Tuesday
July 29, 2014

Posts by Steve


Total # Posts: 24,017

Math
Draw the triangle. One leg is 1, and the hypotenuse is 4. So, the other leg is √15 the cosine of the angle is √15/4

Differential Equations
(x^2+1)dx + x^2y^2dy=0 x^2y^2 dy = -(x^2+1) dx y^2 dy = -(x^2+1)/x^2 dx 1/3 y^3 = -x + 1/x + C ...

Algebra
log0.900.6 - log0.850.6 = 1.7 or, since you probably don't have a button for log0.9x, log(0.6)/log(0.9) - log(0.6)/log(0.85) or even log(0.6)(1/log(0.9)-1/log(0.85))

Geometry
I didn't see where the solid was a pyramid. Usually a prism is a right prism, so the v = (area of base)*height

science
Name it analogously with table salt, which is Sodium Chloride. That -ide suffix indicates that there are just the two elements. Ever heard of the ointment Zinc Oxide? Same deal.

math
the x-coordinate is halfway between the two end x-values: (-3 + -8)/2 = -11/2 Do the y-value the same way.

math
after n cuts, the thickness is 0.1 * 2^n mm. so, evaluate when n=30.

algebra
just solve for t when the height is zero: -16t^2 + 112t + 128 = 0 just a normal quadratic equation.

Alegbra
how many times is this going to be posted? Review the point-slope form of a line: a line with slope m, through the point (h,k) has the equation y-k = m(x-h) So, look at the equation above, and read off m and (h,k)

Alegbra
The point is clearly (-5,4) Now since the slope is 3/2, a second point is up 3 and right 2.

Trigonometry
just figure s(5)-s(1)

physics
The tank weighs the same, regardless of its contents. Figure the volume of material, and multiply that by the material's density. :-)

physics
figure the volume: .18 * .78 * .44 m^3 now multiply that by the density, in kg/m^3

Pre algebra
(5*62 + 50)/6

math
let the numbers be x-1,x,x+1 The sum is 3x = 39 so, the middle number is 13

Math
log740353607 = log40353607/log7 = 9 so, 40353607 = 7^9

math
x = 2^(1/2) since log √x = 1/2 log x, log x = -2 x = 10^-2 lnx = ln(e*(x+1)) x = e*(x+1) ...

Physic
1W = 1J/s 1 kwh = 1000 Wh = 1000J/s * 3600s/h

Math
(9+1)/(9+1+6)

physics
750 + 750 + 625

Calculus 2
actually, the integral isn't so bad if you recognize that the integrand is just x^4 + 1/x^4 http://www.wolframalpha.com/input/?i=arc+length+of+x^5%2F10%2B1%2F%286x^3%29+from+3+to+6

Physics
well, you have the mass of 1 liter. So, what is the mass of 2 liters? Now just look up the conversion factor for kg to lb. A handy site is http://www.onlineconversion.com/weight_common.htm On the home page there, you can find many other conversion calculators.

mqr/117
rewrite f(x) as 5(x + 3/10)^2 + 11/20 and then you can just read off the coordinates of the vertex.

Math
you want the set of elements common to your two sets. So, which numbers are in both lists?

Math
The number of people taking something is 23+32-9 So, that leaves how many taking nothing?

Alegbra
They are perpendicular if the product of their slopes is -1. So, is (-7)(-7) = -1 ?

Math
think of the calendar as units of 24 hours So, 5:44 am on day 10 is the same as 29:44 on day 9. So, subtract 14 from 29 and you have 15:44 of the previous day, or 3:44 pm. Or, you could just subtract 24 hours, giving you 5:44 am of the previous day. But you only wanted to subt...

Alegbra
If you mean y = -3/2 (x+5) you can see easily that y=0 when x = -5. So, that's where the graph crosses the x-axis. Now, since the slope -s -3/2, just mark a second point, 3 down and 2 to the right from there. Join those two points with a line, and that's the graph.

math
I'd say that would be 17+3=20 assuming the ladder is laid vertically against the wall -- an unusual placement, to be sure.

math
the grade would be 15/5280 = 0.284%

Math 221
as with most problems involving fractions, work first with the denominators. They cannot be added or subtracted unless they all have the same denominator. 5/12 + 7/9 The GCD(12,9) = 36. So, what you have is 15/36 + 28/36 Now all the "units" are the same. Just as you ...

maths - oops
Err, I mean one leg=2. So half the chord has length √21

maths
Draw a diagram, including the radii to the ends of the chord. Draw the radius perpendicular to the chord. You now have two right triangles with one leg=1 and hypotenuse=5. Half the length of the chord is √24.

Algebra II
no, since 2x^2+x-15 = (2x-5)(x+3) Just multiply both sides by (2x-5)(x+3) The thing to watch out for is to be sure to note that 5/2 and -3 must be excluded from the domain.

mat/117
you want where P < 0 P(x) = 750x(20-x) You know that P=0 when x=0 or 20 Since the graph is a parabola opening downward, P>0 between the roots. So, P<0 if x>20

mat/117
translating upward just means add 11 to g.

mat/117
f(x) = -5(x - 3/10) + 29/20 If that doesn't tell you the answer, review your forms of quadratics.

mat/117
(fg)(x) = f(x)*g(x) = (-6x-1)(4x^2)

mat/117
(f+g)(x) = f(x) + g(x) so, just add the two polynomials together.

phi 208
life is like a simile.

Math
ok. now what?

math
Surely this treated in your text. You want A/(v-1) + B/(v+2) = 1/(v-1)(v+2) A(v+2) + B(v-1) = 1 Av + 2A + Bv - B = 1 (A+B)v + (2A-B) = 0v + 1 For those polynomials to be identical, all of the coefficients must match. So, we have A+B = 0 2A-B = 1 solve those and you get A = 1/3...

math
You use partial fractions. 1/(v+2)(v-1) = 1/3 (1/(v-1) - 1/(v+2))

science
light is reflected from both sides of the glass.

algebra
set x=0 and evaluate y. That's the y-intercept. Ax+By=C has slope -A/B because By = -Ax+C y = -A/B x + c/B In this case, A=9 and B=5

math
look at your functions. They indicate that the ball rises as time goes on, and never comes back down. h1(t) = 156 - 16t^2

MATH
IF UNIT IS 1, HOW ABOUT 9871 ?

Math
oops - I plugged in π/2 instead of π. The solution above is correct if the fan is 1/4 of a circle.

Math
The fan is a sector of a circle. That means that 198 = 1/2 (x+3)^2 θ Unless you know how much of a circle the fan occupies (that is, what is θ, compared to 2π), there's no way to solve for x. If the fan is a half-circle, θ=π, so 198 = 1/2 (x+3)^2 (...

English
They are all four compound sentences, so there should be a comma after "summer" #1 is probably the best. #2 implies that there is a specific group of people under discussion. #3 and #4 suffer from a mismatch between plural and singular.

English
I think #2 is better. The "still" implies that the study is continuing, rather than having been finished in the past. #1 would be ok if it said something like I studied math for ten years, but never really learned it. #1 is still ok as it is, if you are discussing pa...

English
The problem appears to be math, and yes, the sentences seem to mean the same thing. Now it's time to work on your English. That would be Do the three mean the same? Or, Are the three the same?

Alegbra
the slopes are the same, so they are either parallel or the same line. If you multiply the 1st by -3, the constant term is different from 7, so the lines are parallel.

Surds
Hmmm. I get √(4x+1)+√(x+3)=2 4x+1 + 2√(4x^2+13x+3) + x+3 = 4 5x = -2√(4x^2+13x+3) 25x^2 = 4(4x^2+13x+3) 25x^2 = 16x^2 + 52x + 12 9x^2 - 52x - 12 = 0 (9x+2)(x-6) = 0 x = -2/9 , 6 But x=6 does not satisfy the original equation, so -2/9 is the only solution.

Math
.075x = 600

Math
it is the square root of 1500. That is, it is the number which, when multiplied by itself, equals 1500. √16 = 4 because 4*4 = 16 √25 = 5 because 5*5 = 25 √1500 is not a rational number, but it is approximately 38.73 38^2 = 1444 39^2 = 1521 So, you can see tha...

Math
√1500 so, now what?

electric circuit
are the cells in series or in parallel?

math
13112221

trigonometry
since there's y^2 but no x^2, it's a parabola, opening to the right: 5x = 4y^2 - 3y - 7 x = 4/5 y^2 - 3/5 y - 7/5 x = 4/5 (y^2 - 3/4 y) - 7/5 x = 4/5 (y^2 - 3/4 y + (3/8)^2) - 7/5 - 4/5 * (3/8)^2 x = 4/5 (y - 3/8)^2 - 121/80 so the vertex is at (-121/80,3/8) http://www...

math
what tools do you have at your disposal? Have you learned l'Hospital's Rule yet? If so, that's what I'd use. The limit is the same as for the derivatives: (1/2 cos(x)^-1/2 - 1/3 cos(x)^-2/3)(-sinx) / (1/2 sin(x)^-1/2 * cosx) Take that sinx^-1/2 out of the botto...

math
There are many proofs of this, such as the one here: http://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx However, it relies on the fact that sinx/x -> 1 as x->0. That is usually proven as given here: http://math.ucsd.edu/~wgarner/math20a/sin%28x%...

maths
divide the sum into 5+6+7=18 equal parts of size x. So, 18x = 3600 x = 200 The shares are thus 5*200 = 1000 6*200 = 1200 7*200 = 1400

physics
well you know that AxB = -(BxA) So, if they are equal, they are zero. That means the angle is zero or 180. They are parallel.

maths
look at what we have: a+b+c+d = 66.5 b = a-2 c = a+1.5 d = c+1.5 Start substituting: a+(a-2)+(a+1.5)+((a+1.5)+1.5) = 66.5 a=16.0 b=14.0 c=17.5 d=19.0

PHYSICS
this just algebra I m1*x = m2*3 - m2*x (m1+m2)x = 3m2 x = 3m2/(m1+m2)

PHYSICS
think back to your Algebra I. Collect all the vf terms and factor it out.

PHYSICS
12t + 1/2 at^2 = 25 12 + at = 0 solve for a. Now you can solve for µ by using the resultant acceleration.

PHYSICS
KE = 1/2 mv^2 work is equivalent to energy.

PHYSICS
just a note: that's "mu sub-k," not "muse of k" µk Your class must be an oral presentation, if you never saw it written. Anyway, convert mgh=2.0 * 9.8 * 1.5 to KE, 1/2 * 2.0 * v^2 Using that v, and the frictional force of deceleration, figure the ...

PHYSICS
mgh + 1/2 mv^2 stays constant, so mgh1 + 1/2 m*2^2 = mg(h1-3) + 1/2 mv2^2 divide out all the m's and you have 9.8*h1 + 2 = 9.8(h1-3) + 1/2 v2^2 2 = -9.8*3 + 1/2 v2^2 v2^2 = 62.8 v2 = 7.92

PHYSICS
KE = 1/2 mv^2, so 0.02 = 1/2 * 2 * v^2 ...

Phyiscs
that depends on how long it takes.

science
How many moles of H2SO4 in 10g? The molarity of the final mix is moles H2SO4 / 0.1 L

NS 2
the distance fallen in t seconds is 16t^2. So, when is 16t^2 = 40000? The air speed of 500 mi/hr is irrelevant, since the horizontal speed does not affect the vertical speed.

Statistics
The chance that there are no parents is 10/25 * 9/24 * 8/23 * 7/22 * 6/21 = 6/1265 So, the chance that there is at least one parent is 1259/1265

math
better review what an integer is...

College Algebra
In any case, wolframalpha.com is your friend. It can confirm the results you get through your hard work: http://www.wolframalpha.com/input/?i=%2815x^2-23x-21%29+%2F+%283x-7%29

area
w * 2w = 1000 2w^2 = 1000 w^2 = 500 w = 10√5

math
y = (x-5)(x^2-2x+1) / (x-7)(x^2+2x+3) = (x-5)(x-1)(x-1) / (x-7)(x^2+2x+3) If 5<x<7, the numerator is positive the denominator is negative So, no real value of x between 5 and 7 satisfies the condition that y > 0 That is, unless I have misinterpreted your somewhat garb...

math
the discriminant is negative. That means there are no real roots. That means the graph does not cross the x-axis. That means that the value of y never changes sign. so, your job is to justify why that means that y and a have the same sign.

Geometry
tan x = 100/50

Geometry
x/20 = sin 65° the height is the side opposite the 65° angle. sine is opposite/hypotenuse

Another question (math)
while 2 is 67% of 3, that means that 2 is 33% less than 3. 2 is 1 less than 3. 1 is 33% of 3

maths
since the ratio of height to shadow-length is the same, h/22 = 100/55

math
2 log base2 (x+15) - log base2 x = 6 log(x+15)^2 - logx = 6 (x+15)^2/x = 2^6 (x+15)^2 = 64x x^2+30x+225 = 64x x^2-34x+225 = 0

math
4^y = (2^2)^y = (2^y)^2 so, we have a quadratic in 2^y: (2^y)^2 - 7*2^y - 8 = 0 (2^y-8)(2^y+1) = 0 y=3 2^y is never negative, so 2^y+1=0 has no real solution.

math
3 log x = 1 + log (4x+5)/ log 2 That dividing logs stuff is quite unusual for introductory log problems. I will solve 3 log x = 1 + log (4x+5) - log 2 x^3 = 10*(4x+5)/2 2x^3-40x-50 = 0 2(x-5)(x^2+5x+5) = 0 and that's easy If you really did mean to divide the logs, then I c...

math
10^(2x+1) -7(10^x) -26 = 0 10*10^2x - 7*10^x - 26 = 0 10*10^(2*2log t) - 7*10^(2log t) - 26 = 0 10*10^(4log t) - 7*10^(2log t) - 26 = 0 10*(10^(log t))^4 - 7*(10^(log t))^2 - 26 = 0 10t^4 - 7t^2 - 26 = 0 (10t^2+13))(t^2-2) = 0 t = ±√2 or ±√(13/10) i

Physics
If we let +x be eastward, we have <19.98,13.99> or, approximately <20,14> Add that to <0,-10> and the resultant velocity is <20,4> The (eastward) speed with which the boat is crossing the river is 20m/s. Not sure whether I interpreted your language corr...

math
-39 + 78 - 100 = -61

chemistry
Ya got me. However, the topic is discussed here: http://en.wikipedia.org/wiki/Magnetic_quantum_number

math
review the significance of the equation (x-h)^2 + (y-k)^2 = r^2

trig
If cosθ = 7/25 in QI, then sinθ = 24/25 That means tanθ = 24/7, and you (ahem) know that tan2θ = 2tanθ/(1-tan^2 θ)

math
35/n

math
you need x ml of solution, and 15-x ml of water (0 mg/ml), so 20x + 0 = 10*15 x = 7.5 Since the concentration is being reduced by a factor of 2, the volume needs to be increased by that factor. 2 * 7.5 = 15

math
If the two heights are h1, and h2 after n hours, the height is h(t) = h1 - (h1-h2)/n t Just plug in all those missing numbers that were not in your post. The burn rate is the height difference divided by how long it took to burn away.

math
The formula is above. Plug in r=3. We will assume a smooth, rather than a dimpled, surface :-)

math
4π(2r)^2 / 4πr^2 = 4 the square of the radius ratio

Algebra II
p? do you mean √? √(b^2+a^2) = √c^2 clearly the next step is flawed. √(b^2+a^2) ≠ b+a while √(b^2*a^2) = √b^2 * √a^2, √(b^2+a^2) ≠ √b^2 + √a^2 I figure you can take it from there

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