Friday
September 4, 2015

Posts by steve


Total # Posts: 33,310

Geometry
gotta know what P' is, dontcha think? I will say that a rotation of angle θ maps (0,1) -> (cosθ,sinθ)
August 22, 2015

calc
This is just ∫[0,3] t^2 - 2t dt
August 22, 2015

Algebra
These are just exercises using the distributive property. Clear parentheses to get started. 1.2(x+5) = 1.6(2x+5) 1.2x + 6.0 = 3.2x + 8.0 2.0x = -2.0 x = -1.0 Or, if you dislike decimals, multiply by 5 to start with: 6(x+5) = 8(2x+5) 6x+30 = 16x+40 10x = -10 x = -1 a(y+c) = b(y...
August 22, 2015

Phyics
for   for     stuff   next   more stuff next
August 22, 2015

PleaseHelp! Geometry!
Of we call the two circles r and R, and the center O, draw the tangent and let P be where it touches circle r, and Q be where it intersects R. Then the triangle OPQ is a right triangle with one leg r and the hypotenuse R. The other leg is thus sqrt(R^2-r^2) But, pi*R^2 - pi*r^...
August 22, 2015

Geometry
a circle has a center (8,2). the point (3,7) is on the circle. What is the area of the circle to the nearest square unit?
August 22, 2015

Geometry
a circle has a center (3,5). the point (3,8) is on the circle. What is the circumference of the circle to the nearest unit?
August 22, 2015

ALG 2
the two-point form is (y-y1) = (y2-y1)/(x2-x1) * (x-x1) y-6 = (-2-6)/(3+6) (x+6) y-6 = -8/9 (x+6) 9y-54 = -8x-48 The standard form is thus 8x+9y = 6
August 22, 2015

chem
seems like all but the last significant digit will be certain.
August 22, 2015

Geometry
thank you
August 22, 2015

Geometry
if you trust that the vertices do in fact form a rectangle, then just find the lengths of sides wx and wz wx has length 3√2 wz has length 4√2 the rectangle thus has area 24
August 22, 2015

Geometry
What is the area of rectangle wxyz with vertices w(0,1),x(3,4),y(-1,8) z (-4,5) to the nearest unit?
August 22, 2015

Calculus
position y = 2t^3-6t rad velocity v = dy/dt = 6t^2-6 rad/s acceleration a = dv/dt = 12t rad/s^2
August 22, 2015

algebra
how much of the tank's volume is filled/drained each minute? 1/60 + 1/50 - 1/x = 1/35 1/x = 17/2100 So, it will take 2100/17 = 123.5 minutes
August 22, 2015

graphical geometry need help
It appears that you mean it passes through the point (2,0). So, plug those values in and you have 4+4+k = 0 k = -8 so, y = x^2+2x-8
August 22, 2015

algebra
If x lbs of copper and y lbs or iron are added, then we need 25 + x = .30(100+x+y) 40 + y = .50(100+x+y) Now just solve for x and y. Be sure to check your answers.
August 22, 2015

maths
1/20 + 1/B = 1/12 now solve for B
August 22, 2015

Math
correct.
August 21, 2015

Algebra
or, just √5 x, since 5/√5 = √5
August 21, 2015

Algebra
well, 5x^5/2 (5x)^-3/2 = 5x so, now what do you think?
August 21, 2015

calculus
A. Geez, the trapezoids all have height 1, so the area of each is just the average of the two y-coordinates. B. think of the units on the axes: v * t = distance C. avg speed is totaldistance/totaltime
August 21, 2015

Algebra
Try again. I think you'll have √5 x (5x)^5/2 (5x)^-3/2 = (5x)
August 21, 2015

Algebra
see related problems below
August 21, 2015

Algebra
I'd do it like this. Start by simplifying the numerator into a single fraction. You wouldn't have any trouble combing 2/3 - 7 would you? [-x^3/√(1-x^2) - 2x√(1-x^2)]/x =[(-x^3 - 2x(1-x^2))/√(1-x^2)]/x =(-x^3-2x+2x^3) / x√(1-x^2) = (x^3-2x) / x&#...
August 21, 2015

Algebra
Take a look at what wolframalpha got: http://www.wolframalpha.com/input/?i=2x+%28x-5%29^-3+-4x^2+%28x-5%29^-4
August 21, 2015

Algebra
you have t^2/√(t^2+1) - √(t^2+1) ---------------------------- t^2 Combine the terms in the numerator and denominator t^2 - (t^2+1) --------------------- t^2 √(t^2+1) -1/(t^2 √(t^2+1))
August 21, 2015

Trigonometry and Analysis
Hmmm. How did you get through this step? (.01)(D*2)+(.10)(D)=.84 .01D+.02+.10D=.84
August 21, 2015

Math
Sounds to me like the stock bottle's date will be in the future. If it's more than two years away, your item must still be labeled to expire in a year. If it's less than two years away, your item's date will be midway between today's date and the stock ...
August 21, 2015

Math
Assuming some of each coin must be used, I get 1 quarter 2 dimes 2 nickels 45 pennies Otherwise, you could also have just 2 dimes 8 nickels 40 pennies
August 21, 2015

Algebra
I disagree, if you interpret the expression as 5^-1/2 * (5x)^5/2 * (5x)^-3/2 as he apparently did. I must say though, in Damon's defense, Stephen's wily (wildly?) and inconsistent use of parentheses left things open to misinterpretation. Actually, even that is wrong, ...
August 21, 2015

Algebra
you are correct.
August 21, 2015

Geometry
as with the single dimension, the coordinates of the midpoint of a line in the plane is the average of each coordinate: ((-1+5)/2 , (0+2)/2) = (2,1)
August 21, 2015

Geometry
the midpoint is halfway between the two ends. That means it is the average of the two values: (-2+12)/2 = 5 5 is 7 above -2, and 7 below 12
August 21, 2015

math
I suspect that the pond is 12 ft longer than it is wide. 12 cm is a ridiculous amount. Assuming that, we have the dimensions of w and w+12. Then we are told that (w+4)(w+12+4) - (w)(w+12) = 160 Solve that and you find w=12. So, the pond is 12x24 16*28 - 12*24 = 160
August 21, 2015

Mathematics
well, just pick any 2-digit number, uv The 2nd number will be (9-u)(10-v) so, these are also good: 22 78 88 12 ...
August 21, 2015

Mathematics
Some candidates are 36 64 53 47 ...
August 21, 2015

Mathematics
first thing I want to know, is: which pairs?
August 21, 2015

Trigonometry
If you meant sinx + √3 cosx = 1 then try this √3 cosx = 1-sinx 3cos^2x = 1-2sinx+sin^2x 3(1-sin^2x) = 1-2sinx+sin^2x 4sin^2x - 2sinx - 2 = 0 2(2sinx+1)(sinx-1) = 0 sinx = -1/2 or 1 x = 90 or 210 or 330 But 210 does not work in the original equation, so throw it out.
August 21, 2015

mathmetic
If you mean x^4 = 3.125 then just take the 4th root to get x = 1.339 verify with any calculator. Or did you have something more in mind?
August 21, 2015

Integration help
let u = 2x-1 Then du = 2 dx the integrand then becomes 1/2 u^(-1/2) du Now it's a cinch.
August 21, 2015

algebra
n = d^2-7 (n+6)/(d+6) = 2 I suspect a typo. wolframalpha gets 8+2√14 ----------- 1+√14 However, if 1 is added to the denominator, then the fraction is 2/3 http://www.wolframalpha.com/input/?i=solve+n+%3D+d^2-7%2C+%28n%2B6%29%2F%28d%2B6%29+%3D+2
August 21, 2015

alliance
Can't tell without more information. Pick any speed for the lorry, say 70 km/hr Then the time for the lorry is 4 hr Then the car moves at 98.8 km/hr You can pick any other value for the lorry's speed and find a corresponding speed for the car.
August 21, 2015

Algebra
Hard to say; the parentheses are unbalanced. It could be t^2/√(t^2+1) - √(t^2+1) ------------------------- t^2 Then you could proceed like this t^2 - (t^2+1) ------------------ t^2 √(t^2+1) . . . -1 --------------- t^2 √(t^2+1)
August 21, 2015

Algebra II
If the shortest side is x, then we have x + (x+4) + 3x > 39 5x > 35 x > 7 By the way, longer implies only two items. You want to use longest here, since a triangle has three sides. Especially, since without knowing the value of x, maybe x+4 is bigger than 3x. The ...
August 21, 2015

Math
60/40 = 3/2, so the 60lb child should sit 2/3 as far from the fulcrum.
August 20, 2015

Algebra
I have a hard time parsing the factors, since you eschew parentheses. Why don't you enter your expression at wolframalpha.com and confirm your work. I tried to get it right at http://www.wolframalpha.com/input/?i=5^%28-1%2F2%29+x+%285x%29^%285%2F2%29+%285x%29^%28-3%2F2%29 ...
August 20, 2015

Algebra
Looks good to me.
August 20, 2015

Calculus 1
what's the trouble, forgot your Algebra I already? f(4+h) = 1+2(4+h)-(4+h)^2 = -7-6h-h^2 f(4) = 1+2(4)-4^2 = -7 f(4+h)-f(4) = -6h-h^2 Now divide all that by h and you have -6-h
August 20, 2015

Calculus 1
g(h) = 3h = 3(x-5) = 3x-15 f(g(h)) = g(h)+9 = 3x-15 + 9 = 3x-6
August 20, 2015

Calculus 1
just try the steps. (d): -2f(x) reflect about the x-axis stretch the graph vertically by a factor of 2 the order does not matter here (e): f(6x) stretch the graph horizontally by a factor of 6 6x changes 6 times as fast as x, so x only has to be 1/6 as big to get the same ...
August 20, 2015

Math
x^2+12x+27 try a number. If x=1, does (1+3)(1+9) = 1^2+27 ??
August 20, 2015

Math
Use the distribute property. (x-1)(x-8) = x(x-8) - 1(x-8) = x^2-8x - x + 8 = x^2-9x+8 At least check you answer using a numeric value for x to see whether it works.
August 20, 2015

Calculus 1
(a) stretch the graph vertically by a factor of 7 (b) shift 4 units to the right (c) reflect about the x-axis You offered no ideas here or on your next post. If you truly are lost, you will do well to review your text, and google examples and explanations.
August 20, 2015

math
Ignoring the factor of pi/3, we have 3/4 * 4^2 * 10 = (5/9 h)^2 * h Now just solve for h
August 20, 2015

Physics
see related questions below
August 20, 2015

maths - garbage
try using (a+b)/(x-1) for division. Use * for multiplication is you want to use x for a variable. I have no idea what your multi-line formatting is supposed to convey.
August 20, 2015

math
depends on whether they are hung as landscapes or portraits. Either way, just draw a diagram, and add up the needed heights and spaces!
August 20, 2015

The Chemistry of Life Quiz // Just Answers please
I can see why you're having trouble - you can't read...
August 20, 2015

The Chemistry of Life Quiz // Just Answers please
#1. Carbon is an element, not a complex molecule. Lipids and proteins fit the bill #2 Adhesion sticks stuff to each other cohesion makes stuff stay together #3 looks ok
August 20, 2015

math
since the diameter has been reduced by half over a height of h, it will shrink to zero (the tip of the cone) in another h. So, the cone's height is 2h. Or, using a ratio to find the cone's height H, H/2r = (H-h)/r H = 2(H-h) H = 2h
August 20, 2015

chemistry
4Al + 3O2 = 2Al2O3 2KClO3 --> 2KCl + 3O2 5.1g Al2O3 = 5.1/101.96 = 0.050 moles Al2O3 So, you need 3/2 * 0.050 = 0.075 moles of O2. Thus, you need 2/3 * 0.075 = 0.050 moles KClO3 to produce that needed O2.
August 20, 2015

algebra
regardless of the typo, it's -1/2 I find it hard to understand the difficulty in finding the "m" in y = mx+b to get the slope.
August 20, 2015

algebra
Ok. I'll show some maybe-not-so-divine mercy and help you out. (x+y+z)/3 = 6 (x+y+z+t+u+v+w)/7 = 9 x+y+z = 18 x+y+z+t+u+v+w = 63 18+t+u+v+w = 63 t+u+v+w = 45 (t+u+v+w)/4 = 45/4
August 20, 2015

Test Post?
why indeed? It depends on what "+" is. in binary, 1+1 = 10 in logic, 1+1 = 1 if + joins strings, then 1+1 = 11 I suspect a test posting.
August 20, 2015

modular arithmetic
10
August 20, 2015

Math
m/w = 6/4 (m-5)/(w-5) = 5/3 (m,w) = (30,20) m-w = 10
August 20, 2015

Physics
Draw a diagram. You want the hypotenuse of a 3-4-5 right triangle.
August 20, 2015

The polythecnic Ibadan
since PV is constant under these conditions, (300)(900) = 600V
August 20, 2015

Algebra
-4-4-4+9 = -3 so, they wound up with a loss of 3 yards or, 3(-4)+9 = -3 for the sub, you want -125 + 3(-50) = -125-150 = -275 Your setup yields -125(-150) = 18750 ft in the air! 220-4(35) or, 220+4(-35) Your final answer is correct, though, which shows that you not only don&#...
August 20, 2015

algebra2
first, use the point-slope form: y+2 = 6(x+1) Now move stuff around till you have y = mx+b y+2 = 6(x+1) y+2 = 6x+6 y = 6x+4
August 20, 2015

Math
use your calculator or, just type that into google's search box
August 20, 2015

algebra2
you want y all by itself on the left: y = mx+b So, start moving stuff around. x-y = -7 x = -7+y x+7 = y or y = x+7
August 20, 2015

Physics
first, dodos do not fly. second, dodos are extinct. However, since time=distance/speed, if the bird flies back x km, then (4.9+x)/24.8 = (4.9-x)/6.2 x = 2.94 So, the bird flew 7.84 km
August 20, 2015

Math - eh?
you want to try that again in English?
August 19, 2015

Math
32% = 0.32 "of" means multiply: half of 6 is 1/2 * 6 = 3 So, you want 0.32 * 250
August 19, 2015

Math
3 of the fruits are not apple or peach. So, p=3/12
August 19, 2015

Calculus
while x < 2, -2 < 0, so, |x-2| = -(x-2) So, you have the limit of (3x(-(x-2)))/(x-2) = -3x You can cancel the x-2 since x is not actually 2. The limit is thus -6 The limit from the right, of course would be +6 See the graph at http://www.wolframalpha.com/input/?i=%283x+|...
August 19, 2015

Solid Mensuration
I suspect it will be 4x8, but let's see what the calculations show. If triangle ABC has vertices at (0,0),(16,0) and (h,8) then the sloping sides are lines with the equations y = 8/h x y = 8(x-16)/(h-16) Now, suppose the inscribed rectangle has height k. The the line y=k ...
August 19, 2015

Trig
2sinθ+1 = 0 2sinθ = -1 sinθ = -1/2 sin π/6 = 1/2, so using that as a reference angle in QIII and QIV, we get the solutions π + π/6 and 2π - π/6
August 19, 2015

Geometry
well, UV bisects STU, so 1/4 x + 8 = x+2 6 = 3/4 x x = 8 Now you know x, so you can figure STV=VTU, and STU = STV+VTU I get 20 How did you get 25?
August 19, 2015

Math
I think you mean (8 * 2^10)^2 * 3^7 (2^13)^2 * 3^7 2^26 * 3^7 67108864 * 2187 146767085568 Clearly I have misinterpreted your unusual syntax.
August 19, 2015

Math
36*10/24 = 15
August 19, 2015

Math
5n+10(8-n) = 65 -5n = -15 n = 3 she spent 3 nickels and 5 dimes. So, starting with N nickels and D dimes, 5N+10(20-N) = 140 -5N = -60 N=12 So, she is left with 9 nickels.
August 19, 2015

Geometry
since R is the midpoint of ST, SR is 1/2 ST, so 2(3x+3) = 30 3x+3 = 15 3x = 12 x = 4 not sure what you mean by x being 9 to equal 15
August 19, 2015

Calculus 1
the roots indicate that f(x) = a(x+1)(x)(x-2) Since f(1) = a(2)(1)(-1) = -2a = 8, a = -4
August 19, 2015

algebra
Or, using y(x) = -9/2 x + 3, y(-2) = 9+3 = 12 You want y(-2) = 5, so you have to subtract 7 from the given value, leaving you with y = -9/2 x - 4
August 19, 2015

ethics
google turns up http://www.studydroid.com/printerFriendlyViewPack.php?packId=373583 It would have worked for you, too.
August 19, 2015

algebra
type in your expression at wolframalpha.com It will show the graph. Play around there a while.
August 19, 2015

Math-unit rate
(1 1/2 mi)/(3/5 hr) = (3/2 mi)/(3/5 hr) = 5/2 mi/hr or, 2 1/2 mi/hr if you like mixed numbers
August 19, 2015

algebra
It always helps if you show your work. If it is wrong we can spot the error. Assuming the usual sloppiness with parentheses, I will assume you meant (44/9)x - 7/4 + (12/7)x + 1 = (44/9 - 12/7)x - 7/4 + 1 = (200/63)x - 3/4 I might have thought you were using x for ...
August 19, 2015

algebra
y = mx+b where m is the slope b is the intercept just plug in your values.
August 19, 2015

pre algebra
-|-16| = -16 since |-16| = 16
August 19, 2015

MATH
12/60 = 0.2
August 19, 2015

algebra
y=0 is the same as y = 0x+0 so, its slope is zero. 9x+2y = -8 is the same as 2y = -9x - 8 y = -9/2 x - 4 so its slope is -9/2 Try the others. Rearrange stuff to get y all alone on the left side, as I did above.
August 19, 2015

algebar
two lines are perpendicular if their slopes are negative reciprocals. That is, their product is -1. y = -x-3 has slope -1. So, its reciprocal has slope -1/-1 = 1
August 19, 2015

math
wow - at least you used "whom" correctly. If you are trying to find roots of cubics, you must have already studied quadratics and factoring, maybe even synthetic division. Can you find the roots of quadratics? Like x^2-x-2 = 0 If not, you can forget 3rd-degree ...
August 19, 2015

Math
eschewing all the words, we have 8^2 + 9(12/3 * 2) - 7 64 + 9(4*2) - 7 64 + 9*8 - 7 64 + 72 - 7 129 Now, since you were unclear about just what was being divided, you might have meant 8^2 + 9(12/(3*2)) - 7 64 + 9(12/6) - 7 64 + 9(2) - 7 64 + 18 - 7 75 Parentheses are your ...
August 19, 2015

Math
so, the ratio is 7:26
August 19, 2015

Math
well, how many total cubes are there? How many red?
August 19, 2015

math
there are only 2 numbers larger than 6, so p = 2/8
August 19, 2015

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