Sunday
December 21, 2014

Posts by steve


Total # Posts: 27,663

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

maths
42
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

English
#1
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
42
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

Math
sinB/b = sinA/a sinB = 9(sin28)/15 = 0.2817 B = 16° or 164°
November 24, 2014

Math
since the distance s = rθ the object travels 8.1*10 = 81 cm/s Curious how you got 47
November 24, 2014

Calculus
or, 4 + 4/x^2 :-)
November 24, 2014

Calculus
just do a long division (4x^2+4)/x^2 = 4 + 2/x^2
November 24, 2014

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