Thursday
July 24, 2014

Posts by Steve


Total # Posts: 23,951

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.

help
watch the units and you can see what to multiply or divide 343 m/s * .012s = 4.116 m

Algebra 2
how about this? http://www.wolframalpha.com/input/?i=2%281%2F2%29^x+%2B1

Algebra 1b
to translate to the right by h units, substitute x-h for x. So, your new function is g(x) = f(x-6) = ((x-6)+2)^2 = (x-4)^2

math
you keep asking that question. Does your text not explain? You can google that phrase and come up with a fistful of articles on the topic.

math
7 5/9 + x = 17 2/9 x = 17 2/9 - 7 5/9 x = 16 11/9 - 7 5/9 x = 9 6/9 or 9 2/3

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