# Posts by steve

Total # Posts: 51,184

Chemistry
see related questions below

Science
(30m/s)/(60s) = 0.5 m/s^2

physics
The resistance of the parallel component is 30R/(R+30) If R' is the equivalent resistance of the circuit, R' = 1/(1/30 + 1/R) + 6 = 36(R+5)/(R+30) The current through the 6? resistor is 120/R' = (10R+300)/(3R+15) The voltage drop across R is [30R/(R+30)]/[36(R+5)/(...

Math
T13/T6 = ar^12/ar^5 = r^7 (3/16)/24 = 1/128 = (1/2)^7 so, ...

maths
506 base 6 does not exist, since base 6 numbers consist only of the digits 0-5.

Math
use the law of sines to show that the base is divided into equal lengths. Then that will imply that the angles at the base of the altitude are also equal, so they are both 90 degrees.

math
50 * (1788/3725)

algebra
just solve the equation x^2 + (1/2 x + 11)^2 = (2x+1)^2 x = 8

college algebra
C(x) is just a parabola. Its minimum value is at the vertex, where x = -b/2a = 7

math
90 years is 3 half-lives. That means that 1/8 of the original amount remains. So, the 1 mg that has decayed represents 7/8 of the original amount. So, starting out at 8/7 g, 1/7 g = 14.27mg remains. ---------------------------------- after 4 half-lives, 1/16 of the original ...

college algebra
Sorry, that -3072 means its initial height (at t=0) is 3072 feet below ground.

Math
since |y| > y, y < 0, so |y| = -y x>|y|, so x+y>0 ==> |x+y| = x+y |x+y|-|x|+|y| = x+y-x-y = 0

Math
4^x = 6 2^x = ?4^x = ?6 8^x = (2*4)^x = 2^x * 4^x = 6?6 or, 8^x = (4^(3/2))^x = (4^x)^(3/2) = 6^(3/2) = 6?6

Math
(A+B)/2 = A + B/10 A/2 + B/2 = A + B/10 A/2 = 2/5 B A = 4/5 B A.B = 4.5

Calculus
2?r^2 + 2?rh = 20 so, h = 10/?r - r the volume is v = ?r^2h = ?r^2(10/?r - r) = 10r-?r^3 so, find r when dv/dr=0

Math
If the walk has width w, then since the parkland occupies 80% of the area, (30-2w)(5-2w) = 0.80*30*5 w = 0.4396m

Calculus
h+4s = 14 v = hs^2 = (14-4s)s^2 so find s when dv/ds = 0

Physics
since V is constant, and PV=kT, P/T = k/V is constant. So, you want P such that P/(273+25) = 7/(273+15)

math
because 1/c = c^(-1)

Math
check your prior post in the related questions below ...

consider f'(1) where f(x) = ?x where you should have written the limit as (?(1+h) - ?1)/h

Pre calculus
p(x) = (x-11i)(x+11i) = x^2 - (11i)^2 = x^2+121

Physics
distance = speed * time so, time = distance/speed

22.50 * 1.15 = 25.875

well, how did you figure it out?

Math
well, the base has area 132/11 = 12 so ...

Calculus
(a) c = 13(4x+y+4x+y) + 5(3y) = 112x+41y (c) xy=9, so y=9/x, and c(x) = 112x + 369/x now find x where dc/dx = 0

Math
huh? Just solve (75+x)(225-5x) = 16000 x = 5 so, ...

Precalculus
a) ok b) The average cost is the cost per unit, or c?(x) = c(x)/x So, c?(x) = 0.02x + 0.5 + 40/x The marginal average cost is thus c?'(x) = 0.02 - 40/x^2

Algebra - rats
I see other typos. The final answer is correct, but let me just do it right: Since the vertex and focus both lie on the line x = -2, the axis of symmetry is vertical, meaning the equation is (x-h)^2 = 4p(y-k) Since the focus above the vertex, p is positive. You know that the ...

Algebra - typo
As you noticed, the axis is vertical, on he line x = -2

Algebra
Since the vertex and focus both lie on the line x = =2, the axis of symmetry is horizontal, meaning the equation is (x-h)^2 = 4p(y-k) Since the focus above the vertex, p is positive. You know that the parabola x^2 = 4py has the vertex at a distance p from the focus. Here, that...

Math, Algebra
If you drop an altitude to the center of the base, then looking from the side you have a right triangle with legs 4 and 22. So, the hypotenuse of the triangle (the slant height of the pyramid, and the altitude of each triangular face) is h = ?(4^2+22^2) = ?500 = 10?5 That ...

MAth help connexus
c - review the section on functions, esp. the vertical line test.

math - trigonometry
one walks on a heading, not a bearing. a) Note that angle Q is 90 degrees, so you have a right triangle. Easy... b) This is the correct use of "bearing." If the bearing is x, then tan(x+25) = 18.7/11.4 A diagram will show you why.

Math Measurment unit test
1. A = bh 2. A = bh/2, so looks good.

math
2/s = 1/4 + 1/5

math
well, the volume of water flowing in every second is 1.2cm * 350cm/s = 420 cm^3/s Now divide the volume of the tank by the inflow rate to get the time (in seconds)

calculus
The 13 is just a scale factor, and has no bearing. You know that ? ? 1/10^n = 0.11111111 = 1/9 n=1

Maths
If the 5th is 4 times the 3rd, then r=2 a+ar = -4 a+2a = -4 a = -4/3 now take it from there.

math
Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

math
a?

math
again c? aa

math

math
before: 00AF

math
before: AFc after: cAF

math
c-bar ̅

Math
well, the last digit is 5 start there.

Physical science
2Na + 2H2O = 2NaOH + H2 now just multiply everything by 3/2

Math
y = x-12

Math
write them as 4x-6y = -48 x+6y = 18 add them together and you get 5x = -30 ...

chem
assuming a constant temperature, PV = kT is constant. So, you want P such that P*2.94 = 0.988*3.35

Math
y = 1+2x 3x+(1+2x) = 11 ...

chem
assuming a constant temperature, PV = kT is constant. So, with 5/4 the pressure, you get 4/5 the volume

Math
square both sides write cos^2 = 1-sin^2 Then you have a quadratic in sinx

physic
how long does it take to fall 160m? The horizontal speed does not affect that. 4.9t^2 = 160 Now, the horizontal speed does not change, so the body travels 20t meters

Math1
You want t years, where 2100(0.95)^t = 600 0.95^t = 2/7 t = log(2/7)/log(0.95) = 24.42

Pre-cac
well, even without completing the square, you know the vertex is at x = -b/2a = 3/2a So, a(3/(2a))^2 - 3(3/(2a)) + 5 = 15 5 - 9/(4a) = 15 a = -9/40 But, in the spirit of completing the square, ax^2-3x+5 = a(x^2 - 3/a) + 5 = a(x^2 - 3/a + (3/2a)^2) + 5 - a(3/2a)^2 = a(x - 3/2a...

Maths
4000*1.015^2 = 4120.90

Math
a. correct b. The volume with the cuts made and the sides folded up is v = (12-2x)(18-2x)x = 4x^3-60x^2+216x If you have calculus, then dv/dx = 12(x^2-10x+18) dv/dx=0 when x=5-?7 ? 2.35 If no calculus, then a graphical or numeric method is needed.

Math
(x,y)-> (x-4,y+1) is correct. But you still botched it: (-3,1) -> (-3-4,1+1) = (-7,2) + means ADD: 1+1 = 2, not 0! same for subtracting: -3-4 = -7 -3+4 = 1 -1 is just plain bogus, man.

Math
left 4 means subtract. as you said, up 1 means add. But even if your translation were correct, you did not do the math right 1+1 ? -2 Try again. You're getting the +'s and -'s mixed up some.

Math
naturally, we can see no graphs here. What are your choices for the others?

Math
(a) trés simples, non? (b) 2x cosy - x^2 siny y' - cosy y' = 0 y' = (2x cosy)/(cosy + x^2 siny) So, at (0,?), y'=0 (c) so, the tangent is a horizontal line, and the normal is a vertical line through (0,?).

Pre-calculus
I will assume a typo, and work with x^2+10x+4y+9 = 0 That may not be what you had in mind, but you can follow the method using your corrected equation. x^2+10x+4y+9 = 0 4y = -x^2-10x-9 y = -1/4 x^2 - 5/2 x - 9/4

Math 120
6+2 + 2 (conversion+safety) 6+1 + 3 6+2+2 (two safeties) 3+3+2+2 2+2+2+2+2

math
the nice thing about Ø is that Ø-1 = 1/Ø

math
sinx = cos^2x sinx = 1-sin^2x sin^2x + sinx - 1 = 0 now solve for sinx, and pick the positive solution.

Calculus - Newton's Method
well, f'(x) = 1-sinx So plug that into Newton's method. Here is a nice web site: http://keisan.casio.com/exec/system/1244946907

calculus
you will need to use integration by parts, twice. 1st step: u = t^2 dv=sin(2t) dt du = 2t dt v = -1/2 cos(2t) That makes the first integration by parts: ?u dv = uv - ?v du ?t^2 sin(2t) dt = -1/2 t^2 cos(2t) + ?t cos(2t) dt Then repeat, letting u = t dv = cos(2t) dt You should ...

Calculus
I suspect a typo, since what you have written is just f(x) = x/(x+x^2) = 1/(1+x) f' = -1/(1+x)^2 f" = 2/(1+x)^3 Anyway, fix that, find f", and recall that f"=0 means an inflection point f" > 0 means concave up f" < 0 means concave down

calculus
use integration by parts. That is just the product rule in reverse. d(uv) = u dv + v du u dv = d(uv) - v du ?u dv = ?d(uv) - ?v du ?u dv = uv - ?v du So, here we just let u = (lnx)^2 dv = dx du = 2lnx * 1/x dx = (2lnx)/x v = x ?(lnx)^2 dx = x(lnx)^2 - ?2lnx dx Now repeat, this...

math
x >= 15000/12 = 1250 So, consider how long a ride might take, and how long the park is open each day.

math
5 divides evenly any multiple of 5. Not sure what you mean by "5 divide into equaly" [sic]

Help please I am lost, algebra
if g(14) = -6, then that means you have the point (14,-6) on the graph. Using the point-slope form, then, you get y+6 = -5/4 (x-14) Now massage that to the slope-intercept form: y+6 = -5/14 x + 35/2 y = -5/14 x + 23/2

Math
The first model is linear because the changes are constant. In fact, y = x/2 - 1 For the second, check the differences: 1st: 5.1, 20.4, 81.6, 326.4 2nd: 15.3, 61.2, 244.8 If t were quadratic, the 2nd differences would be constant. Since they are also growing rapidly, you ...

2700x+21000 = 83400 just solve for x 2010 is 7 years after 2003, so just plug in x=7 for P(x)

Physics
Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

Physics
Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

Math
p(red) = (#red)/(#total)

Math
start with 7.2 Since 10^0, that is just 7.2x10^0 Now, lowering the power of 10 moves the decimal place to the left, so 7.2x10^0 = 7.2 7.2x10^-1 = 0.72 7.2x10^-2 = 0.072 and so on The number of leading zeroes after the decimal point is 1 less than the negative power of 10.

Calculus
every polynomial is continuous and differentiable everywhere. At the midpoint, x = (a+b)/2 f'(x) = 2?x+? So, show that f'((a+b)/2) = (f(b)-f(a)/(b-a)

calculus
One way: Theorem of Pappas If the edge goes from (0,0) to (0,1), then the center is at (?3/2,?3/2). The area of the hexagon is 3?3/2. The radius of rotation is ?3/2, so its path has length ??3. So, the volume of the solid is ??3 * 3?3/2 = 9?/2 Another way: calculus. Using ...

Maths
I worked it out, and also got a 4th-degree equation in x. So what? Just solve it for x using whatever method works best. I did get z=x rather than z = -2x, but maybe I made a mistake.

math
A10-A7 = 3d = 15 Now you know d, so you can get a, and then the terms.

Math1
2^24 - 1

algebra 1
well, did you check it? -16*36 + 46*6 + 6 = -294 So, stop guessing and do the math! h = -2(8t^2-23t-3) = -2(8t+1)(t-3) So now what do you think?

#1 ?[0,4] arcsin(x/4) dx = 2?-4 To do this one, let x = 4sin(u) arcsin(x/4) = arcsin(sin(u)) = u dx = 4cos(u) du Now you have ?[0,4] 4u cos(u) du That you can easily do using integration by parts. Note that in changing variables, ?[0,4] f(x) dx = ?[0,?/2] g(u) du #2 Using ...

Math
x(?/4) = ?2 y(?/4) = 1 dy/dx = (dy/dt)/(dx/dt) = sec^2(t)/(sect tant) = sect/tant = csc t so at t=?/4, y' = ?2 and the tangent line is y-1 = ?2 (x-?2) y = ?2 x - 1 Note that x^2 = 1+y^2. So, to check the graphs, see http://www.wolframalpha.com/input/?i=plot+x%5E2-y%5E2%3D1...

Precalculus
|x| is a tricky one, since it changes at x=0. Consider it a |x| = ?x^2. Then, using the chain rule, d/dx ?x^2 = 2x/(2?(x^2)) = x/|x| Note that this correctly captures the change of slope at x=0. d/dx[5(x^2 + 3|x|)] = 5(2x + 3x/|x|) Also, the function is not differentiable at x=0.

Math
you don't say whether the radius, diameter, circumference is 28. Anyway, just plug in the formula: A = ?r^2

maths
remember the 3-4-5 right triangle? Just scale it up by 2.

math real and complex numbers lesson
(7+3,-9+5) = (10,-4)

Maths
x-28 = 42-x

math
It is true that Anna is not 1000mm taller, but in this case, the "times" indicates a multiplicative factor, and almost no one would interpret it as you have indicated.

physics/maths help damon or steve or scott
s(t) = s0 + v0t + a/2 t^2 so, s0 + 6v0 + 18a = 246 s0 + 9v0 + 81/2 a = 246+69 Solve for v0

trigonometry
draw a diagram, and you can figure angle T. Then, use the law of sines.

trigonometry
use the law of sines.

math
x-y = 1/10 y = 4/7 x - 4/7 = 1/20 x = 4/7 + 1/10 = ?

Maths
P = R-C break-even when R=C (P=0)

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