Tuesday
July 26, 2016

Posts by Steve

Total # Posts: 42,093

math
well, how far does the hare go? distance = speed * time
June 12, 2016

math
probably the latter, as the previous post used half-angle formula. So, eku, I guess that gives a clue to this one, too, eh?
June 12, 2016

maths
x+y+z = 26 y = 3x You want minimal x^2+y^2+z^2, so check out a few possibilities: x y z ∑*^2 1 3 22 488 2 6 18 332 3 9 14 208 ... I think you can figure it out.
June 12, 2016

math
use your half-angle formula: tan(A/2) = (1-cosA)/sinA you can easily find cosA, and then just plug and chug.
June 12, 2016

Maths
Draw the unit circle. Draw a right triangle in standard position (right angle on the x-axis). Now label the sides. The hypotenuse is 1 The height is x Let angle A be at (0,0) So, sin(A) = x/1 = x That is, A = sin^-1(x) csc(A) = 1/sin(A) = 1/x So, A = csc^-1(1/x)
June 12, 2016

math
so, what's the problem? Get out your protractor and ruler.
June 12, 2016

math
upstream time is m/(r-s) downstream time is m/(r+s)
June 12, 2016

Math
something is messed up. I suspect a typo. In particular, I think 4.6 cakes will take a lot more than 3/5 lb of flour, unless they are very small cakes. Hmmm. 2/3 lb is about 3/5 cup. I know I can't make 4 cakes with that much flour!
June 12, 2016

Math
suppose you know how much you need to make 3 cakes. To make one cake, you just divide by 3, right? So here, just divide by 4 3/5. (2/3)/(4 3/5) = (2/3)/(23/5) = 2/3 * 5/23 = 10/69 All fractions work the same way.
June 12, 2016

Algebra
Usually people don't talk about "prime factors" of polynomials, but a complete factorization should do the job. Here are a few: a. 2a^2 - 2b^2 = 2(a^2-b^2) = 2(a-b)(a+b) b. 6x^2 - 6y^2 = 6(x^2-y^2) = 2*3(x-y)(x+y) c. 4x^2 - 4 = 4(x^2-1) = 2*2(x-1)(x+1) d. ax^2 - ...
June 12, 2016

Physics
so, did you draw the path? where did you end up? Hint: label the start (0,0) Distance covered is just the sum of all the line segments. Final displacement is found using the normal distance formula, which is just the Pythagorean Theorem.
June 12, 2016

Trigonometry
nothing to do but convert to x-y form, add them up, and then convert back. Luckily, they can be treated as complex numbers, making the job easier, using polar form. And, you can let wolframalpha.com do all the work (or any other handy calculator you know). You can check your ...
June 11, 2016

Mathematics
Nope. The A+B+C=180 Note that the sides AC = b AB = c Use the law of cosines to get a^2 = b^2+c^2-2bc cosA Now, having a, you can use the law of sines to get A: sinA/a = sinC/c
June 11, 2016

Math - Year 10 - Simult. equations
you know that 4y = -3x, so use that in 16x^2 + 16y^2 = 400 16x^2 + (4y)^2 = 400 16x^2 + 9x^2 = 400 and I think you can take it from there, right?
June 11, 2016

pre-algebra
Interesting. As a position relative to the surface, the value is -550. But, as you say, the depth is indeed 550 ft. "Depth" carries with it an implied negative value. I'd check to see just how they want you to interpret positive and negative quantities.
June 11, 2016

Math
best bet is to convert all to decimals. The it will be easy. SO, 2/3 = 0.6666 0.2 = 0.2000 and so on
June 11, 2016

Algebra
(a+b)(a+b) Now just expand that us usual
June 11, 2016

maths
if two polynomials have the same roots, one is a multiple of the other. So, x^2+px+q = 2(x^2-(5/2)x-(3/2)) so, p = -5/2 and q = -3/2
June 11, 2016

maths
If the roots are p and q, then we have pq = k Since p = 1/q, pq = 1 So, k=1 x^2-5x+1 has roots (5±√21)/2 I leave it to you to verify that the two values are reciprocals.
June 11, 2016

Logarithm
Your observation appears correct; the right side is 1/√(27^2) (3^x)^3 = 3^(3*x) = 3^(3x) 9 = 3^2, so 9*3^(3x) = 3^2 * 3^(3x) = 3^(3x+2) Now, on the right, for any value n, √(n^2) = n, so we have 1/27 = 3^-2 So, we want x such that 3^(3x+2) = 3^-2 3x+2 = -2 3x = -4 ...
June 11, 2016

Maths
Actually, the number is 58.
June 11, 2016

Algebra
reciprocals of equals are equal. Unless the equals are zero...
June 11, 2016

Calculus
as usual, for a given perimeter (sum), a square has maximum area (product).
June 10, 2016

math
(50*60 + 25*56 + 25x)/(50+25+25) = 58 now solve for x
June 10, 2016

math (significant digits)
you only have one s.d. .03 + 0.2 = .23 which becomes 0.2
June 10, 2016

math
that looks better.
June 10, 2016

math
since they are of equal weight, their average is just the arithmetic average of the two scores: 87 Why do I suspect that the problem was misstated?
June 10, 2016

Math
ar^2 = 4 So, you want to know a^5 r^10 = (ar^2)^5 = 4^5 = 1024
June 10, 2016

Math
a 1-cm thick layer of water has a volume of π*35^2 cm^3 = 3.848 L So, you want to know how long it takes to drain 20cm = 76.97L 76.97L ÷ 10L/hr ≈ 7.7 hr
June 10, 2016

maths
what does a circular pool is 300 mean?
June 10, 2016

maths
If 1/3 were bad, then 2/3 were good. So, he made (5 1/4)*(3/4)(712)(2/3) =
June 10, 2016

math
Just do the division. The remainder is (m-3)y + (n+3) To be divisible, the remainder must be zero, so that means m=3 and n = -3. Check: y^4 + 3y^3 + 2y^2 - 3y - 3 = (y^2-1)(y^2+3y+3)
June 10, 2016

Algebra
You must group terms with like exponents. For example, #20 3x^2 – [7x- (4x – x^2) + 3] = 3x^2 - [7x-4x+x^2+3] = 3x^2 - [x^2+3x+3] = 3x^2-x^2-3x-3 = 2x^2-3x-3 You can see this at this url: http://www.wolframalpha.com/input/?i=3x^2+%E2%80%93+[7x-+%284x+%E2%80%93+x^2%29...
June 10, 2016

Physical Science
That would depend on the applied force. F = ma You can take it from there.
June 10, 2016

O98 algebra
The sum of her first 5 scores is 382 6*77 = 462 6*85 = 510 So the last score must satisfy 462 < 382+x < 510 80 < x < 128 So, any score above 80 will get her a C grade.
June 10, 2016

Math: Inverse Function (Plz help)
f = 8+√(8+x) to find f^-1, swap variables and solve for f: x = 8+√(8+f) x-8 = √(8+f) x^2-16x+64 = 8+f f = x^2-16x+56
June 9, 2016

analytical math
no idea. How old is Mary now?
June 9, 2016

Math
42
June 9, 2016

Math
.20 * 20 = 4
June 9, 2016

Pre-Cal: Domain (cont.)
#8 the domain is all real numbers except 0 and -7 While the domain of [5(x+7)]/[7x] excludes only 0, (f/g)(x) requires evaluating both f and g, and since g(-7) is not defined, neither is (f/g)(-7)
June 9, 2016

Math
just keep adding 11
June 9, 2016

Algebra
or, since you are given a point and a slope, try using the point-slope form of the line: y-11 = (7/3)(x-3) That's good enough for me. What you want depends on what you mean by "the equation" of a line.
June 9, 2016

math
the surface consists of three pairs of rectangular faces. You have the length and width of each face, so find the three areas, add 'em up, and double that (since there are two of each size)
June 9, 2016

algebra 2B
I suspect a typo g(x) =− 2 −x 2+ 4 is the same as -2 - x^2 + 4 = 2-x^2 Clean it up and show how far you got.
June 9, 2016

algebra
y = (2x-3)/(7x+1) see http://www.wolframalpha.com/input/?i=%282x-3%29%2F%287x%2B1%29
June 9, 2016

Math
if you want the height, drop the altitude to the base. It divides the base into two parts, x and 12-x. Now, using the Pythagorean Theorem, you can find the height h using x^2 + h^2 = 8^2 (12-x)^2 + h^2 = 7^2 subtract and you get rid of h, leaving x^2 - (12-x)^2 = 64-49 24x - ...
June 9, 2016

Physics- Help!!
120 * (1200/100) = ?
June 9, 2016

math
do you see what a useless response that is? Restrict how? Anyway, I gave you the information you need. How about showing some effort of your own here?
June 9, 2016

math
infinitely many. Or did you want to restrict the available area? In the first quadrant, (4,4) is on the curve. There will be none to the left of (1,16) or to the right of (16,1). And don't count the lattice points on the curve...
June 9, 2016

Pre-Cal: Domain
the domains include all real numbers except where the denominator is zero. So, figure the resultant function, and then exclude any places where the denominator is zero. AND, exclude 0 and -7 because at those values f or g is undefined, so even though some mixture of them might...
June 9, 2016

Calculus
you are correct. 1/(x-1) -> ∞ I tried to pound a round peg into a square hole.
June 9, 2016

Calculus
note that if u = 1/(x-1) then what you have is sin(u)/u You have probably seen that this limit is 1, so follow the same argument. Or, try google. A good discussion is at math.ucsb.edu/~jcs/SqueezeTheorem.pdf
June 9, 2016

Math/Dosage Calculations
just add up the amounts (in fl oz): (1/3)(8) + (1/2)(16) + 3 = 41/3 fl oz. Now just convert that to mL. 1 oz = 29.57 mL Hmmm. I get 404 mL
June 9, 2016

Math
Just take each sentence and place the required digit in for one of the x's. Start with xxxx My hundreds digit is the last odd number. x9xx and move right along.
June 9, 2016

Math
w*2w = 1250 Now get w, then the length is 2w
June 9, 2016

Math
that would be the area of the inner cylinder, plus the area of the outer cylinder, plus the area of the two rings at the end. So, if R = outer radius r = inner radius h = length of pipe the total area is 2πrh + 2πRh + π(R^2-r^2) = 2πh(r+R) + π(R+r)(R-r...
June 9, 2016

Math - Year 10 - Simult. Equations
just plug in y=3x and you get x^2 + (3x)^2 = 10 Now x is easy, and then y=3x.
June 9, 2016

geography
how many time zones in between? That's the number of hours. Or, if you know the longitudes, since there are 24 hours in a 360° circle, each hour covers about 15°
June 9, 2016

geometry
since j is in the middle, mn = mj+jn = 6 3/4 + 6 3/4 = ?
June 9, 2016

trigonometry
If that fails, try cot (x-y)/2 and use your half-angle formula, and more parentheses next time.
June 8, 2016

math
sure, if so designated
June 8, 2016

Math
even without calculus, you can do these. Just think of what you know about lines and parabolas. Then you can verify your Algebra I with calculus. What do you think?
June 8, 2016

math(bearing)
There seems to be a lot of noise here If the bearing of Y from Z is 280, then the bearing of Z from Y is 280-180 = 100
June 8, 2016

Pre-Cal (Help Plz)
come on. x^2-4 is negative on the interval (-2,2) So, since |x^2-4| is always positive, that little arc below the x-axis is flipped up above it. Everywhere else, the two functions are identical. g(x) = -f(x) if |x| < 2 g(x) = f(x) if |x| >= 2
June 8, 2016

Pre-Cal (Help Plz)
take a look at the graphs and see what you can say. And why not use || for absolute value? It's not like you don't have the characters... http://www.wolframalpha.com/input/?i=plot+y%3Dx^2-4,+y%3D|x^2-4|
June 8, 2016

math
ok
June 8, 2016

Trigonometry
off course as measured how? Actual distance between target and position, or distance perpendicular to the intended course? In the first case, use the law of cosines. Both sides of the included angle are 152*2
June 8, 2016

Trigonometry
draw the diagram. It should be clear that if the height is h, h cot32° - h cot40° = 12
June 8, 2016

Trigonometry
draw the diagram. It should be clear that north: 83 cos37° west: 83 sin37°
June 8, 2016

math
looks good to me.
June 8, 2016

Math - eh?
NO IDEA! Where the heck is X?
June 8, 2016

PreAlgebra
x^2 = 22^2 - 7^2 now just crank it out
June 8, 2016

Math
your formula is correct, but your answer is not. Oh, well.
June 8, 2016

Math
a = 2πr(r+h) = 2π(9)(9 + 19) = 504π So, D How did you get 523?
June 8, 2016

Math
yes, it is correct.
June 8, 2016

Science
PV/T is constant, so you want T such that 1.82*18.7/353 = 1.41*25.1/T T ≈ 367
June 8, 2016

aptitude
clearing fractions and decimals, we have 125x + 5y = 21 3x + y = 3 now you can substitute y = 3-3x to get 125x + 5(3-3x) = 21 Now it's easy to solve for x, and then you can get y.
June 8, 2016

Algebra
Seems we want cube roots: ∛540r^3 s^2 t^9 = ∛27*20 r^3 s^2 (t^3)^3 = 3rt^3 ∛20s^2 so, yes, you are correct
June 8, 2016

maths
just plug in values for t: x(2) = 16*2 - 2*2^2 = 32-8 = 24 likewise for t=6
June 8, 2016

math
starting with 1, after chocolates, 3/5 remains after gift to sister, she has 8/9 * 3/5 = 8/15 after books, she has 1/4 * 8/15 = 2/15
June 8, 2016

Math
so, which ones did you get? Show some work, eh? This is a massive homework dump. And sorry, you will have to describe the graphics is possible.
June 8, 2016

Trigonometry
as usual, with fractions, cross-multiply, and you will see one of your standard identities.
June 8, 2016

Trigonometry
I assume you mean 4sin^2(3θ) - 3 = 0 sin^2(3θ) = 3/4 sin(3θ) = √3/2 3θ = 60° or 120° θ = 20° or 40° Since sin(3θ) has period 360/3 = 120°, add multiples of 120° to those values. You will find six solutions in the ...
June 7, 2016

Trigonometry
you have tanx = -2 so, the solutions will be in QII and QIV.
June 7, 2016

Trigonometry
since sin^2x = 1 - cos^2x, make that substitution, and then solve the quadratic for cos(x)
June 7, 2016

Trigonometry
No idea what a double identity is, but draw the triangle. The missing side is √24. In QII, that means x is negative, so cosθ = x/r = -√24/5 cotθ = x/y = -√24/1
June 7, 2016

math
clearly the major axis has length 13, and the minor axis has length 12. So a = 13/2 b = 6 c^2 = a^2-b^2 = 25/4, so c = 5/2 The center is at (13/2,0), so h = 13/2 and k=0 The foci are at (h±c,k) Since the major axis is horizontal, that means the equation is (x-h)^2/a^2...
June 7, 2016

Math
so, no, A is not correct.
June 7, 2016

math
a = 0.9 o so, o = a/0.9 = 1.111a so, the orange is 11% heavier than the apple. The grapefruit is just noise.
June 7, 2016

math
do you even look at what you type? That's "sides" not "size"! and "menion" just escapes me totally! If the two diagonals are x and y, then using the law of cosines, and the fact that consecutive angles are supplementary, x^2 = 6^2+9^2 - 2*6*9 ...
June 7, 2016

Algebra
It sounds like you want a recursive sequence, where T(n+1) = 4Tn - Tn^2 If so, then if Tn = 4*2.4 - 2.4^2 = 3.84 T(n+1) = 4*3.84 - 3.84^2 = 0.61
June 7, 2016

math
5000*1.01^8 + 10000*1.01^16
June 7, 2016

Math Help Please
Note which side is opposite to A and adjacent to A. Now review your basic trig functions. You can see that sinA = BC/AB cosA = AC/AB so you are correct. Extra credit: How did I figure it out, with no triangle to refer to?
June 7, 2016

value
you don't move on a bearing. You move on a heading. You observe on a bearing. Starting from R at (0,0), P moves to (-20/√2,-20/√2) Q moves to (15√3/2,15/2) now just find the distance between those points. Or, use the law of cosines. The angle between ...
June 7, 2016

algebra
12 mg / kg * 1kg/2.2lb * 120lb = 655mg
June 7, 2016

maths
What do you mean when you say when it is perpendicular to it ?? when what is perpendicular to what?
June 7, 2016

Maths
1+1 = 2 You have some other questions?
June 7, 2016

Maths
DBA = BDC = 28° DBC = 90° - DBA = 62°
June 7, 2016

Math (money)
(x - 200)(.80) - 131 = .20x x = 485 check: start: 485 dress: 200 leaves 285 bag: 57 leaves 228 shoes: 131 leaves 97 = 20% of 485
June 7, 2016

MATH - ??
Ouch! I got confused on the period/comma usage disparity. Or, I could just say I was figuring in km instead of meters!
June 7, 2016

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