Tuesday

July 29, 2014

July 29, 2014

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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