Thursday

April 24, 2014

April 24, 2014

Total # Posts: 26,121

**math**

3sin = 1.2 sinØ = .4 (set your calculator to RAD) Ø = .41152 or π-.41152 which is 2.73008 but you wanted from 0 to 4π so add a period , or 2π, to each of the above answers Ø = .41152 , 2.73008 , .6947, and 9.01326

**trig**

I drew a circle, and a vertical radius of 12 m In 40 s, it rotates 360°, so in 5 sec it rotated 45° let the vertical position from the centre be y cos45 = y/12 y = 8.485 m so he is 12-8.85 or appr 3.5 m high after 5 seconds

**Math**

just translate the English into Math, 4x - 6 = 2x + 4 then solve for x

**Algebra**

y-5 = -5x + 10 5x + y = 15

**math**

We will need to find the sides angle P = 180 - 60 - 75 = 45° let PQ=x , QR = y , PR = z x/sin75 = y/sin45 = z/sin60 let's assign an arbitrary value of y = 1 to our smallest side using x/sin75 = 1/sin45 we get x = .1.366025 using 1/sin45 = z/sin60 z = 1.224745 so sum of...

**Math**

ways to choose 5 of the 6 multiple choices = C(9,5) = 126 number of ways to choose 2 of the 6 essay questions = C(6,2) = 15 number of ways to answer the test = 126x15 or 1890 ways

**Finance**

I have now answered 2 of these kind of questions for you. Exactly where are you finding difficulties with these? Do you know the 4 basic formulas we have to use for these ?

**Finance**

PV = 10000(1 - 1.08)^-10)/.08 + 20000(1 - 1.08^-30)/.08 (1.08)^-10 = 171391.45 or pretend you are gettting 20,000 for 40 years - the 10,000 for the first 10 years = 20000(1 - 1.08^-40)/.08 - 10000(1 - 1.08^-10)/.08 = 171391.45

**Finance**

150000 =PAY( 1 - 1.07^-20)/.07 solving for PAY, I got $ 14,158.94 Balance owing after 7 years = 150000(1.07)^7 - 14158.94( 1.07^7 - 1)/.07 = $ 118.335.46

**math**

I will assume you meant: log3 (2x + 5) = 1 then 2x+5 = 3^1 2x = -2 x = -1 If otherwise, let me know

**survey math 140**

Number of ways to select 5 of 19 is C(19,5) = 19!/(5!14!) = 11628 most calculators have that function built-in look for something like nCr

**algebra**

James, I gave you a detailed solution yesterday for the same question on the assumption that your symbol was supposed to be ≥ You later told me that it was to be ≤ So why don't you just switch all the conditions e.g. all the domain that worked before, now will ...

**Math**

I am guessing that P(number < 2) is supposed to mean probability that the number is less than 2 What number ???? Are you tossing a die ? confirm

**calcules**

let base be x by x let the height be y x^2 y = 8 y = 8/x^2 SA = base + 4 sides = x^2 + 4xy = x^2 + 4(8/x^2) = x^2 + 32/x d(SA)/dx = 2x - 32/x^2 = 0 for a minimum of SA 2x = 32/x^2 2x^3 = 32 x^3 = 16 x = cuberoot(16) = appr 2.52 then y = 1.26 the base is 2.52 by 2.52 and the he...

**Algebra 2**

same idea as before, factor first, then divide, restrict what you divided by Again, I am putting in the brackets, they are extremely important here h(x)=(x^2-9)/(x^2-4x+3) = (x+3)(x-3)/(x-1)(x-3)) = (x+3)/(x-1) , x ≠ 3

**Algebra 2**

I have a feeling you meant: (49X^6+7X^7)/(28X^8) take out a common factor = 7x^6( 7 + x)/(28x^8) now divide = (7+x)/(4x^2) now we divided top and bottom by a variable. If that variable is zero, we just divided by zero, which is a mathematical no-no. so we have to state a restr...

**algebra**

I have a strong feeling you meant (x-4)(x+2)/( (x-3)(x+5) ) ≥ 0 I good and fast way is to look at the graph of y = (x-4)( (x+2)/(x-3)(x+5) ) http://www.wolframalpha.com/input/?i=y+%3D+%28x-4%29%28x%2B2%29%2F%28%28x-3%29%28x%2B5%29%29 It shows the graph to be above the x-...

**Geometry**

You are missing one of the dimensions of the floor, its length Once you have that, Cost = 105 ( 33 * 1/2 * ??)/27 units of money where ?? in your length we divide by 27 since there are 27 cubic feet in 1 cubic yard If the concrete is sold in whole cubic yards, you will have to...

**ALGEBRA**

the t of the vertex of your parabola is -b/(2a) = -20/-32 = 5/8 at t = 5/8 h = -16(25/64)+20(5/8) + 6 = 12.25 nope!

**math**

avg rate of change = (23500 - 8750)/(8 = ...

**Math**

treat it as two ordered pairs (t, c) where t is temperature and c is consumption so we have (90,220) and (76, 178) slope = (220-178)(/(90-76) = 42/14 = 3 so: c-220 = 3(t-90) c = 3t - 270+220 c = 3t - 50 check: if t = 90, c = 270-50 = 220 if t = 76, c = 228 - 50 = 178

**Math**

no, 26x^2 ≠ x√26 Whatever made you think so. let x = 4 26(4^2) = 26*16 = 416 xV26 = 4√26 = appr 20.4 is 416 = 20.4 ???? However, you could write 26x^ as (x√26)^2

**Math**

Imagine "opening up" a cylinder, what would you get? 2 equal circles + a rectangle whose length is the circumference of the circle and whose height is the height of the cylinder. so SA = 2π(6^2) + 2π(6)(20) = 72π + 240π = 312π = appr 980 No w...

**Math**

I assume you pick a card, then throw the die primes from 1-10 : 2,3,5,7 , so 4 of them primes on a die: 2 3 5, so 3 of them prob(2 primes) = (4/10)(3/6) = 1/5 prob(not 2 primes) = 4/5 odds in favour of getting two primes = (1/5) : (4/5 = 1 : 4

**2nd question - math help!!**

(x+y)^2-x-y = (x+y)^2 - (x+y) = (x+y)(x + y - 1)

**math help!!**

To make it easier to see, let 2x^2 - x = a so you have 2a^2 - 3a - 9 = (a-3)(2a+3) put the original back in = (2x^2 - x - 3)(4x^2 - 2x + 3) = (x + 1)(2x - 3)(4x^2 - 2x + 3)

**Math**

cosine law .... 5.4^2 = 6.2^2 + 3.6^2 - 2(6.2)(3.6)cosR cosR = 22.24/44.64 = .4982.. R = 60.1°

**Math**

direct application of the sine law: x/sin41 = 96/sin71 x = 96sin41/sin71 = ....

**Calculus Help Please!!!**

According to Newton's Law of Cooling T(t) = roomtemp + (37 - 20)e^(-kt) , where t is the time in hours and k is a constant so we get two equations: 32.5 = 20 + 17e^(-kt) ---> 12.5 = 17e^(-kt) and 30.3 = 20 + 17e^(-k(t+1)) ---> 10.3 = 17e^(-kt - k) divide them: 115/10...

**Algebra**

did you try factoring both expressions? They factor quite easily. Then divide out the common factor, don't forget to state the restriction.

**trig**

Not sure what notation you are using when you say "blowing in at 53° " is North your 0° and you are going clockwise, or is 0° your positive x - axis and you are going counterclockwise ?

**Calculus**

just using ln a^b = b ln a ln (243^3/5 *32^4/5) = ln ( (3^5)^(3/5) * (2^5)^(4/5) ) = ln ( 3^3 * 2^4) = ln (27*16) = ln(432) 1/5 ln (243^3 * 32^4) = ln [ (243^3 * 32^4) ^(1/5) ] = ln (243^(3/5) * 32^(4/5) ) = .... = ln(432)

**Calculus**

I agree with Damon's "huh" since ln (243^3/5 *32^4/5) = 1/5 ln (243^3 * 32^4)

**FINANCE**

choice A: pay 3100(.85) or 2635 now choice B: pay 12 payments of 270 present value of the 12 payments at a monthly rate of i = 270( 1 - (1+i)^-12)/i= 2635 hard to solve, let Wolfram do it for us (I changed the i to x, since Wolfram thinks i = √-1 ) http://www.wolframalph...

**math 2**

let E(x,y) be your point use ratios ... for the x: (x-3)/(11-3) = 3/8 8x-24 = 24 8x = 48 x = 6 for the y: (y-4)/(3-4) = 3/8 8y - 32 = -3 8y = 29 y = 29/8 E is (6,29/8)

**math**

y - 6 = .5x - 3.5 y = .5x - 3.6 + 6 y = .5x + 2.5

**math**

slope of AB = 4/-2 = -2 so slope of new line = +1/2 new line: y-6 = (1/2)(x-7) expand and doctor it up any way you want.

**argggh - Calculus**

messed up in my expansion volume should have been 4x^3- 120x^2 + 800x and V' = 12x^2 - 240x + 800 = 0 3x^2 - 60x + 200=0 to get x = 4.23

**Calculus**

First things first: width --- s length ---- 2s 2s^2 = 800 s^2 = 400 s = 20 so the piece of metal is 20 by 40 let the side of the square to be cut out be x so the width is 20-2x the length is 40-2x the height is x Volume = x(20-2x)(40-2x) = 2x^3 - 120x^2 + 800x d(Volume)/dx = 6...

**Algreba**

What about it ?

**Calculus**

you should have recalled that sin (-x) = -sinx so that sin(-.1) could not have been positive. did you mean -.1 ?

**Math**

slope of new line must be -2 so y =-2x + b plug in the given point (2,-7) -7 = -2(2) + b -3 = b y = -2x - 3

**Calculus**

yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5

**math**

times 8 8B = 3(A-10) 8B = 3A - 30 8B+30 = 3A A = (8B+30)/3

**Math**

divide the fist equation by 2 to get y = 9x now plug that into the second: 9x - 6 = 2x 7x = 6 x = 6/7 then y = 9(6/7) = 54/7 x = 6/7 y = 54/7

**math**

I suspect that your equation is C = 6u^2 v (usually they would not separate factors of 6 and 2 like you did, and would have C = 12uv instead) Please confirm.

**Math**

prob(2dimes) = (8/14)(7/13) = 4/13

**Math**

consider the equation of the circle with centre (1,2) and radius 10 Its equation is (x-1)^2 + (y-2)^2 = 100 (7, 10) satisfies that equation, (7-1)^2 + (10-2)^2 = 100 6^2 + 8^2 = 100 36+64 = 100 100=100 so it is (7,10)

**College Calculus**

let Ø be the angle between them the angular velocity of the minute hand = 2π/60 rad/min = π/30 rad/min the angular velicity of the hour hand = 2π/(12(60)) or π/720 rad/min then, so dØ/dt = (π/30 - π/720) rad/min dØ/dt = 23`...

**Math**

looks like a combination recursion let term(n) be the nth term, term(1) = 2 if n is odd: term(n) = 3term(n-1) if n is even: term(n)= term(n-1) - 2 so the next terms are: 26, 78, 76, 228, 226, 678 .....

**integer Math**

Since they gave the answer as 7 , I am taking a guess that they wanted √52

**Math**

x( 1.07^27 - 1)/.07 =25000 x(74.483823..) = 250000 x = $ 3356.43

**Precalculus II**

don't you just love Wolfram http://www.wolframalpha.com/input/?i=plot+sec%5E2%28x%29%2B+3+tan%28x%29%3D5%2C+-2π+%3C+x+%3C+2π

**math**

Steve, that is really scary.

**math**

period of first = 2π/(12π) = 1/6 period of 2nd = 2π/(18π) = 1/9 1/3 is a factor of both, so the period = 1/3 verification: http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29

**Finance**

300( 1 - 1.01^-n)/.01 = 2000 300(1 - 1.01^-n) = 20 1 - 1.01^-n = 1/15 14/15 = 1.01^-n ln both sides and use rules of logs ln 14 - ln15 = -n ln 1.01 n = (ln 15 - ln 14)/ln 1.01 = 6.934 appr 7 months of course I could have used log 15 etc. and obtained the same result.

**math**

Who makes up these questions or what kind of strange paint is this? To paint a ceiling of that size should take about 1/2 gallon ( I know, I have too much time on my hand)

**Math**

number of adults --- A number of kids ----- C A + C = 35 12A + 7C = 315

**calcules**

Just noticed that both Damon and I answered a very similar question in the first of the Related Questions below http://www.jiskha.com/display.cgi?id=1268848081 I suggest you print it out , and change the numbers, and units.

**math**

solve 2 = e^(.07t) hint: take ln of both sides and use your log rules remember ln e = 1

**math**

what is 48000( 1.0105)^40 ?

**Trigonometry**

tan Ø = -√3 I know that tan 60 = +√3 and Ø could be in II or in IV in II , Ø = 180-60° = 120° or 2π/3 in IV, Ø = 360-60 = 300° or 5π/3

**Calculus**

let the number be x, and the sum as stated be S S = x^2 + 1/x dS/dx = 2x - 1/x^2 = 0 for a max/min 2x = 1/x^2 2x^3 = 1 x^3 = 1/2 x = (1/2)^(1/3) or the cube root of 1/2

**Math**

Brady, after all that work, you blew the final answer x+3x+6x = 180 10x=180 x = 10 but I called the angles x, 3x, and 6x so the angles are 18° , 54° , and 108° and of course 108° is the largest angle

**Math**

let the angles be x , 3x and 6x x + 3x + 6x = 180 take over ....

**Grade 12 Calculus**

I hope your function looks something like this: R(x) = (5000 - 100x)(30 + x) = 150000+ 5000x - 3000x - 100x^2 = -100x^2 + 2000x + 150000 this is a standard parabola opening dowwards , so it will have a maximum the x of the vertex is -b/(2a) = -2000/-200 = 10 So there should be...

**Trigonometry**

if sinx = -2/√5 in III y = -2, r = √5 , by Pythagoras, x^2 + 4 = 5 x = -1 in III cosx = -1/√5 tanx = sinx/cosx = (-2/√)/(-1/√5) = 2 sin 2x = 2sinxcosx = 2(-2/√5)(-1/√5) = 4/5 cos 2x = cos^2 x - sin^2 x = 1/5 - 4/5 = -3/5 tan 2x = 2tanx...

**math**

spent on perches --- x litter -------------- x -326 litter and perches combined = 2x - 326 nesting = 2(2x-326) 2x-326 + 2(2x - 326) = 4050 should be relatively easy to solve for x I get x = 838

**Algebra 2**

help with what? you didn't ask a question. your function simplifies to ... d(x) = 54x^10/(24x^8) = 4x^2 / 9 surely that wasn't your question, was it ?

**MATH**

so 2 + 4 + 8 + 16 + ... = 178 sum(n) = a(r^n - 1)/(r-1) 2(2^n - 1)/1 = 178 2^n - 1 = 89 2^n = 90 I know 2^6 = 64 2^7 = 128 2^8 = 256 So I agree with your answer , at the end of 7 you only have 128 but you need 178 so it must be the 8th month how did they come up with 10? perh...

**Math**

first tell me what you got for your inverse matrix

**Geometry B**

x^2 + y^2 − 2x + 2y − 1 = 0 , notice how we indicate exponents complete the square x^2 + y^2 − 2x + 2y = 1 x^2 - 2x + 1 + y^2 + 2y + 1 = 1+1+1 (x-1)^2 + (y+1)^2 = 3

**math**

http://www.wolframalpha.com/input/?i=y+%3D+1%2F%283-x%29 asymptote at x = 3

**discrete mths**

(white, red) ----> 12 13 14 15 16 (5 of them ----> 23 24 25 26 (4 of them) ----> 34 35 36 (3 of them) ----> 45 46 (2 of them) ----> 56 just one so 5+4+3+2+1 = 15 prob(your event) = 15/36

**algebra 2**

complete the square ... y = -4(x^2 - (3/4)x .....) - 6 , (we usually don't say +-6 to adding a negative 6 ) = -4(x^2 - (3/4)x + 9/64 - 9/64) - 6 , ( take 1/2 of 3/4 to get 3/8, now square that ----> 9/64 = -4( (x - 3/8)^2 - 9/64) - 6 = -4(x-3/8)^ + 9/16 - 6 = -4(x - 3/8...

**Trigonometry**

http://www.wolframalpha.com/input/?i=y%3D2sin%28x-2pi%2F3%29 for x-intercepts, y = 0 2sin(x-2pi/3) = 0 sin(x-2pi/3)=0 but sin 0 = 0 and sin π =0 and sin 2π = 0 so x - 2π/3 = 0 and x -2π/3 = π and x - 2π/3 = 2π x = 2π/3 or x = π + 2&...

**math**

amount in B ---- x amount in A -----x - 8000 .04x + .08(x-8000) = 1040 times 100 4x + 8(x-8000) = 104000 I am sure you can finish it

**Algebra**

-5 + 2x^2 = -6x 2x^2 + 6x - 5 = 0 x = (-6 ± √(36 - 4(2)(-5))/4 = (-6 ± √76)/4 = (-6 ± 2√19)/4 = (-3 ± √19)/2

**Implicity**

1 + 4x dy/dx + 4y (1) = 2y dy/dx 1 + 4y = 2y dy/dx - 4x dy/dx dy/dx(2y - 4x) = 1 + 4y dy/dx = (1+4y)/(2y-4x)

**Calculus A**

I will assume you meant: h(x) = x^2 + 5x + 4/(x-1) h ' (x) = 2x + 5 - 4/(x-1)^2 = 0 for max/min 2x + 5 = 4/(x-1)^2 (2x+5)(x^2 - 2x + 1) = 4 2x^3 - 4x^2 + 2x + 5x^2 - 10x + 5 = 4 2x^3 + x^2 - 8x + 1 = 0 hard to solve, Wolfram has this http://www.wolframalpha.com/input/?i=2x...

**math**

after 1st round 7 people receive email after 2nd round 7^2 or 49 receive email after 3rd round 6^3 or 343 receive email after 4th round 7^4 or 2401 receive email after 5th round ...........16807 receive email number receiving email in 5th round = 7^5

**math**

correct, so .....

**math**

what is √(300^2 + 50^2 ) ?

**Maths**

in groups of 4 with 2 left over: 6 10 14 .... 94 98 102 106 110 114 in groups of 5 with 1 left over : 6 11 16 21 .....96 101 106 111 116 .... looks like 106 or 4a + 2 = 5b + 1 4a = 5b - 1 a = (5b-1)/4 but 5b+1 > 100 5b > 99 b > 99/5 or 20, 21, ... let b = 21, then a= ...

**Algebra 1 Answer Evaluation**

check by expanding your answer, you will see that the first one is wrong you probably meant a^3 - 5a^2 + 2a -10 , says by grouping, so do that ... = a^2(a-5) + 2(a-5) = (a-5)(a^2 + 2)

**Algebra**

17*w*(2w+4) = 2720 2w^2 + 4w = 160 w^2 + 2w + 1 = 80+1 , I completed the square (w+1)^2 = 81 w+1 = ± √81 w = -1 ± 9 = 8 or some negatiave, which I will reject the width = 8 inches

**Math**

general equation of a conic: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 we can eliminate the xy term by finding the angle of rotation Ø , so that tan (2Ø) = B/(A-C) and replacing the x and y with a new X and Y, so that x = XcosØ - YsinØ and y = XsinØ...

**Algebra**

If x=-4 and x = -1 are zeros to one or more of the given functions, then dividing them by both x+1 and x+4 should yield a remainder of zero. I divided x+1 into each of the given functions (I used synthetic division), each yielded a remainder. So x+1 did not divide into any of ...

**good catch , Calcules**

yup, looked over my work and found an error in my SA substitution. SA = 2(4xy) +2(x)(4x) + 2(xy) .... = 10x(231/x^2) + 8x^2 ---->10x(231/(4x^2)) + 8x^2 to produce your answers

**Calcules**

let the height be x then the width is 4x , (the height is 1/4 of the width, this way I have no fractions ) let the length be y volume = (x)(4x)(y) = 4x^2 y 4x^2 y = 231 y = 231/(4x^2) SA = 2(4xy) +2(x)(4x) + 2(xy) = 8xy + 8x^2 + 2xy = 10xy+8x^2 = 10x(231/x^2) + 8x^2 = 2310/x +...

**MATH HELP!!**

from the 2nd: 2c + 6d = -34 c + 3d = -17 c = -3d-17 plug into the 1st: 3(-3d-17) - 7d = -3 -9d - 51 - 7d = -3 -16d = 48 d = -3 then c = -3(-3) - 17 = -8 c = -8 , d = -3

**Algebra II**

double the 2nd c - 6d = 16 add to the first 3c = 30 c = 10 back into the 1st 20 + 6d = 14 6d = -6 d = -1 c = 10 , d = -1

**algebra 2**

what is 3500(1.025) ?

**trig**

sin(anything) lies between -1 and +1 so -18sin(71π t) lies between -18 and +18 then p lies between 83-18 and 83+18 or between 65 and 101 period of your function = 2π/(71π) = 2/71 min or appr 1.69 seconds 1.69 seconds = 1 beat 1 second = 1/1.69 beats 60 seconds =...

**maths**

distance along flight path = (3/4)(220) = 165 km measured horizontally: cos 25° = x/16 x = 165cos28 = 49.54 km

**Math**

Just noticed that Steve answered the same question when you reposted it just a few entries above this Please avoid reposting the same question, especially when it still shows near the top of the list of questions like it did here. It avoids unnecessary duplication of solutions.

**Math**

vector ab = (-3,4,1) vector dc = (3, -4, -1) = vector cd since their magnitude is the same, and they simply have opposite direction they must be equal and parallel So the figure is a parallogram vector cb = (0,-2,6) area = cross product of ab and cb = (-3,4,1) x (0,-2,6) = (26...

**Math**

loan at 2.8% --- $ x loan at 4.5 % ---- $ 31000-x solve for x .... .028x + .045(31000-x = 1024.40 times 1000 28x + 45(31000-x) = 1024400 etc

**Algebra**

Just noticed a typo (sticking 3 key) <taking the first 3 I got: a = 5.5 , b=-12.5 , c = 12> should say: taking the first 3 I got: a = 53.5 , b=-12.5 , c = 12 btw , I did not show how I solved those 3 equations in 3 unknowns, I used a webpage for that http://www.1728.org/...

**Algebra**

I did the usual analysis and found the first differences to be 145, 250, 358, and 465 and the second differences to be 105, 108, and 107 which appear to be relatively constant at appr 106, so I suspect a quadratic. let N = ad^2 + bd + c, where d is the number of days, and N is...

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