is the point where he wants to go, AB = 30 Let P be the optimum point between A and B, let AP = x, then PB = 30-x distance in water = MP MP = (x^2 + 256...
*April 30, 2016*

**Math**

In your sketch , draw a perpendicular from the vertex to the base. You now have 2 identical right-angled triangles. let the base for each be x units (your whole base would then be 2x) by simple trig, cos 67.5° = x/10 x = 10cos67.5 = 3.8268.. , Use your calculator for this ...
*April 30, 2016*

**MATH**

a = 11 d = 3 term(n) = a + (n-1)d 83 = 11 + (n-1)(3) 72 = 3n - 3 3n = 75 n = 25 83 is the 25th term check: term(25) = a + 24d = 11 + 24(3) = 83
*April 30, 2016*

**Math**

did you make your sketch? On mine I labeled the top of the pole as P and it bottom as Q. I marked the bird on the tree as A Draw a horizontal from A to meet PQ at R let PR = x, then PQ = 10.65+x In triangle ARQ tan60° = 10.65/AR AR = 10.65/tan60 Triangle ARP is right-...
*April 30, 2016*

**algebra**

Volume = (4/3)π (1.9)^3 = 28.7309... SA = 4π (1.9)^2 = 45.36459... ratio of V : SA = 28.7309.../45.36459... = .63333... in general , ratio of volume/SA = (4/3)πr^3/(4πr^2) = (1/3) r using our values above ratio vol. / SA = (4/3)π(1.9)^3 / (4π (1.9...
*April 30, 2016*

**Algebra**

This question makes absolutely no sense to me. You say that you already have a pool . Are you going to change it?? How deep is the pool to be? Will people be able to stand with their heads above water? Is the pool circular? That way you would have the largest surface area, but...
*April 30, 2016*

**Math**

factors of 40 : 2,4,5,8,10,20 but only 5, 8, 10 fall within our domain So numbers which are even OR a factor of 40 are: 5,6,8,10,12,14 --> 6 of them prob(of your event) = 6/10 = 3/5
*April 30, 2016*

**Math**

1.8 m = 180 cm length = 18900/180 cm = .. make sure you express above in metres.
*April 30, 2016*

**geometry**

sketch a cross-section, and complete the right-angled triangle let the radius be r r^2 = 10^2 + 15^2 r = √325 depth of water = 10 + √325 = ...
*April 30, 2016*

**math**

final value = $60(.8)(.9)(1.55) = $66.96
*April 30, 2016*

**math**

original fraction : x/y new fraction : (.5x)/(.75y) = (2/3) (x/y) so the new fraction is 2/3 of the old one, thus it was decreased by 1/3
*April 30, 2016*

**math**

According to your wording: - you wanted the percentage increase , so my answer is correct 3.5/.432 = 8.102 so the new price is 810% of the old one, but the increase is 710% e.g. suppose the cost of a coat went from $100 to $120 so it increased by 120%, but the percentage ...
*April 30, 2016*

**math**

number of dozen in the bucket = 450/12 = 37.5 so cost price per dozen = 16.20/37.5 = .432 So they bought them at $ 0.432 per dozen and sold them at $3.50 per dozen percentage increase = 3.5/.432 - 1 = 7.102 or 710%
*April 30, 2016*

**consumer math**

I will assume you are using compound interest and the monthly rate is .13/12 or i = .0108333... n = 15 payment = p p( 1 - 1..0108333..^-15)/.0108333... = 1380 I get p = 100.17
*April 30, 2016*

**Maths**

I see that you corrected your post, and inserted a time of 2 hours So go back to my previous reply to the same question, replace t with 2 and repeat the steps. (or just plug t=2 into my answer for x)
*April 30, 2016*

**Maths**

"how far are apart" ? After what time ? Let the time passed since they left be t hours My diagram shows a triangle with sides 5t and 7.5t and an angle of 134° between those sides. If the distance between them is x, by the cosine law: x^2 = (5t)^2 + (7.5t)^2 - 2(...
*April 30, 2016*

**Calculus**

Make a sketch and draw in the rectangle. Let the top-right point be P(x,26-x^2) and the bottom-right point be Q(x, x^2 + 2) So the width of the rectangle is 2x and the height is 26-x^2 - x^2 - 2 = 24 - 2x^2 area = 2x(24-2x^2) = 48x - 4x^3 d(area)/dx = 48 - 12x^2 = 0 for a max ...
*April 29, 2016*

**Math**

2x - 1 = x+3 x = 4 , then y = 7 the solution is (4,7) which is not listed The wording is poor. "No solution" implies that there is no answer to our intersection, but there is! It should have said "none of the above"
*April 29, 2016*

**Algebra**

let's rephrase the question. For what values of k will the quadratic x^2 - kx + k^2 = 0 have 2 solutions when b^2 - 4ac > 0 k^2 - 4(1)(k^2) >0 -3k^2 > 0 k^2 < 0 any number squared is always positive, so there is no value of k for which the graph will cross the ...
*April 29, 2016*

**Geometry**

cosine law: DE^2 = 70^2 + 50^2 - 2(70)(50)cos54° = .. carry on
*April 29, 2016*

**math**

number of men --- x number of men --- 3x men wearing glasses = (3/5)x number of women wearing glasses = (1/3)(3x) = x x - (3/5)x = 120 times 5 5x - 3x = 600 2x = 600 x = 300 people at concert = x + 3x = 4x = 1200
*April 29, 2016*

**College Algebra**

#1 4 - 3(x+1) = 2x 4 - 3x - 3 = 2x -5x = -1 x = -1/-5 = 1/5 #2 15x^2=x=2 , assuming you meant 15x^2 + x=2 since the = and + sign are on the same key 15x^2 + x - 2 = 0 which factors to (3x-1)(5x+2) = 0 x = 1/3 or x = -2/5 by formula: x = (-1 ± √121)/30 = 1/3 or -2/...
*April 29, 2016*

**@Steve**

Thanks Steve Had an inkling thats what he was doing, but then it was contradicted in how he worked the last one. btw, was it overkill in my solution to http://www.jiskha.com/display.cgi?id=1461944692 Almost gave up on it, but found some clues on a webpage.
*April 29, 2016*

**College Algebra/pre-calculus**

#1 How did you get -2 ?? log 6^(1/36) = (1/36) log 6 = appr .0216 #2 ln(1/e^4) = ln1 - ln e^4 = 0 - 4lne = 0 - 4(1) = -4 #3 log 7^1 = log 7 = appr .845 #4 log 4^64 = 64 log4 = appr 38.532 #5 log 10^8 = 8log10 = 8 #6 --- the only one you got right
*April 29, 2016*

**Trigonometry**

One of my all-time favourite topics in Math is the Golden Ratio of (1 + √5)/2. I happen to know that cos 36° = (1+√5)/4 Notice also that in a regular pentagon , we have interior angles of 108° , and if we draw in some diagonals, we have all kinds of 36, 72 ...
*April 29, 2016*

**Math**

When they meet, they both would have traveled the same time. Let that time be t hrs so 60t + 80t = 210 140t = 210 t = 1.5 hrs take over
*April 29, 2016*

**algebra**

given: 8l = 15w then w = 8l/15 Perimeter = 2l + 2w 2l + 2(8l/15) = 230 times 15 30l + 16l = 3450 46l = 3450 l = 75 then w = 8(75)/15 = 40 the yard is 40 ft by 75 ft check: is 15(40) = 8(75) ??? YES is 2(40) + 2(75) = 230 ?? , YES
*April 29, 2016*

**Math**

Your question makes no sense. Must be reach a certain amount before withdrawing?
*April 29, 2016*

**Math**

correction: on this good earth of ours the equation would be h(t) = -16t^2 + 35t + 1 I assume you had a typo. the t of the vertex (instead of the normal x) = -b/2a = -35/-32 so h(35/32) = -16(35/32)^2 + 35(35/2) + 1 = appr 20.14 (exact answer is 1289/64)
*April 29, 2016*

**College Algebra Help?!**

number of choices = C(20,2) x C(32,2) = 190(496) = 94240 ways
*April 29, 2016*

**Math (Probability)**

1) prob(r,r) = (12/20)(8/13) = 24/65 ----> B 2) prob = (6/20)(2/19) = 3/95 ----> C 3) you want (1/2)^12 = 1/4096 ----> A
*April 29, 2016*

**Algebra**

So we need the vertex of the parabola h(t) = -16t^2 + 293t + 7 the t of the vertex is -b/(2a) = -293/-32 = 293/32 seconds or in 9.15625 seconds plug that into h(t) = ... = appr 1348.4 ft your next two questions have just been answered
*April 29, 2016*

**sails math**

amount of the 70% solution --- x L amount of the 45% solution--- 300-x L .70x + .45(300-x) = .65(300) time 100 70x + 45(300-x) = 65(300 70x + 13500 - 45x = 19500 25x = 6000 x = 240 So 240 L of the 70% stuff, and 60 L of the 45% stuff check: .7(240) + .45(60) = 195 .65(300) = ...
*April 29, 2016*

**alg**

f(x) = 4(x^2 - 6x + 9 - 9) + 20 = 4( (x-3)^2 - 9) + 20 = 4(x-3)^2 - 36 + 20 = 4(x-3)^2 - 16
*April 29, 2016*

**math**

1. π --- irrational √3 --- irrational √2 --- irrational 1.333.... = 4/3 ---- Rational 2. If n is your symbol for π then your choice if a) is correct
*April 29, 2016*

**math**

yes, notice that 300, 400, and 500 is simply a multiple of 3,4, 5 3,4,5 would form the smallest right-angled triangle with integer sides.
*April 29, 2016*

**math**

Just good ol' Pythagoras .... L^2 = 300^2 + 400^2 L = .....
*April 29, 2016*

**Math Help**

Wolfram shows that x = -π/12 and π/36 are intersection values and the region forms a closed area. area = ∫(cos 12x - sin 6x) dx from -π/12 to π/36 = (1/12)sin 12x + (1/6)cos 6x | from -π/12 to π/36 = .. take over
*April 29, 2016*

**Error - Geometry**

This question makes no sense. You don't have a right-angled triangle , since 6^2 + 4^2 ≠ 7^2 from sinA = 6/7 , A = appr 59° from cosA = 4/7, A = appr 55° Which one is it ?
*April 29, 2016*

**math**

avg vel = total distance / total time find the time from 2:00 pm to 5:45 pm, write it as a decimal and go for it.
*April 28, 2016*

**Algebra**

ummmhh, if the points don't form a straight line, then the function is not linear.
*April 28, 2016*

**math**

I don't see any choices. y = 2x^3 - 4x + 1 dy/dx = 6x^2 - 4 at x = -1, dy/dx = 6-4 = 2 y = -2 + 4+1 = 3 so we have slope = 2, point is (-1,3) equation of tangent: y - 3 = 2(x + 1) dress it up to whatever form you need.
*April 28, 2016*

**math**

those codes don't work here, I read that as: C(x) = x^2 + 2 R(x) = 2x^2 - x equate them: 2x^2 - x = x^2 + 2 x^2 - x - 2 = 0 (x-2)(x+1) = 0 x = 2 or x = -1 if x=2, y = 6 if x = -1, y = 3 you had (2,-6) , don't see how you got y = -6 C(x) can never be negative, you are ...
*April 28, 2016*

**geometry**

Assuming that the peak of the house is in the centre of the width. tanØ = 40/15 = 8/3 Ø = appr 69°
*April 28, 2016*

**Math**

since both are expressed as y = ... we can equate them: x^2 + 2x = 3x + 20 x^2 - x - 20 = 0 (x-5)(x+4) = 0 x = 5 or x = -4 if x = 5, y = 3(5) + 20 = 35 if x = -4, y = 3(-4) + 20 = 8 x=5, y = 35 x = -4, y = 8 check: http://www.wolframalpha.com/input/?i=solve+y%3Dx%5E2%2B2x,++y%...
*April 28, 2016*

**Alias robert**

a = 2 v = 2t + c, where t is in seconds when t=0, v = 0 , (it started from rest) 0 = 0 + c, c = 0 v = 2t s = t^2 + k when t = 0, s = 0 , (hasn't gone anywhere) after 10 seconds v = 20 m/s s = 100 m now goes for 20 s, at 20 m/s, covering 400 m so it can covered 500 m, and ...
*April 28, 2016*

**Algebra**

In a multiplication of a number and a variable, we write the variable last, so Cost = 2a + 4c
*April 28, 2016*

**math**

done, look back at your other post
*April 28, 2016*

**math**

Assuming people are sitting on the ice while the Rangers are losing, .... area = π(202)^2 ft^2 = 40,804π ft^2 number of square ft per spectator = 40804π/20234 = appr 6.34 ft^2
*April 28, 2016*

**Math**

let the original amount be x he spent 3x/8, leaving him with 5x/8 he spends half of that , leaving him with 5x/16 5x/16 = 6.25 5x = 100 x = 20 He started with $20.00 check: he spends (3/8)(20) or $7.50, leaving him with $12.50 He has 1/2 of that left or (1/2)(12.50) = $6.25 My...
*April 28, 2016*

**math**

no, you have to use trig, or else know that the ratio of sides of the 30-60-90 triangle is 1:√3:2 So if the short side is 2, the sides are: 2 : 2√3 : 4 or make a sketch, mark the shortest side adjacent to the 60° angle as 2 and the hypotenuse as h cos60° = ...
*April 28, 2016*

**Math**

The product of distance x mass on both sides of the fulcrum must be the same, so 100d1 = 10d2 10d1 = d2
*April 28, 2016*

**centimeter dot grid**

Here is page full of printable graphpaper, many of which are metric. https://images.search.yahoo.com/search/images;_ylt=AwrB8qEruSJXTCoAA2KJzbkF;_ylu=X3oDMTBsZ29xY3ZzBHNlYwNzZWFyY2gEc2xrA2J1dHRvbg--;_ylc=...
*April 28, 2016*

**Math**

integral 10x/(x^2 + 1) dx from 0 to 5 = 5ln(x^2 + 1) | from 0 to 5 = 5ln 26 - 5ln1 = 5 ln 26 - 0 = 5 ln 26
*April 28, 2016*

**math**

PV = ?? Amount = 12500 i = .12/4 = .03 n = 4(12) = 48 PV(1.03)^48 = 12500 PV = 12500/1.03^48 = 3,024.99
*April 28, 2016*

**Plz do help..GEOMETRIC SEQUENCES**

You are looking at a GS with a = 32000 r = 1.04 term(n) = a r^(-1) term(n) = 32000(1.04)^(n-1) 32000(1.04)^(n-1) = 40000 1.04^(n-1) = 1.25 take logs of both sides and use log rules (n-1)log1.04 = log1.25 n-1 = log1.25/log1.04 = 5.689 n = 6.689 The question does not say when ...
*April 28, 2016*

**Algebra**

brackets are essential here don't you want to say x ≠ instead of x = ??? A 1/(6-x) , x ≠ 0,6 2nd one: 5(7+x) , x ≠0,-7 ----> choice A
*April 28, 2016*

**Math**

length = area/width = (2/3) / (1/2) = (2/3)(2/1) = 4/3 km check area = (4/3)(1/2) = 4/6 = 2/3 all is good
*April 28, 2016*

**,math**

let y = x^2 + 10x + 12 = (x^2 + 10x + 25 - 25) + 12 = ( (x+5)^2 - 25) + 12 = (x+5)^2) - 25 + 12 = (x+5)^2 - 13 we have found the vertex to be (-5,-13), which for a parabola would be the turning point.
*April 28, 2016*

**maths**

number of children -- c number of sweets per child -- s sc = 60 or c = 60/s 2nd scenario: number of sweets per child = s-1 (s-1)(c+2) = 60 sc+ 2s - c - 2 = 60 60 + 2s - c - 2 = 60 2s - c = 2 2s - 60/s = 2 2s^2 - 60 = 2s s^2 - s - 30 = 0 (s+5)(s-6) = 0 s = 6 or s is a negative ...
*April 28, 2016*

**8th grade math - system of equations**

#23 The larger number is three more than the smaller ---- l = s + 3 you had "the larger is 3 times the smaller" l - s = 3 l + s = 27 add them 2l = 30 l = 15 and 15+s= 27 s = 12 24. 5% ---> .05, so .05x + .09y = 380 multiply by 100 5x + 9y = 38000 ** first equation...
*April 27, 2016*

**algebra**

larger x smaller y x+y = 83 x - 3y = 19 subtract them: 4y = 64 y = 16 , then x = 67 larger is 67, the smaller is 16
*April 27, 2016*

**matc**

The $5,500 is irrelevant, all you want is the annual rate equivalent to 6% per annum, compounded monthly let that annual rate be i 1+i = (1 + .06/12)^12 1+i = 1.005^12 = appr 1.06168 the equivalent annual rate is 6.168 %
*April 27, 2016*

**algebra, how to do fractions?**

Don't let the fractions scare you .... slope = (15/32 - 1/4)/(5/8 - 1/3) = (15/32 - 8/32)/(15/24 - 8/24) = (7/32) / (7/24) = (7/32)(24/7) = 3/4 so y - 15/32 = (3/4)(x - 5/8) y - 15/32 = (3/4)x - 15/32 times 32 32y - 15 = 24x - 15 24x - 32y = 0 3x - 4y = 0
*April 27, 2016*

**math**

1(1.045)^n = 3, where n is the number of half-years. using logs ... n log 1.045 = log 3 n = log3/log1.045 = 24.95888 or 25 half-years. I would say 12.5 years.
*April 27, 2016*

**PreCalc**

when t=0 , temp = 35 when t = 12, temp = 50 Period = 24 hours or k = π/12 how about Temp = 7.5cos (π/12)(t + 12) + 42.5 check: when t = 0, Temp = 7.5cos(π) + 42.5 = 35 when t = 12, Temp = 7.5cos(2π) + 42.5 = 50 You try it with a sine curve, be aware that ...
*April 27, 2016*

**prealgebra**

#1, ok #2 .245 = 24.5% , move decimal 2 places to right, tag on the % sign #3 28% = .28 = 28/100 = 7/25, so C #4 .367 -----> .367 36.5% --- > .365 9/25 -----> .36 so what do you think?
*April 27, 2016*

**Probability**

prob = (18/30)(17/29) = 51/145 = appr .352
*April 27, 2016*

**MATH PLS HELP**

I can't quite see your work for this assignment.
*April 27, 2016*

**Trig**

h/23 = tan 40 h = 23tan40 = ....
*April 27, 2016*

**Math**

Logy=1/3(logx-log27) logy = 1/3 log (x/27) log y = log (x/27)^(1/3) antilog it y = (x/27)^(1/3) or y = (1/3)x^(1/3)
*April 27, 2016*

**math**

Just translate it to Math 2(x+7) < x by 19 2x + 14 = x-19 x = -33 check: add 7 to -33 ---> -26 double it -----> -52 19 less than the number = -33-19 = -52 YEAH
*April 27, 2016*

**math**

a = 1.6 b = 2 c = 2.5 x = (-b ± √(b^2 - 4ac)/(2a) (you MUST memorize this formula) x = (-2 ± (√(4 - 4(1.6)(2.5))/3.2 = (-2 ± √-12)/3.2 This is a complex or imaginary number, so there is no REAL solution. Is that your problem? Have you ...
*April 27, 2016*

**pre-calculus**

so arccos(?) is an angle, so let arcos(x/2) = θ that means cosθ = x/2 that is cosθ = adjacent / hypoenuse = x/2 so we are looking at a right-angles triangle with angle θ, adjacent = x, hypotenuse =2 Make a sketch, then x^2 + y^2 = 4 y^2 = 4-x^2 y = √(...
*April 27, 2016*

**Math**

let the initial population be 1 or 100% after 10 years: pop= 1(2)^(-10/7) = .3715 or 37.15%
*April 27, 2016*

**Help Steve or Damon, Solid Mensuration**

Am I overthinking this ???? volume of water in cylinder being upright = π(2^2)(41/12) inches^3 , (arrhhhg -- non-metric units) = (41/3)π in^3 Now lay it on its side, and make a diagram of the cross section Shade in the water which is a segment of the circle, label ...
*April 27, 2016*

**calculus**

How does this question relate to your two previous questions, let's see.... Let the base be x by x inches, and the height be y inches V= x^2 y 27 = x^2 y y = 27/x^2 material = 2x^2 + 4xy = 2x^2 + 4x(27/x^2) = 2x^2 + 108/x d(material)/dx = 4x - 108/x^2 = 0 for a min/max of ...
*April 27, 2016*

**calculus**

see my previous reply to this same idea.
*April 27, 2016*

**calculus**

width --- x length -- y 2x+2y = 320 y = 160-x area = xy = x(160-x) = -x^2 + 160x this is a downwards opening parabola with a vertex at (80, 6400) (I assume you know how to find the vertex) the max area is 644 m^2 , when x = 80m that is, when the rectangle is a square, which ...
*April 27, 2016*

**Math**

After giving to his son, he has 3x/8 left after giving to his daughter he has 3x/16 left 3x/16 = 150 3x = 2400 x = 800 check: first gift = (5/8)(800) = 500 amount left = 300 2nd gift = (1/2)(300) = 150 amount left = 150 Editorial: Looks like sexism in continued in math ...
*April 27, 2016*

**algebra**

width --- y length --- 3y area = y(3y) or 3y^2
*April 27, 2016*

**math**

most scientific calculators have the ! function built in on mine I press: 5 2ndF 4 -----> on mine the ! is with the 4 key = 120
*April 27, 2016*

**Maths**

x = 2cos t y = 2sin t dx/dt = -2sin t dy/dt = 2cos t slope = dy/dx = (dy/dt) / )dx/dt) = 2cost/-2sint = -cost/sint when t = pi/6 sint = 1/2 cost= √3/2 slope = (-√3/2)/(1/2) = -√3 point: (2cos pi/6, 2sin pi/6) or (√3 , 1) So now you have m = -√3, ...
*April 27, 2016*

**algebra**

let the first 4 terms of the AP be a-d, a , a+d, and a+2d new sequence is a-d+1, a+2, a+d + 7, and a+2d+20 so (a+2)/(a-d+1) = (a+d+7)/(a+2) (a+2)^2 = (a-d+1)(a+d+7) a^2+4a+4 = a^2+ad+7a-ad-d^2-7d+7a+d+7 -4a = -d^2 - 6d + 3 4a = d^2 + 6d - 3 ** (a+d+7)/(a+2) = (a+2d+20)/(a+d+7...
*April 27, 2016*

**maths**

I will assume you meant: 3 log9 9^2 = 6 log9 9 = 6(1) = 6
*April 27, 2016*

**maths**

did you mean: log √(x+1) + 9logx ?? then = log √(x+1) + log x^9 = log ( x^9 √(x+1) )
*April 27, 2016*

**maths**

I will assume you meant: log(x^2 y^3) then: = log x^2 + log y^3 = 2logx + 3logy = .... take over
*April 27, 2016*

**math**

y + 2x - 12 = 0 or y = -2x + 12 has a y-intercept of 12 5x + 12y = 8 has a slope of -5/12 so your new line is y = (-5/12)x + 12
*April 27, 2016*

**math**

Interest = 100,000(.06)(30) = 180,000 (This is a completely meaningless answer. Nobody would charge simple interest for such a period of time. The formula assumes that there is always 100,000 owing, but aren't there payments made in a "house loan", generally ...
*April 26, 2016*

**PreCal**

I am missing the speed of the wind.
*April 26, 2016*

**PRECALC**

#1, look how I did this similar problem, and follow the same steps http://www.jiskha.com/display.cgi?id=1461697741 #2 2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ) 2cosθtanθ - 2cos + tanθ - 1 = 0 2cosθ(tanθ - 1) + (tanθ -1) = 0 by ...
*April 26, 2016*

**mathh**

y - 67/36 = (1/4)(x - 4/9) expand, then multiply each term by 36, the LCD
*April 26, 2016*

**precalc**

square both sides cos^2 x + 2sinxcosx + sin^2 x = 1 1 + 2sinxcosx = 1 sin (2x) = 0 2x = 0 or 2x = π or 2x = 2π x = 0, x = π/2, x = π the period of sin 2x is π, so adding multiples of π will yield more answers so in the domain 0 < x < 2π...
*April 26, 2016*

**Calculus**

let the height of the water be h m let the radius of the water level be r m Make a sketch of the cross-section. By similar triangles: r/h = 40/10 r = 4h or h = r/4 V = (1/3)π r^2 h = (1/3)π(4h)^2 h = (16/3)π h^3 dV/dt = 16π h^2 dh/dt plug in the given ...
*April 26, 2016*

**Math**

What is 22,000(.94)^6 ??
*April 26, 2016*

**Calculus**

V = (4/3)πr^3 dV/dt = 4πr^2 dr/dt when r = 5 and dr/dt = 2 dV/dt = 4π(25)(2) = 200π cm^3/min SA = 4πr^2 d(SA)/dt = 8πr dr/dt = 8π(5)(2) = 80π cm^2/min
*April 26, 2016*

**Geometry**

Remember that for each chord , a perpendicular from the centre will right-bisect the chord so if you let the height to the shorter chord be h1, and the height form the centre to the longer chord be h2 you have two right-angled triangles, the first one sides 6, h1, and ...
*April 26, 2016*