# Posts by steve

Total # Posts: 52,268

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)

Math
this is a perfect square. (x-y)^2 = x^2-2xy+y^2 Now just substitute in x = 3b y = 4a

Geometry
depends on which direction the plane is heading. The speed could be anywhere between 250 and 350 mph.

ctpd
if it's a circular sector, then it's 2r+s where s is the arc length subtended.

Maths
assuming you mean whole numbers, 1+49 = 50 the smallest sum is 7+7 = 14 this is just the same as noting that the minimum perimeter of a rectangle with a given area is when it's a square.

Algebra
you'll have to do the drawings yourself. Not too hard, I expect. For scaling the figure, just multiply all the coordinates by the scale factor (2 or 1/2) and plot the new points. for scaling by 2, then (1,1) -> (2,2) (-3,1) -> (-6,2) and so on. No algebra involved at...

Algebra
well, 5^(2x) = (5^2)^x = 25^x so, what do you think?

math
----1 = 1 draw the number line place a closed circle (dot) at 1 shade to the left

Algebra
I assume you mean x/(x-2) + (x-1)/(x+1) = -1 using a common denominator of (x-2)(x+1), we have x(x+1) + (x-1)(x-2) = -1(x-2)(x+1) 3x(x-1) = 0 x = 0 or 1

Math pls
plot the two points. The slope is the change in y divided by the change in x. y changes from 2 to -2 x changes from 6 to 4 so, the slope is (-2-2)/(4-6) = -4/-2 = 2

the slope is (5+2)/(-3+4) = 7, not 1/7 so, using the point-slope form, y+2 = 7(x+4) work with that. 4 1/6 = 25/6 As written, none matches. ?64 = 8

#1 Nope. 2*5-3 ? -7 #2 Nope. 1 ? -4(7)+3 In fact, I suspect a typo. None of the choices works.

Maths
did this for you last night. see related questions below.

Algebra 2
since the lowest value of cos(x) is -1. the lowest temperature is 3.8(-1)+2.2 = -1.6

Math
a negative times a negative is positive. So, (-7)(-12) = 7*12 I'm sure you can manage that ...

math
If the shadow length is s, and the height is h, then h = ks That means that h/s = k, a constant. So, you want s such that 6/15 = 20/s

math

maths
draw a diagram. It should be clear that tan? = 65/42

Math
what, no cubits, chains or roods?

math - eh?
There seems to be some context missing. You want to clarify things a bit?

Math
heck - just set the two equal: -x^2+9 = 3/x x^3-9x+3 = 0 cubics usually require a numeric or graphical method. I assume you have studied some of those. http://www.wolframalpha.com/input/?i=x%5E3-9x%2B3%3D0

Math
clearly t= 7508.4 i think is not a reasonable answer. 7500 years? 300 e^(5k) = 1500 e^(5k) = 5 5k = ln5 k = ln5/5 = 0.32 so, y(t) = 300 e^(0.32t) y(10) = 300 e^3.2 = 7360 300 e^(0.32t) = 12500 e^(0.32t) = 41.67 0.32t = ln 41.67 = 3.73 t = 3.73/0.32 = 11.65

Math
find k using 300 e^(5k) = 1500 use that k with t=10 finally, use that k to find t when 300 e^(kt) = 12500

math
50lb = 22.73kg so, you will need 1.5*22.73 = 34.1 mg . . .

science
150 mi/hr * 1609 m/mi * 1hr/3600s = 67 m/s

Maths - Matrices
oops - misspoke: A-1 = 1/2 (1 2) (1 4) So, X = (0 0) (4 4) see http://www.wolframalpha.com/input/?i=(inverse+%7B%7B4,-2%7D,%7B-1,1%7D%7D)*(2%7B%7B-4,-4%7D,%7B2,2%7D%7D)

Maths - Matrices
If you write this as AX = B then X = A-1B A-1 = (1 1) (1 2) now just crank it out.

Science
of what?

Maths
630 = 2^4•3•13+6 940 = 2^3•3^2•13+4 so, your number is 2^3•3•13 = 312 630 = 2*312+6 940 = 3*312+4

math
no, (a) has a negative slope. Rearrange things into slope-intercept form and you get 5x + y = 50 y = -5x+50 slope = -5, intercept=50 do that for the others, and it will then be clear which is what you want.

math
first step: which have positive slopes?

Algebra
you want to try that without TeX? x^n - 1/x^n = p(x - 1/x) ... where does z come in?

Algebra

Algebra
xf(x) + f(1-x) = x(x-1)(x+1) (1-x)f(1-x) + f(1-(1-x)) = (1-x)((1-x)-1)(1-x+1) multiply the first by (1-x): x(1-x)f(x) + (1-x)f(1-x) = x(x-1)(x+1)(1-x) f(x) + (1-x)f(1-x) = (1-x)(-x)(2-x) subtract to get (x(1-x)-1)f(x) = (x(x-1)(x+1)(1-x))-((1-x)(-x)(2-x)) f(x) = -x(1-x)(x^2-x+...

Algebra
If y=f(x) maps a value of x to a value of y, then look at the first line. It says f(4) = -2 f(4) = 2 it cannot be both. So, (A) is not a function.

Algebra
if a value of x maps to two different y's, it is not a function. So, look for a line with a repeated 1st element.

Algebra
ya think? 3f(1/x)+(2f(x)/x)=x^2 now, if x = -2, 3f(-1/2) + 2f(-2)/-2 = 4 3f(-1/2) - f(-2) = 4 if x = -1/2, 3f(-2)+2f(-1/2)/(-1/2) = 1/4 -4f(-1/2) + 3f(-2) = 1/4 f(-2) = 67/20 ------------------------ or, we have ------------------------ 3f(1/x)+2(1/x)f(x) = x^2 3f(x) + 2xf(1/x...

physics
conserve momentum: 3*5 + 4*0 = 3*0 + 4v

Math
The number of fish in a tank decreases by x% each year. Given that the number of fish halves in 8 years, (1-x/100)^t = (1/2)^(t/8) t log(1-x/100) = t/8 log(1/2) log(1-x/100) = log(2^(-1/8)) 1 - x/100 = 2^(-1/8) x/100 = 1 - 2^(-1/8) x = 100(1 - 2^(-1/8)) = 8.3

Math Help TIMED!
but yes, it is A.

Algebra 2
not quite... 5?8^(4x) = 376 8^(4x) = 75.2 4x log8 = log75.2 x = log75.2/(4log8) or, since 4log8 = log4096, x = log409675.2

math
you are correct. The question is, why did you use that value? Just think it through, and you should see why it is correct.

Chemistry
start by recalling that 1 mole occupies 22.4L (dm^3) at STP Then use the fact that PV=kT since all the items are given in the same units, the formula works just fine. Just find the one which matches the standard values.

trigonometry
is the building uphill or downhill from the post? If the building is downhill from the post, at a horizontal distance of x, then let a = vertical distance from the base of the building to the base of the post x = horizontal distance between building and post h = height of post...

trigonometry
Draw a diagram. Let a = distance from A to the base of the tower b = distance from B to the base of the tower h = height of the tower Then we have b^2 = a^2+50^2 h/b = tan18° h/a = tan30° Now you can find a,b and thus h.

Science