# Posts by STEVE

Total # Posts: 52,055

**Math**

uh, 51 ?

**Math**

50

**Math**

well, every digit except the 8 must be 9, right?

**Math**

After x months they will be equal if 310-15x = 90+15x Now, try to make some effort on the other problems, ok? The idea of this site is not to do your homework assignments. We can help, but expect you to bring something to the table, especially when several problems are similar...

**English**

#1 not #2,3 are both ok.

**English**

yes, but I've never heard, nor would I say #3 That phrase is usually reserved for nouns with superlative adjectives, as in your other example. Such as ... far and away the tallest mountain the best student the unluckiest man on earth

**Calculus**

Because sin^2? = 1-cos^2?, the logical choice is x = 2sin? 4-x^2 = 4-4sin^2? = 4cos^2? ?(4-x^2) = 2cos? dx = 2cos? d? Now your integral becomes ?3x?(4-x^2) dx = ?3*2sin? * 2cos? 2cos? d? = 24?cos^2? sin? d? Now let u = cos? and the integral is just = -24?u^2 du = -24(1/3 u^3...

**Math**

so, what are the even multiples of 13, less than 100?

**geometry**

OK - I may have misread it again, assuming that the base of the triangle is parallel to the x-axis. This is much trickier than it looks, unless the size of the triangle is somehow determined.

**geometry**

Nah - that's just too complicated. Take a look at an equilateral triangle, and slice off the top of it. (That's the piece of the x-axis between the sides of the triangle.) That small cap of the big triangle is also an equilateral triangle, and always has the same base ...

**geometry**

so, two of its vertices are (-h,-k) and (1+h,-k) Thus, the length of the base is (2h+1) That means the altitude is (1/2 + h)?3, making its coordinates (3/2, k+(1/2 + h)?3) See whether you can work out the relationship between h and k, and thus the equation for the path ...

**math**

those sure look like primes to me

**Algebra 2**

A: you have the starting value, and the decay factor, so v(t) = 250 * 0.98^t where t is the years since 2000 B: just plug in t=11 C: all pure exponentials look just the same, up to scaling.

**Calculus**

well, you are still vague. I assume you mean to revolve the triangle around the y-axis. So, revolve the small triangle. The volume is v = ?[1,2] 2?rh dx where r = x and h = y-1 = 2x-2 v = ?[1,2] 2?x(2x-2) dx = 10?/3 to verify, do it again with discs of thickness dy, where v...

**Calculus**

revolve around what? And why reflect it as well? I will say that the line from (1,1) to (2,3) is y = 2x-1 You can use that when doing the volume of a shell, which is v = 2?rh dx

**Mathematics-Integration**

Hmmm. That's a possibility. You might also try doing integration by parts twice to yield the recursive sequence derived here: https://math.stackexchange.com/questions/416162/a-recursive-formula-for-a-n-int-0-pi-2-sin2nxdx-namely-a-n

**maths**

Hmmm. That's not what I get. (1+(1/2.7176022)) = 1.36797 1.36797^3.7176022 = 2.20537 (2000/1999)^1999 = 2.7176022 close, but not nearly correct. (1+1/e)^(e+1) = 3.20527 I get a solution at x = -2000 (1+(1/-2000))^(-2000+1) = 2.7176022

**Algebra 1B**

enter your polynomials here and see all the details http://calc101.com/webMathematica/long-divide.jsp

**Maths**

or, doubling the first equation, 2x+4y = 18 2x-4y = 2 now just add the two equations, and y goes away...

**physics**

(200-11.6)/14.9 = ?

**Mathematics-Integration**

how about this: x = sin? ?(1-x^2) = cos? dx = cos? d? so, d? = dx/cos? = dx/?(1-x^2) Then the integrand is ln((2sin?+3)cos?) d? Unfortunately, that doesn't integrate any better. We can't use the same trick from before, since we don't have a definite integral. If we...

**Math**

well 10 is 5 times 2, so the distance will also be 5 times as big x/25 = 10/2

**MATHS**

see related questions below

**Geometry**

fast!

**math**

This is clearly an exercise in completing the square. 3x^2 - 6x - 2 3(x^2-2x) - 2 now add and subtract 3, leaving the value unchanged: 3(x^2-2x+1) - 2 - 3 3(x-1)^2 - 5

**Algebra 2 read plz**

what you need to do is recognize the special angles with known trig values. ?/6 is one of those angles. sin(5?/6) = sin(?/6) = 1/2 the real question is: why did you calculate (5-pi)/6 instead of just doing 5pi/6 ? If your function is f(x)=15.3sin(?x6)+44.1 propagating your ...

**Algebra 2**

stuck how? Just replace x with 5 and evaluate! too bad you could not be bothered to show us what you did. f(x) = 15.3sin(?x/6)+44.1 f(5) = 15.3sin(5?/6)+44.1 = 15.3(1/2)+44.1 ...

**Maths**

well, distance = speed * time, so 70x + 80*0.5(x+3) = 460 ...

**maths**

w*4w = 1024 w^2 = 256 ...

**Maths**

naturally the number of steps will not be measured in meters. Each 3 steps, she advances 0.5 meters (0.5+0.5-0.5) So, after 2*3*19 = 114 steps, she has advanced 19 meters. On the 116th step she has gone the last meter, and does not need to step back again.

**math**

well, surely that is 0.125 * 13650 = ?

**math**

even if you fix the mismatched parentheses, I don't see an easy algebraic way to solve this. You'd better use a graphical or numeric method. What tools do you have?

**Math**

I'd say it depends on the set. Do you have some further context?

**math**

c = ks/?m plugging your numbers, c = 55k/4 If you have an actual value for c, then you can find k.

**math- ouch!**

I got that wrong. The angles are not in the same ratio as the sides. The sines of the angles are. So, you can still draw the triangle, but then you need to circumscribe it. You can easily find online the relationship between the radius and the sides. In this case, with sides ...

**Math**

so, draw the circle. The central angles subtended by the sides will be 100,120,140 degrees. It is easy to construct a 120° angle, so you can draw the side of length 6x first. Then from its ends draw arcs of radius 5x and 7x. They will intersect at the third vertex.

**physics**

draw the velocity vectors. The resultant speed has magnitude v=?(2^2+8^2) It drifts downstream by an angle ? such that tan? = 2/8 without knowing the distance across the river, it's hard to say how far downstream it will have drifted. Also, you don't define exactly ...

**Science**

mass(g) = density(g/cm^3) * volume(cm^3)

**Algebra**

(x + 1/x)^2 = x^2 + 2 + 1/x^2 so, x^2 + 1/x^2 = a^2-2 (x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3 so, x^3 + 1/x^3 = a^3 - 3(x + 1/x) = a^3-3a

**Algebra**

ah! that makes all the difference! Since the center line is at y = -1, the distance to the extremes is the amplitude. So, the amplitude is 4 and the vertical shift is -1. That means y = 4sin(b(x-c))-1 since sin(0) = 0, that means y+1=0 at x=6, so the horizontal shift is 6 the ...

**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.

**Grade 12 Trigonometry**

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

**Grade 12 Trigonometry**

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