# Posts by STEVE

Total # Posts: 52,314

Algebra
What do you mean by a "zero" value? You do not include a vertical shift term. The minimum of -5 indicates to me that y = 5sin(b(x-c)) I assume your zero value is supposed to help define the period...

Algebra
let u = 3^x Then your equation becomes 3^(2x+1) = 5*3^x + 2 3*3^(2x) = 5*3^x + 2 3u^2-5u-2 = 0 ...

Multivariable calculus
dw/dv = (dw/dx) / (dv/dx) dw/dx = ?w/?x + ?w/?y dy/dx + ?w/?z dz/dx and similarly for u,v See where you get with that.

? = 15 rev/min * 1min/60s * 2?rad/rev = ? rad/s s = r? = 12cm * ? rad/s * rs = ? cm

these are standard angles - learn the trig function values they will pop up over and over.

Maths
i) ?(9/16) = 3/4 ii) since C?r, the same ratio.

Math
You can see all the details here: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

@Bosnian got it
I neglected the fact that there were two parents... Always read the problem carefully!

math-ed 16
(90-72)/2 = 9

math 5
so, start off with the millions place: 5,xxx,xxx The rest is pretty vague. One possibility is 5,040,100 The 4,1 can be replaced with any other two values that add to 5.

Maths
if dropping 2°/hr, then 9 hours ago, it was 2*9 = 18° higher than it is now.

Math
just plug your numbers into the formula, which I'm sure you have. We can check your work . . .

Physics
recall that s(t) = 1/2 at^2 so, solve s(2) = 20 for a, and then use that a to find s(6). Your final answer is s(6)-s(2)

Math
You got x = -3,2 correct, but your final answer is wrong.

Math
correct, since the discriminant b^2-4ac is positive

steve reiny proportion help maths reiny!!!
If y is the illumination c is the candlepower d is the distance, then y = kc/d^2 so, if y is constant, c/d^2 = y/k, which is constant So, you want d such that 8/150^2 = 5/d^2 d^2 = 5*150^2/8 d = 118.56 cm or, using a proportion, you use c2/c1 = d2^2/d1^2 d2/d1 = ?(c2/c1)

math
well, just 1 section out of the 10, so ...

Math
there are 4/5 as many boys as girls, so ...

math
assuming you want an integer value, then 349

Math
counting in seconds, 1/45 - 1/60 = 1/x x = 180 so, it will take 3 minutes

Math
since cos(x) = sin(90-x) sin(x+24) = sin(90-x) x+24 = 90-x 2x = 66 x = 33 check: sin(57) = cos(33) yep

physics
v = at

math
he just multiplied length,width and depth of water added

Trigonometry
this diagram is no trick. Draw a horizontal line: the water draw a vertical line: the lighthouse. Where the vertical line hits the water, call that point B: bottom of tower At the top, label it T. The height of the vertical line is 25 Now somewhere out on the water, label a ...

Algebra
first off, you have no equation -- just an expression (as you might expect, an equation needs an equal sign: =) The only commutative parts I can see here are (3+a+b)3 = 3(3+a+b) now, if you want to talk about commutative addition, or distributive properties, then we can go on ...

Math
correct. a rectangle is rotated about one of its sides.

math-probability
If you want permutations of elements, that implies no duplications, unless there are duplicate elements. If you just wall all possible 4-letter strings of ABCD, then there are 4 choices for each position in the string: 4^4 = 256 If you want all strings of length up to 4, then ...

Math
P(white) = (#whites)/(#marbles) so, how many marbles are white? how many total marbles are there?

Math
what - you can't replace x with 5 and evaluate the result?

Math
8(2 - 1/2) = 12 I suspect a typo.

Math
well, f(x) = 3x +4 so f(-1) = 3(-1)+4 ...

physics
draw the velocity vectors. They form a 3-4-5 right triangle, with the straight-across side of length 3. So, scale it up by a factor of 5/3 to get an equivalent distance triangle. He will have to row 25/3 km along his path, while drifting downstream 20/3 km, landing exactly 5 ...

math
right. So, 1/100 chance of getting it.

math
so, in the numbers from 00-99 how many are 44?

math
20C5 = (20*19*18*17)/(1*2*3*4*5)

Math
(3/4)/9 = 3/4 * 1/9 = 3/36 = ?

math
15/16 as many men, so 16/15 as much time 5/4 as many tables, so 5/4 as much time 9 * 16/15 * 5/4 = 12 days or, using the man-days of labor, there are 16*9/800 man-days/table 1000 tables * 144/800 m-d/table = (1000*144/800 m-d)/(15 men) = 12 days

Math: Probability
P(some hearts) = 1-P(no hearts) = 1 - (39/52)(38/51)(37/50) = 0.58647

Mathematics
You had me with 2*1+1^2 = 3 since A was the only sequence starting with 3.

Mathematics -Integration : to Steve
actually, a bit more examination of your attempt is in order. We have ?[0,?/4] ln(sinx+cosx) - ln(cosx) dx recall from your cosine subtraction formula, that this becomes ?[0,?/4] ln(?2(cos(?/4-x)) - ln(cosx) dx = ?[0,?/4] ln(?2)+ln(cos(?/4-x)) - ln(cosx) dx and with the little...

Mathematics -Integration : to Steve
your idea of splitting the log is wrong, since ln(1+tanx) = ln((cosx+sinx)/cosx) = ln(cosx+sinx) - ln(cosx) but ln(cosx+sinx) ? ln(cosx)+ln(sinx) and you can't integrate those either.

Mathematics -Integration : to Steve
You may not have come across the trick that says that ?[0,a] f(x) dx = ?[0,a] f(a-x) dx It's kind of like integrating from right to left, instead of left to right, but the area is the same. Now you have to include the limits of integration as part of the substitution. x = ...

Mathematics-Integration
try using x = tan? dx = sec^2? d? see where that takes you!

math
well, the discriminant b^2-4ac is negative, so what does that tell you?

math
(g?f)(-5) = g(f(-5)) = g((-5)^2+7) = g(32) = (32+3)/32 = 35/32 or, g(f) = (f+3)/f = (x^2+7+3)/(x^2+7) = (x^2+10)/(x^2+7) so, (g?f)(-5) = (25+10)/(25+7) = 35/32

Algebra
if no duplicates, then 5P2 = 20 if duplicates allowed, then 5^2 = 25

Math
median=10, 6 numbers, so median is between 3rd and 4th .. 9 11 . . mode=11 .. 9 11 11 . range=4 7 8 9 11 11 11

math
(x+y)^2 + (x-y)^2 = x^2+2xy+y^2 + x^2-2xy+y^2 = 2(x^2+y^2) ...

Math
apparently white is + and black is - big black square: -x^3 small black square: -x rectangles: x^2 or 1 See what you can do with that...

math
xa-xb = x(a-b) = 12 a-b = 2*3 = 6 x = x(a-b)/(a-b) = 12/6 = 2

math
a/x = (b/x)(a/b) so, 36/x = 36*6 1/x = 6

math
your copy/paste mangled the 2nd expression, but if it is (a-b)^2 = 64, then (a+b)^2 + (a-b)^2 = a^2+2ab+b^2 + a^2-2ab+b^2 = 2(a^2+b^2) so, 2(a^2+b^2) = 100+64 a^2+b^2 = 82

math
x^2-y^2 = (x-y)(x+y) = ab

maths
if you don't like the law of sines, just study the tan/cot functions. You can easily see that the height h can be found from h cot25° - h cot37° = 57

Calculus
the line from (1,1) to (3,2) is just y-1 = 1/2 (x-1) y = 1/2 x + 1/2

math-limit
some parentheses would also help. Since (?5 + x - ?5)/x = 1, that's probably not what you had in mind. (?(5+x)-?5)/x -> 0/0 so, multiply top and bottom by (?(5+x)+?5) and you end up with ((5+x)-5)/(x(?(5+x)+?5)) see where that takes you...

math
sorry - still not much use...

math
solve for r in (1+r)^15 = 426/258

math
the "mid" or "bi" or "med" indicates the middle, so ...

Science(maths)
(# moles)*(H atoms per molecule)*6.023*10^23

science
when: 100-4.9t^2 = 25t-4.9t^2 where: evaluate either expression at the found value of t.

math
25cm/3m = 25cm/300cm = 25/300 = ?

Science
almost, but no.

Mathematics
nope. It's just that the series converges iff |t| < 1 If you look at the formula, it's the same whether t<1 or t>1. The signs of the numerator and denominator both change, but the result is the same.

Mathematics
If t = (5x+6)/(3x-2) then |t| < 1 if -4 < x < -1/2

Pre-Calculus 12
well, you have to know the basic steps to finding intercepts and asymptotes. Review the examples in your text, and then it's just a matter of figuring out the relevant features of the graph. The intercepts and stuff are just handy landmarks to pinpoint specific places.

Pre-Calculus 12
y = (x-5)(x+2)/(x-2) a fraction is zero when its numerator is zero, right? Damon was just trying to give you the x-intercepts as an aid to graphing the curve. With Damon's input, you have the x-intercepts, the asymptote, and the y-intercept. Unfortunately, the asymptote is...

math
is that 1/z + 3 or 1/(z+3) ? Take a look at https://math.stackexchange.com/questions/1792628/complex-variable-limit-at-infinity

Physics

math
convert all dimensions to yards, and you have v = 6/3 * 160/3 * 1/4 = 80/3 yd^3

Physics
Ah. I see I forgot to include the initial height of 2 meters. I assume you discovered that, and made the required adjustment to the equation.

Physics
recall that the ball follows the path y = tan? x - g/(2 (vcos?)^2) x^2 plugging in your numbers, then, we need to solve tan39° * 8 - 4.9/(v cos39°)^2 * 64 = 3.04 6.478 - 519.243/v^2 = 3.05 v = 12.307 m/s

Physics
Hmmm. I also get 4.36 We forgot the ball's initial downward velocity of 5sin15° = -1.294 m/s. Unfortunately, that makes it worse, since it falls faster. Now we have to find t such that -1.294t - 4.9t^2 = -4 t = 0.781 and that means the ball only goes 5cos15° * 0....

Physics
just realize that when the ball leaves the ramp, its horizontal speed remains constant at 5cos15° How long does it take to fall 4 meters? 4.9t^2 = 4 use that time to see how far the ball travels horizontally.

Math
cos2x+sinx = 0 1 - 2sin^2x + sinx = 0 (2sinx+1)(sinx-1) = 0 sinx = -1/2 in QIII,IV sinx = 1 I expect you can take it from there.

Math
just remember to use the product rule. Also, dx/dx = 1 x^2y^2-3xy+4xy^3=5 2xy^2+2x^2yy' - 3y-3xy' + 4y^3+12xy^2y' = 0 y'(2x^2y-3x+12xy^2) = -2xy^2+3y-4y^3 y' = -2xy^2+3y-4y^3 --------------------- 2x^2y-3x+12xy^2

math
yes.

ok ok I see that you are unwilling to confirm what you can online. The simple polynomial divisions can indeed be done at either site. #1 is wrong #2 area is length*width so, length = area/width x^3 - 7x + 6 = (x-6)(x-1) try again. #3 makes no sense to me. How did you arrive at...

you can confirm your answers by typing in your expressions at wolframalpha.com be sure to use enough parentheses so that it interprets your input correctly. Or, you can see all the details of the divisions at http://calc101.com/webMathematica/long-divide.jsp

Algebra 1 B Unit 6: Rational Expressions and Func
well, (-18x^3+17x+6) = -(3x+2)(6x^2-4x-3) so, what do you think?

algebra 1
Think about it, and you will see that your answer is way off. At the very least, the fact that the question is asking about permutations should tip you off. There are 8 ways to pick the first position. For each of those 8 choices, there are 7 ways to pick the next one. ...

Math
at any rate, 60 = 12*5, so it will take 12 time-units.

math
surely you must have some ideas on these. It's not rocket surgery, ya know ...

Math
they travel for 1.5 hours, at a combined rate of 120 mi/hr, so ...

math
5000*(1+.085)^4*(1+.0925)^3

math
the area scales by the square of the linear factor. So, 160 is 4 times the model's area.

Algebra 2
May is the 5th month. So, f(4)=4.5sin(4?/6)+11.8 = 4.6*?3/2 + 11.8 = 15.784 and it must be a strange location, since the minimum temperature occurs in October . . .

@oops on (iii)
sorry. I figured the distance in meters, not the velocity in m/s. See whether you can fix my mistake.

physic, please correct is am wrong
(i) one revolution is 2?radians, so ? = 200*2? = 400? radians (ii)angular velocity is measured in radians/second, so ? = ?/t = 400?rad/24s = 50?/3 rad/s (iii)v = r?t v = 1/4 * 50?/3 * 24 = 100? m/s or, since the circumference is ?d = ?/2 meters per revolution, v = 200rev/s...

math 11
A = x(50-x)

physic
any information on the directions?

math
If you mean 2 2/5 - 1 5/9 then that would go 12/5 - 14/9 and using an LCD of 45, 108/45 - 70/45 38/45

maths
if you draw a side view, you can easily see that the slant height s is 13. So, the area is a = ?r^2 + ?rs

science

Pre-Calculus
sin ?/6 = 1/2, so that is your reference angle In QIII, x = ?+?/6 = 7?/6 so, 2x = 7?/3 = 2?+?/3, in QI So, tan2x = ?3

Maths
since corresponding angles are congruent, we have 3y+30 = 10y-40 4x-100 = 3x-30 Now just crank it out.

Math
depends on which angle is at the vertex. If Y is at the top, then 2y+y+2y = 180 Otherwise, y+2y+y = 180

math
you should recognize a scaled-up 3-4-5 right triangle. So, the diagonal is 100 ft. The rest is a cinch, right?

maths
I will assume that A and ? are the same Draw a triangle. The legs are a and b, so the hypotenuse is ?(a^2+b^2) Now you know that sec? = 1/cos? = ?(a^2+b^2)/b I expect you can handle the rest of the algebra...

Math
you need a denominator which is the least common multiple of the given denominators. For example, if you have 2/3 and 3/5, the LCD is 3*5 So, these work the same way. #1: 2x^2 #2: 7z #3: 5(x+2) #4: (m+n)(m-n)