Monday

July 28, 2014

July 28, 2014

Total # Posts: 23,988

**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

**Algebra II - Bogus**

I suspect typos. The function is littered with junk. p? +7+8?

**mathematics**

2x^2-y^2+4x+4y-4=0 2x^2+4x - y^2+4y - 4 = 0 2x^2+4x+2 - y^2+4y-4 -4-2+4 = 0 2(x+1)^2 - (y-2)^2 = 2 (x+1)^2 - (y-2)^2/2 = 1 Now just consult the properties of hyperbolas. x = 2cost y = 3cost First off, I think you have a typo, since that is just 3x=2y If you meant x = 2cost y =...

**Math**

so, if you don't want math jargon, what do you mean by parametrically? A simple web search will produce lots of explanations, of varying mathematical sophistication.

**Combinationa and permutation**

There are 3! ways to arrange the three colors. Within each color, there are 5!,3!,4! ways to arrange the different marbles. So, there are 3!5!3!4! = 103680 ways to arrange the marbles as specified.

**algebra**

4x = y+7 x+28 = 2y The numbers are 6 and 17

**physics**

its horizontal velocity is unchanged its vertical velocity is the same speed, but the opposite direction. Play around with that and see what you get.

**Maths- calculus**

They approach at 35 knots. So, when they have gone 55 miles together, they are 45 miles apart. That takes 55/35 hours. How long to consume the whole 100 miles? 100/35 hours. How far has ship A gone by then? How long to cover 130 miles? 130/35 hours. I assume you can convert el...

**Math pre-calculus**

you know that sin(pi/4 x)=0 when pi/4 x is a multiple of pi. That is, pi/4 x = k*pi x = k*pi * 4/pi = 4k So, when x is a multiple of 4, sin(pi/4 x) is zero. That is where csc(pi/4 x) has vertical asymptotes.

**Basic Physics**

If the vector is in -y direction, the x-component is zero.

**Algebra**

It will still be a trinomial. Each term is just multiplied by a single value. The degree may change, but no new terms will be added or deleted.

**calculus**

P = 2/√g √L dP = 2/√g * 1/2√L dL = 1/√(gL) dL So, the % error in P is dP/P = 1/√(gL) dL/P = 1/√(gL) * √g/2√L dL = 1/√g * √g/2 dL/L = 1/2 dL/L

**math**

I redid the problem using polar coordinates, where I set the (0,0,0) at the base of the paraboloid section, so that z = 3 - (x^2+y^2) That means that we have only to evaluate S = ∫[0,2π]∫[0,√3] r√(1+4r^2) dr dθ and we get π/6 (13√13...

**math**

so, what headway have you made? See any mistakes in my calculations?

**math**

S = ∫[-13,3] 2πx√(1+x'^2) dy x = √(3-y) x' = -1/2√(3-y) 1+x'^2 = 1 + 1/4(3-y) = (13-4y)/(3-y) So, S = ∫[-13,3] 2π√(3-y)(13-4y)/(3-y) dy = 2π∫[-13,3] (13-4y)/√(3-y) dy = 2π (2/3 (4y-15)√(3-y))...

**math**

3.10*11.3 km/s

**Math**

(i) ok (ii) T = 0.06x (iii) S = 20P

**Geometry**

clearly, 10x-7 = 5x + 4x+6 x = 13 so, take it from there.

**math**

The speed must increase by a factor of 17500/1530 = 11.438 So, we need to find x such that x^610 = 10.438 x = 1.004 So, the speed must increase by 0.4% each second.

**chemistry**

It takes 2 moles of HCl to react with each mole of Mg. 48.6 g of Mg = ? moles 150.0 g of HCl = ? moles If there are less than half as many moles of Mg as HCl, it will be the limiting reagent.

**Precal - eh?**

I don't see any statement; just a hard-to-parse expression. Try using 3^n if you want exponents, and fix the statement.

**maths**

Is ST a line in the interior of PQR? If so, I must be missing something. Just knowing the ratio of two sides of PQR tells me nothing about the areas of either triangle. Better explain the overall figure, not just a couple of lines.

**science**

just watch the units: 9.6 J/s * 3.0s = 28.8 J The height lifted is irrelevant, since that will just be part of the work.

**marh**

a/27 = (1/3)^2

**MATH**

not quite. Multiply, instead of dividing, just as you did for the first line. When you see "of" in a calculation, it means "times". 1/2 of 5000 = 5000 * 1/2 3/5 of 2500 = 2500 * 3/5

**business math**

multiply by (1+.30) or 1.3

**Math**

no, it's the next line. The squares are equal; it's the assumption that the roots are equal which is wrong.

**Math**

There is a + and a - root of each squared term. Just because (-4)^2 = 4^2 does not mean -4 = 4.

**Geometry**

they are regular, and all that that entails.

**Math**

ax^2 + bx + c = 0 a(x^2 + b/a x) = -c a(x^2 + b/a x + (b/2a)^2) = -c + a(b/2a)^2 a(x + b/2a)^2 = b^2/4a - c (x + b/2a)^2 = (b^2-4ac)/4a^2 x + b/2a = ±√(b^2-4ac)/2a x = (-b±√(b^2-4ac))/2a

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