Friday

July 25, 2014

July 25, 2014

Total # Posts: 23,956

**Trig**

since cosb < 0, b is in QII, so sina = 4/5 cosa = 3/5 sinb = 5/13 cosb = -12/13 Now just evaluate ain(a+b) = sina cosb + cosa sinb

**Algebra**

what's the trouble? They actually give you the equations to solve. What do you get for answers?

**trig**

depends on the positions of the two named animals. It will between 8*360 and 9*360 degrees

**math**

there are 201 numbers from 50 to 250. So, clearly, if 202 people are polled, at least two of them must have the same number.

**Calculus**

well shucks. The base of the trapezoid is just the long axis of the ellipse, so you want to find two points (-x,y) and (x,y) on the ellipse which gives maximum area a = 1/2(2x+6)y = (x+3)y Now, we know that x^2/9 + y^2/4 = 1, so y^2 = 4(1 - x^2/9) so y = 2/3 √(9-x^2) a =...

**Geometry**

scalene trapezoid?

**Math (Quadratic Equations)**

10th grade? High time to learn calculus, on your own! Anyway, we don' need no steeking calculus for this one. If the side parallel to the river has length x, and the other side is y, then we have x+2y = 400 The area a of the field is just xy, so a = xy = (400-2y)y = 400y -...

**ALG- timed**

you have the center at (4,3), so the equation is (x-4)^2 + (y-3)^2 = r^2 Now you just need r. Since the point (1,7) is on the circle, plug it in: (1-4)^2 + (7-3)^2 = 9+16 = 25 So, (x-4)^2 + (y-3)^2 = 25

**Math**

see Reiny's solution at http://www.jiskha.com/display.cgi?id=1394074310

**Alg.**

y = -1/7 x^2 + x - 3 = -1/7 (x^2 - 7x) - 3 now complete the square y = -1/7 (x^2 -7x + (7/2)^2) - 3 + 1/7 (7/2)^2 y = -1/7 (x - 7/2)^2 - 5/4 Now you can just read off the coordinates of the vertex, no? graph at http://www.wolframalpha.com/input/?i=-1%2F7+x^2+%2B+x+-+3

**Math**

43 marbles in all, so P(red,blue) = 8/43 * 12/43

**Algebra**

since the bases are in the ratio of 2/3, the areas are in the ratio of (2/3)^2 = 4/9 A(ABC) = (4/9)*(1/2)(18)(12) = 48

**precal**

Obviously y = a(x-2)(x-6) Since y(4) = 8, a = -2 and y = -2(x-2)(x-6) = -2((x-4)^2 - 4) = -2x^2 + 16x - 24

**Word Problem**

just multiply each salary by 1.25

**math**

multiply 15000 by 1.30 to get the new total of people.

**Math Problem**

500 times 10 will give the total cost.

**Socail Studies**

8. Which of the following statements about the ancestry of most of the people of Central America is most accurate? (2 points) People in Central America are of African ancestry. People in Central America are of mestizo ancestry. People in Central America are of Spanish ancestry...

**calculus**

this is just a geometric series, where a = 20 r = 1/4 So, the sum is S = a/(1-r) = 20/(3/4) = 80/3

**calculus**

neither

**Math**

the interest is 5000*.025*10

**columbus**

it says, the boys are twice as many as the girls. Read the problem carefully.

**arithmetic**

well, is 2 times a number more than 1 times the number?

**trig**

as usual, draw a diagram, and you will see that (h + 150*sin25°)/(150*cos25°) = tan65°

**Math 3**

15 days in 3 weeks, so divide by 15

**Math 2**

(2*32 + 3*16)/8 = ? Sadly, much punch will be spilled if he fills each cup right to the top ...

**Math**

If your spacing means 2/y^2 - 3x/(y-x) - 3/y then the common denominator is (y-x)y^2 and you wind up with (-3xy^2 + 3xy - 2x - 3y^2 + 2y) / (y-x)y^2

**Algebre**

just remember that lna - lnb = ln(a/b) lna + lnb = ln(a*b) ln a^b = b*lna ln3 - 3ln9 + ln18 ln3 - 3*2ln3 + ln(9*2) ln3 - 6ln3 + 2ln3 + ln2 -2ln3 + ln2 ln 1/9 + ln2 ln 2/9 #2 has a typo I suspect a typo in #3 as well, since ln4 ln8 = ln(8^ln4) or ln(4^ln8)

**Sam**

since 2/9 wanted, 7/9 did not want it. 2800/(7/9) = 3600

**math**

in point-slope form, you have y-2 = -8(x+10) now just rearrange that into standard form

**Algebra**

if you want to find values of a where this is true, then putting all over a common denominator of (a+3)(a-3), we have -9(a+1) / (a^2-9) = 0 so, a = -1 a graph can be seen at http://www.wolframalpha.com/input/?i=solve+a%2F%28a%2B3%29+%3D+%282a%29%2F%28a+-+3%29+-+1

**math**

the price per ounce of the brands, with coupons: x: (3.89-0.75)/28 y: (1.89-0.25)/18 z: 1.29/12 calculate those values and pick the lowest.

**WORD PROBLEMS UGH**

#1 is obviously wrong, since your weights don't add up to the desired 4 lbs. If there are x lbs of pretzels, 2x + 2.4(4-x) = 2.15*4 x = 2.5 so, 2.5 lbs pretzels and 1.5 lbs cereal #2 correct

**math**

3 + -9 = -6 so, what's (-6)(-6)

**math**

2*3^3 - (-9+5)^2 2*27 - (-4)^2 54 - 16 38

**math - eh?**

Do we have to use them all? Can we repeat any of them? Are we restricted to add/subtract and multiply/divide? Can we use parentheses for grouping?

**ALGEBRA**

better get good at factoring. x^2-3x-10 = (x+2)(x-5) now divide out the x+2

**Trigonometry.**

since a is in QIII, sina = -4/5 cosa = -3/5 You sure that's not cos b = 24/25? cot < 0 in QIV. If so, then we have a 7-24-25 triangle. sinb = 7/25 cosb = 24/25 now just use your difference formula: cos(a-b) = cosa cosb + sina sinb

**Trigonometry**

sin^2+cos^2 = 1, so sec^2 + csc^2 = 1/cos^2 + 1/sin^2 = (sin^2+cos^2)/(sin^2 cos^2) = 1/(sin^2 cos^2) = sec^2 csc^2 so, (sec csc) / (sec^2 csc^2) = 1/(sec csc) = sin cos = 1/2 sin(2x) #2 is missing too many parentheses to work on it. That dangling cos x bothers me.

**pre algebra**

is the following a non linear function? y = 3x squared + 1

**trig**

well, where does 2 + 4cosθ = 6cosθ ? 2 = 2cosθ cosθ = 1 θ = 0,2pi,...

**Calculus**

A = ∫[1,3] 1/x^3 dx = -1/2x^2 [1,3] = 4/9 Now, we want to find c such that ∫[1,c] 1/x^3 dx = ∫[c,3] 1/x^3 dx (-1/2c^2 - (-1/2)) = (-1/18 - (-1/2c^2)) (c^2-1)/2c^2 = (9-c^2)/18c^2 c = 3/√5

**Trigonometry**

By "the angle" I assume you mean the angle between the line from the station to the plane and the line joining the stations. In that case, Label the diagram as follows. A = station 1 B = station 2 P = plane Q = point on AB closes to the plane PQ┴AB) y = PQ a = ...

**Algebra help please!**

wolframalpha can be a great resource here. Enter your matrix as a set of rows. For #1, you'd enter {{6,-5,8},{5,-4,3}}-{{7,5,-6},{4,3,-4}} = {{-1,-10,14},{1,-7,7}} for inverse, just type inverse {...}

**Math**

log5(log4(log2(x))) = 1 log4(log2(x)) = 5 log2(x) = 4^5 = 2^10 = 1024 x = 2^1024 = 10^308.25

**Calculus**

You can't always just plug in e for the base of the exponent. After 1 day, .93 remains. After t days, .93^t remains. So, we have 88 * .93^9 = 45.80 lbs Now, if you want to use e as the base, recall that .93 = e^ln(.93) = e^-.0725 So, .93^t = e^(-.0725t) In your formula, yo...

**Algebra**

the table does not represent a function, since you have y(-1) = 0 and y(-1) = -1 All ordered pairs must have a unique x value. B: f(h) = 3h+1, so f(3) = 3(3)+1 = 10 she wins 10 matches if she practices 3 hours a day. The only question I have is, if she spends all that time pra...

**calculus help**

Recall that sinhx = (e^x-e^-x)/2 coshx = (e^x+e^-x)/2 so, sinhx + coshx = e^x 2e^x/(sinhx+coshx) = 2e^x/e^x = 2 makes things kinda simple, eh?

**calculus help**

Just use Leibniz's Rule: d/dx(∫[1-2x,1+2x] t sint dt) = (1+2x)sin(1+2x)(2) - (1-2x)sin(1-2x)(-2) = 2(1+2x)sin(1+2x) + 2(1-2x)sin(1-2x)

**math**

#3 is indeed B #4. If Ann's rate is 4.75 Fred's rate is 5.00 Sam's rate is 5.50 I'd say Sam's has the steepest line.

**Math**

use the same proportion: 350 * (21/50) = 147 How did you come by d?

**Math**

assume the population has the same ratio as the sample. So, 36500 * (350/500) = 25550

**algebra**

for x^2+bx+c you are looking for factors (x+h)(x+k) = x^2 + (h+k)x + hk So, you want to find two numbers h and k such that h+k = b hk = c Same thing for the 2nd one, except that now you have to contend with factors of a as well.

**maths**

If you mean 2/(x^2-9xy^2) - 3/(3x+12y) then that's 2 / x(x-9y^2) - 1/(x+4y) (-x^2+9xy^2+2x+8y)/(x^3-9x^2y^2+4x^2y-36xy^3) I suspect a typo

**maths**

(x-3)(x+2)/6xy * 2x^2y/(x-3)(x+3) 2x^2y(x+2) / 6xy(x+3) x(x+2)/3(x+3)

**maths**

(x-y)(x^2+xy+y^2) / z(x-y)^2 (x^2+xy+y^2) / z(x-y)

**maths**

(5x)(15y) / (7)(8x) 75xy/56x 75y/56

**algebra**

x^2+2x+24 does not factor over the reals. However, x^2+2x-24 = (x+6)(x-4)

**computers - Programming**

Here's a little perl ditty that should do the trick. Adapt to the language of choice. my @max = (10,50,100,99999); my @sc = (15,10,5,0); do { print "enter amount ordered: "; my $amt = <>; last if $amt <= 0; printf "Order: %5d...

**Precalculus**

#1 (a) ok (b) u10 = a+9d = a+81 u7 = a+6d = a+54 a+81 = 2(a+54) a = -27 #2 ok

**ALGEBRA**

since TV = k is constant, T(5) = (15)(20) In the real world, T is usually in Kelvin degrees.

**algebra**

a) just take logs of both sides. Since log(x^n) = n*logx, we have log 343 = 3*log 7 Now, it would help to use base 7 for the logs, to make the nice and pretty equation log7343 = 3 since 5^2 = 25, 5^-2 = 1/5^2 = 1/25 So, (1/5)^-2 = 1/(1/25) = 25 Using base 1/5 logs, that is log...

**Math**

Just draw a diagram (right triangle). The true course is one leg, and the actual course is the hypotenuse. The error is the other leg. So, with an hypotenuse of 121, error/121 = sin 2°

**Math**

C is in fact correct

**Precalculus**

The reason they usually use [0,2pi) is that 0 and 2pi are really the same angle. So, your solution set need not include them both. cos^2x-2sinx-2 = 0 1-sin^2x-2sinx-2 = 0 sin^2x+2sinx+1 = 0 sinx = -1 so, yes x = 3pi/2

**ALGEBRA**

x^2-9 - (x+3)(x-3) so, cancelling the x+3 factors, you have (x-3)/(x-5)

**math 2 questions!!!**

How can you have NO CLUE about finding the slope of a line between two points? The slops is the change in y divided by the change in x. SO, between the two points (3, 4) and (2, 6), y changes from 4 to 6, or +2 x changes from 3 to 2, or -1 m = 2/-1 = -2 Similarly for #8 Simila...

**ALGEBRA**

since the denominators are the same (x+3), just subtract the numerators: (-5x-7)/(x+3)

**Algebra**

2020 is 10 years at 5% and 5 years at 8%, so 2000 * 1.05^10 * 1.08^5 = 4786.76

**Mathematics**

(w+2*10)(3w+2*10) = (w+20)(3w+20) so you just solve 3w^2 = (w+20)(3w+20) - 3w^2 + 1200 3w^2 = 3w^2+80w+400 - 3w^2 + 1200 3w^2 - 80w - 1600 = 0 (3w+40)(w-40) = 0 w = 40 or -40/3 If you can't do that, you have some serious reviewing to do.

**Mathematics**

If the lot's width is w, w*3w = (w+2*10)(3w+2*10) - w*3w + 1200 w = 40 so, the lot is 40x120 the total area is 60x140 = 8400 the lot's area is 40x120 = 4800 so, the walk's area is 3600 and the lot's area is 1200 more than that

**ALGEBRA**

well, 12k^2+2k-4 = 2(3k+2)(2k-1) so, we have (k+3)/2(2k-1) * 2(3k+2)(2k-1) now the 2(2k-1) cancels, leaving (k+3)(3k+2) No idea about the 11.

**Math**

since time = distance / speed, t =1/r + 1/.70r = 1.70/.70r = 2.43/r or 17 / 7r

**Trigonometric Functions**

It appears that the person on the wheel is at height 4 at t=6 and t=18 Since the person on the wheel is at the lowest point at t=0, we have y = r(1-cos(t)) Since t=6 going up, t=18+6=24 when the person is back on the ground. So, the period is 24 and the height of 4 is at 1/4 o...

**LOGS (ALGEBRA)**

y = 10^(5x+3) - 10 (y+10) = 10^(5x+3) log(y+10) = 5x+3 x = (log(y+10)-3)/5 so, f^-1(x) = (log(x+10)-3)/5

**Algebra, Logirithms**

y = e^(4x+2) - 10 y+10 = e^(4x+2) 4x+2 = ln(y+10) x = (ln(y+10)-2)/4 so, f^-1(x) = (ln(x+10)-2)/4

**One Algebra Question~!**

you are joking, right? Driving faster, it takes a much longer time? Maybe if you look at it like this: since distance = speed * time, and both distances are the same, 65*t = 55*7

**Math**

each point of the 7 is connected to 6 others. So, going through all 7 points, you have 7*6 = 42 connections. But, having gone all the way around, you have drawn each chord twice, once from each end. So, divide the total by 2 to get 7*6/2 = 21 chords

**geometry**

6 = 2*3 12 = 4*3 6*12 = (2*3)(4*3)/(2*4) = 3*3 = 9

**pre algebra**

find the solution y = 2x - 1 and y = x +3

**pre algebra**

find the solution y = 4x and y + x = 5

**american history**

I feel that answer D would be the most correct

**Mathematics, simplify**

factor out the 5a: 5a(c+2b-5d)

**add maths**

find the midpoint: (1,2) find the slope: 1 slope of perp. line: -1 so, now you have a point and a slope: y-2 = -(x-1)

**FRaction**

to combine thirds and fourths, you need a common denominator: 12 1/3 = 4/12 1/4 = 3/12, so 3/4 = 9/12 You can't subtract 49 from 4, so you need to borrow 12/12 from the 3. After that, you just have 2 16/12 - 1 9/12 2-1 = 1 16-9 = 7

**Algebra**

7x+x^2 = x(7+x) divide and cancel the x factor, leaving 1/(x+7) But, you cannot divide by zero, so x = -7 is excluded. You also cannot simply cancel the x factors, if x=0. So, (C)

**math**

r+20/60 = r + 1/3 = (3r+1)/3

**math**

Discard the noise about years 3 and 4. ABC grew 8% of 150,000 = 12000 As you can see, the numbers don't add up even close: 150000(1.08*1.02^2 - 1) = 18,544.80 Where did the 45,000 come from?

**math**

pi is about 3, so d is about 120/3 or 40. But, pi is slightly larger than 3, so d is slightly smaller than 40. (B)

**math**

area of top circle T: pi*3^2 = 9pi = 28.27 area of sides S: pi*6*18 = 108pi = 339.29 (a) black = S/2 = 169.645 (b) white: T + S/2 = 197.915 (c) C = (.03/12)b + (.04/15)w (d) C = .424 + .526 = 0.95 (e) yes Aside from your typo on C, I pretty much agree with your figures.

**math**

I agree with you.

**Math**

all that algebra went ok, and you have trouble with arithmetic? C = x = 14 D = x+4 = 18 A+B+C+D = 28+21+14+18 = 81

**Math**

well, if y=4x, then 4x+x=5, so x=1.

**Math**

Find the solution. y = 4x & y + x = 5

**Algebra**

(1/2)^(t/5730) = .74 t = 5730 * log(.74)/log(0.5)

**Calculus**

2ln6 = ln 36 2ln3 = ln 9 ln36 - ln 9 = ln(36/9) = ln 4 or 2(ln6-ln3) = 2(ln(6/2) = 2ln2 = ln(2^2) = ln 4

**algebra**

I find it easier to deal with integers, so my first step would be 14x - 5y = 13 4x + 11y = 41 now, to eliminate the y's, do some multiplying to get 154x - 55y = 143 20x + 55y = 205 add them together to get 174x = 348 x = 2 so, y = 3

**algebra**

(2+1)^2 + (y+3)^2 = 5^2

**algebra**

which elements are in both sets? {3,4,5} Don't get sloppy with your notation, or things will get confusing as the problems get more involved. Your second line is just nonsense, but it's easy to figure out what you meant in this case. (I think!)

**algebra**

{(1,2),(1,4)...(6,4),(6,9)}

**Algebra**

multiply the first by 3 and you have -6x-12 = 3 12 = -6x-3 You can see that they are the same line. Plug any value of x into either equation, and you will get the same value for y.

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