Monday

December 22, 2014

December 22, 2014

Total # Posts: 27,667

**two step equation-fraction**

4 + m/3 = 5/6 multiply all by 6: 24 + 2m = 5 now subtract 24: 2m = -19 now divide by 2: m = -19/2
*November 29, 2014*

**Math**

nowhere sinx is defined everywhere x is defined everywhere so, sinx - x is also defined everywhere. The only time you can run into trouble is when dividing functions. Then if you try to divide by zero, things are undefined.
*November 29, 2014*

**Algebra B**

18x^3 / 6x^2 = 3x The rest don't matter - we just want the x term after the division.
*November 29, 2014*

**math**

(85-72)/72 = 13/72 = .18055 = 18.1%
*November 29, 2014*

**math**

5gal 1qt = 4gal 6qt = 4gal 5qt 2pt Now you can subtract 2qt 1pt and you have 4gal 3qt 1pt
*November 29, 2014*

**math**

2c+2c + 5oz+2oz = 4c 7 fl oz Just add the cups and oz separately; be sure to remember that 8 fl oz = 1 cup Extra credit: what is the difference between an oz and a fl oz?
*November 29, 2014*

**Algebra 2**

we see that y^2 = 17-4x, so 2x^2 + 5(17-4x) = 53 2x^2 - 29x + 32 = 0 2(x-2)(x-8) = 0 ...
*November 29, 2014*

**Algebra 2**

if you substitute y = 9-x^2, you have 16x^2 - 9(9-x^2)^2 = 144 9x^4 - 178 x^2 + 873 = 0 (x^2-9)(9x^2-97) = 0 Bot those quadratics are easy to solve, no? Each is the difference of two squares.
*November 29, 2014*

**TRIGONOMETRY**

If the width of the street is w and the height of the other house is h, then if you draw a diagram, it should be clear that 9/w = tan 60° (h-9)/w = tan 30° Now you can easily find w, and then h.
*November 29, 2014*

**Geometry**

Label the areas of the triangles with O as a vertex, in the order named above. If we call their areas a,b,c,d then we have a+b=5 b+c=9 c+d=10 d+a=6 I find no unique solution to that system of equations. I'll have to think on it some more, I guess. Some other geometric ...
*November 29, 2014*

**Additional maths**

(x-1)(2x+1)(4x+1) = 0 so, tanθ = 1 or -1/2 or -1/4 0 < θ < 18? That's a weird domain. Anyway, you now have the starting values, so plug and chug.
*November 29, 2014*

**math**

assuming the eye is on the top of the observer's head, it is clear that (22-1.5)/20.5 = tanθ so, what angle θ has tanθ = 1?
*November 29, 2014*

**math**

but, since you don't have a base-2 log button, you'll have to use the change of base formula: log23 = log3/log2 and you can use whatever base you want for that.
*November 29, 2014*

**math**

heck no -- use your own calculator, cantcha?
*November 29, 2014*

**math**

Assuming base 2 throughout, note that log4 = 2 log8 = 3 So, we have 1/4 log4 + 1/8 log8 + 3/8 log(8/3) + 1/4 log 4 1/4 (2) + 1/8 (3) + 3/8 (log8-log3) + 1/4 (2) 1/4 (2) + 1/8 (3) + 3/8 (3-log3) + 1/4 (2) 1/4 (2) + 1/8 (3) + 3/8 (3)- 3/8 log3 + 1/4 (2) 1/2 + 3/8 + 9/8 + 1/2 - 3...
*November 29, 2014*

**Maths**

well, first you had to get rid of the 2, so you could then concentrate on evaluating what was inside the brackets. You could also have processed the brackets by multiplying by 2 on the left first: 2(3x/5 - 1) = 10 6x/5 - 2 = 10 6x/5 = 12 6x = 60 x = 10
*November 29, 2014*

**Maths**

2(3x/5 - 1) = 10 3x/5 - 1 = 5 3x/5 = 6 3x = 30 x = 10
*November 29, 2014*

**Pre-Calculus**

In that case, if each cage has width x and length y, the total fencing used is 9x+8y = 1400 and the area is a = 6xy But we know that y = (1400-9x)/8, so a = 6x(1400-9x)/8 = 1050x - 27/4 x^2 That is just a parabola, with its vertex at x = 700/9 So, y = 700/8 You can finish up ...
*November 28, 2014*

**Pre-Calculus - incomplete**

You need to specify more about the layout of the cages. Are they all stand-alone? Do they share sides in some way?
*November 28, 2014*

**ALGEBRA 2 - incomplete**

There are infinitely many right triangles. More information is needed.
*November 28, 2014*

**Math**

Hmm. I get 5b( 3a^3 - 2b + 4a^2b^2) Other than that, I see no useful factorizations. Who said anything about a GCF? You need at least two expressions to have a "common" factor...
*November 28, 2014*

**Math - PS**

In general, it would be (Ax+B)/(x^2+4) + (Cx+D)/(x^2+4)^2 In this case, D just happens to be zero.
*November 28, 2014*

**MATH**

Looks like you need to review your compound interest formula. $P invested at at a rate of r, compounded n times per year for t years grows to P(1+r/n)^(nt) So, knowing that (1+.05/4)^(4*6) = 1.347, you now just have to solve 1.347P = 65000
*November 28, 2014*

**MATH**

solve for P in P(1+.05/4)^(4*6) = 65000
*November 28, 2014*

**physics**

330 cos 42°
*November 28, 2014*

**College Algebra**

A: s = 105 B: s = 60 + .08x C: s = .12x
*November 28, 2014*

**physics**

F = GMm/r^2 = ma, so a = GM/r^2 r^2 = GM/a You have M and a, and can find G. So, plug and chug.
*November 28, 2014*

**programming**

I assume you know C, so just code up rate = (amt < 10000) ? 0.03 : 0.05; interest = rate * amt * years; Better fix things, so that an exact amount of 10,000 is included somewhere in the condition.
*November 28, 2014*

**algebra**

if the supply pump can pump p gal/min, and the outlet pumps each draw q gal/min, 30(p-q) = 8450 45(p-2q) = 10950 (p,q) = (320,115/3) Now you can convert that to gal/hr.
*November 27, 2014*

**algebra**

boat=b, current=c 225/(b+c) = 5 225/(b-c) = 9 (b,c) = (35,10)
*November 27, 2014*

**Algebra 2 honor**

Just as a reminder, revenue is price * demand. That is, toe total income for all the items sold. recall that for y = ax^2+bx+c the vertex is at x = -b/2a. So, for this one, the vertex is at x = 112.5/22.5 = 5 Since the parabola opens downward, the vertex is a maximum. So, the ...
*November 27, 2014*

**Algebra 2 honor**

if there are x 75-cent increases, then there are 300-15x mugs sold. So, now we have the revenue as r(x) = (7.50 + 0.75x)(300-15x) = -11.25x^2 + 112.5 + 2250 Now just find the vertex of the parabola.
*November 27, 2014*

**Maths**

5x = 3x+24 x = 12 36 cattle, 60 sheep
*November 27, 2014*

**Integumentary System**

google is your friend.
*November 27, 2014*

**maths**

5x = 3x+24 x = 12 I'll let you decide which is which. You canto have a ratio cattle:sheep = 3:5 and yet have more cattle than sheep. There are 36 of one and 60 of the other.
*November 27, 2014*

**maths**

1/2 : 3/4 = 2/4 : 3/4 = 2:3 That should help, eh?
*November 27, 2014*

**math**

ar^2 = 9a so, r = ±3 Now we have a problem. We know that r=3, so the 5th term must be 27 times the 2nd term, regardless of the value of a. And, as you say, there is no way to determine a from the information given so far. You sure it's not 24 less than the 5th term?
*November 27, 2014*

**Math**

Since all the sides are equal, we have 3x 2 = 2y-x 2y-x = y 3 Fix your typos and then solve for x and y. If I assume that your "+" key is not working, then we have 3x+2 = 2y-x 2y-x = y+3 (x,y) = (2,5) So, the sides are 8 and p=24.
*November 27, 2014*

**math**

if N's digits are a,b,c, then we know that c>a, since reversing the digits increased the sum. cba - abc = 99(c-a) = 11(a+b+c) Since 99 is a multiple of both 9 and 11, a+b+c must be a multiple of 9. So, a+b+c is 9 or 18, since 7+8+9=24 is the maximum sum of digits. Now, ...
*November 27, 2014*

**IT**

Here's a nice little perl program. I'm sure you can modify it for the language of your choice. #pay off a loan in 10 equal payments, except for possibly the last, due to roundoff. print "Customer name: "; my $name = <STDIN>; chomp $name; print "...
*November 27, 2014*

**Math**

a + 6a + 2a = 180 a = 20 so now figure B and C
*November 27, 2014*

**Mathematics**

56/16
*November 27, 2014*

**Preamble to the Constitution**

Take a look at some of the recipients of the Liberty Medal. It is awarded to honor those deemed to have labored to secure the blessings of liberty. It will give you some idea of what might be considered to give meaning to the phrase. http://constitutioncenter.org/libertymedal/
*November 27, 2014*

**Algebra**

x+y = 156 x = y+28
*November 26, 2014*

**Math**

.09x + .11(x+400) = 117.00
*November 26, 2014*

**Math**

oops. That's (2±√32)/2 = 1±√8
*November 26, 2014*

**Math**

(b) t = -b/2a = 10/10 = 1 (a) find h(1) (c) solve for t when h=0 -5t^2+10t+35 = 0 or, t^2-2t-7 = 0 t = (2±√30)/2 (use quadratic formula) (d) correct
*November 26, 2014*

**Calculus**

dy/y^2 = 11x^2 dx -1/y = 11/3 x^3 + c Now plug in your initial condition to find c.
*November 26, 2014*

**math**

3/10 * 2/9
*November 26, 2014*

**English**

#2 is the most common Even it is not punctuated correctly. There should be a comma after "conditioner." Without the comma, it appears that one would "turn on the air conditioner to save electricity." #3 or #6 could also be used. The others are incorrect.
*November 25, 2014*

**TRIG!**

just replace t with 3t. They are the same curve. In either case, y = x^2+1
*November 25, 2014*

**physics**

the initial vertical speed is 47 sin 31° = 24.2 m/s So, the height y = 24.2t - 4.9t^2 Now use your algebra to find the vertex of that parabola. That will be the maximum height.
*November 25, 2014*

**Algebra**

v = k*pq/s^2 Now just plug in the numbers to find k.
*November 25, 2014*

**Math**

We need to keep the ratio 10:6 112 = 16*7, so we need to add 10*7 = 70 white balls 6*7 = 42 yellow balls
*November 25, 2014*

**trigonometry**

the circle is clearly the unit circle with center at (0,0) theta goes from 3pi/4 to 3pi/2
*November 25, 2014*

**trig**

2rcosθ + 3rsinθ = 5 r = 5/(2cosθ+3sinθ) rsinθ = 1/2 rcosθ tanθ = 1/2 θ = arctan(1/2) No r involved.
*November 25, 2014*

**Math Help!**

Correct .25 = n/350
*November 25, 2014*

**Math Help!**

820 = .20 n Looks like B to me when it starts out with "820 is" you need to start looking for "820 ="
*November 25, 2014*

**Math Help!**

Correct
*November 25, 2014*

**trigonometry**

θ = π/6 tanθ = 1/√3 y/x = 1/√3 y = 1/√3 x r = 8cosθ r^2 = 8r cosθ x^2+y^2 = 8x
*November 25, 2014*

**trig**

x = -2 + 12t y = 6 - 10t 0 <= t <= 1
*November 25, 2014*

**pre calc**

since v = kT/P, PV/T is a constant. So, 342*V/10 = 380*2.3/20
*November 25, 2014*

**Math**

oh. In that case, recall that N^0 = 1 for any value of N.
*November 25, 2014*

**Math**

none of those offered.
*November 25, 2014*

**easy math**

you are correct
*November 25, 2014*

**Calculus**

Let u = 1+lnx du = dx/x and the integrand is u du
*November 25, 2014*

**Calculus**

This is just the chain rule in disguise f'(x) = (x^3)^2 (2x) = 2x^5 Read up on the 2nd fundamental theorem of calculus.
*November 25, 2014*

**Calculus**

If you mean dx/x (lnx)^(1/2) then let u = lnx du = dx/x and the integrand becomes u^(1/2) du
*November 25, 2014*

**math**

c(t) = 420t where t is in hours
*November 25, 2014*

**Trigonometry**

csc^2 + sec^2 1/sin^2 + 1/cos^2 (sin^2 + cos^2)/(sin^2 cos^2) 1/(sin^2 cos^2) sec^2 csc^2 Not sure what the 2nd line is saying It's not an identity, just an expression.
*November 25, 2014*

**algebra**

7P3 = 7*6*5
*November 25, 2014*

**Problem Solving: Draw Picture**

draw a line 22.5 inches long mark a spot every 1.5 inches
*November 25, 2014*

**math**

just solve for y in: 1500 + (7500-1500)y = 7080
*November 25, 2014*

**English**

They all look good to me.
*November 25, 2014*

**English**

#1 is correct. Extra credit: what is bad about #2?
*November 25, 2014*

**Geometry**

the three medians intersect at the centroid, which is where the triangle will balance.
*November 25, 2014*

**Calculus**

the average value of f(t) over the interval [a,b] is ∫[a,b] f(t) dt ------------------ b-a So, for this problem, that would be (∫[0,5] .96t^2+25 dt)/(5-0) = (.32t^3 + 25t [0,5])/5 = 165/5 = 33
*November 25, 2014*

**Algebra math Question**

well, you have 2(w + 2.4w) = 20.4 Now just solve for w, and the length is 2.4 times that.
*November 24, 2014*

**math**

Oh, please. You provide no numeric details at all -- how do you expect an answer? Since 42 is the answer to the ultimate question of life, the universe, and everything, I thought surely it was the answer to your obfuscated question!
*November 24, 2014*

**math!!**

algebraically, you want 8m >= 3m+25 or, just note that Sam saves an extra $5/month. SO, it will take 5 months to gain $25.
*November 24, 2014*

**MATH**

P(1+0.01375/4)^(4*3) = 15000
*November 24, 2014*

**calculus**

So, looks like C to me.
*November 24, 2014*

**calculus**

since (arctan(u))' = 1/(1+u^2) u', we have d/dx arctan √(3x) = 1/(1+3x) (√3)/(2√(3x)) = √3 / (6x+2)√x
*November 24, 2014*

**Pre-Calc/Trig**

well, that would depend on n, don't you think? multiples of 2 are even; otherwise, odd
*November 24, 2014*

**Algebra**

the domain is all the values of x where f(x) is defined. f(x) = 4 if -6 <= x < -2 |x| if -2 <= x < 8 ∛x if 8 <= x <= 14 So, clearly the domain is [-8,14] since f(x) is defined everywhere inside the interval, and nowhere outside it. Doesn't matter ...
*November 24, 2014*

**Math**

Ya got me. I don't find any rational roots at all. Makes factoring kinda tricky. You sure it's not 2y^4-y^3-10y+5 ? That could be done by grouping y^2(2y-1) - 5(2y-1) (y^2-5)(2y-1) For your function as given, I don't see any way. Wolframalpha confirms this: http://...
*November 24, 2014*

**maths**

If you want the radius r of the circle, just draw a diagram and note that (4/2) = r sin(60°/2)
*November 24, 2014*

**math**

(7/2)mi / (221/4) min = 7/2 * 4/221 mi/min = 14/221 mi/min
*November 24, 2014*

**algebra**

Nope. As you state it, it makes no sense. One does not add and subtract denominators.
*November 24, 2014*

**algebra**

I'm guessing you meant y/(y-5)+5/(5-y) = y/(y-5) - 5/(y-5) = (y-5)/(y-5) = 1
*November 24, 2014*

**math - eh?**

1/a + 1/b = 1/60 12/a + 36/b = 1 You sure there's no typo? I get a negative value for a.
*November 24, 2014*

**Calculus**

Let u^2 = x+9 Then √(x+9) = u x = u^2-9 dx = 2u du Then the integral becomes ∫(u^2-9)/u (2u du) = ∫2(u^2-9) du = 2/3 u^3 - 18u = 2u/3 (u^2-27) = 2/3 √(x+9) (x-18) For other problems, you can check your results at http://www.wolframalpha.com/input/?i=%E2...
*November 24, 2014*

**Calculus**

u=5x du = 5dx and the integrand becomes 1/5 sec(u) tan(u) du That should look familiar
*November 24, 2014*

**Calculus**

let u = x^9 then du = 9x^8 dx and the integrand is now 1/9 e^u du
*November 24, 2014*

**math**

distance gone will be 45*4 = 180 km poles/km = 1000/50 = 20 So, 180*20 = 3600 poles
*November 24, 2014*

**Calculus**

let u = 7sinx+35 du = 7cosx and the integrand now becomes 1/7 du/u
*November 24, 2014*

**Math**

gee - why not follow the hints? Use cross products: if a/b = c/d, then ad = bc So, for the first, try each pair: 1. 24/96 , 27/108 ? 24*108 = 96*27 YES 2. 17/102 , 12/70 ? 17*70 = 102*12 NO 3. 21/51 , 35/85 ? 21*85 = 51*35 YES 4. 45/75 , 63/105 ? 45*105 = 75*63 YES Try the ...
*November 24, 2014*

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