Thursday

September 3, 2015
Total # Posts: 33,249

**math**

We may have taken different logs. Base 10 vs base e. Looks good to me. Does this fit any of the other data points very well?
*August 30, 2015*

**math**

if you know about exponents, you should know about logs, which are the inverse function. a^1000 = 1.096 1000 log(a) = log(1.096) a = log(1.096)/1000 = 0.0000917
*August 30, 2015*

**math**

huh? a^1 = 1 and a^-1 = 1/a, so 4 = ba 16 = b/a now divide: 4/16 = ba/(b/a) 1/4 = a^2 a = 1/2 so, b=8 f(x) = 8*2^-x
*August 30, 2015*

**Math**

A= ((r+z)/3)m A/m = (r+z)/3 3A/m = r+z 3A/m - z = r
*August 30, 2015*

**trig**

sec^4x=11tan^2x+5 (1+tan^2x)^2 = 11tan^2x+5 tan^4x + 2tan^2x + 1 - 11tan^2x - 5 = 0 tan^4x - 9tan^2x - 4 = 0 That's just a quadratic in tan^2x, so solve it, then just take the square root.
*August 30, 2015*

**Math**

recall that (a+b)(a-b) = a^2-b^2. So, you have (√37-√23)/(√37+√23) Now multiply by (√37-√23)/(√37-√23) and you have (√37-√23)(√37-√23) / (√37+√23)(√37-√23) = (37-2√37√23...
*August 30, 2015*

**Math**

a+m = 50 m-10 = 2(a-10) Now just solve for a and m.
*August 30, 2015*

**Geometry**

since 1L = 1000 cm^3, if the height ish, then we know that (20)(15)(h) = 4800 h = 16 So, the wet surface area is bottom + 2 long sides + 2 short sides = 20*15 + 2*16(20+15) = 1420 cm^2
*August 30, 2015*

**equation**

If you mean (9^x)^(-2) + (3^3)^x = 81 then you have 3^(-4x) + 3^(3x) = 81 if u = 3^x, then you have 1/u^4 + u^3 = 81 I'm sorry, but I don't see any algebraic solution. you sure there's no typo? Wolframalpha gets this: http://www.wolframalpha.com/input/?i=3^%28-4x%...
*August 30, 2015*

**Math**

well, divide x by 2 and then subtract 2 24/2 - 2 = 12-2 = 10 and so on for the others.
*August 30, 2015*

**equation - eh?**

Not sure what your parentheses mean. Multiplication, or more powers 9^x(-2) means -2*9^x or (9^x)^-2 = 9^(-2x) Why do you sometimes use ^ for powers, and other times not?
*August 30, 2015*

**math calculus**

0.5^(x/5730) = 0.95 x = 424 The 1815 date (195 years old) would still have 0.5^(195/5730) = 97.7%
*August 30, 2015*

**math**

just solve for t in (1/2)^(t/5730) = 0.95
*August 29, 2015*

**Trigonometry/ please help!**

you are correct. However, S=0 when t=1,3,5,7 That may have been what they intended to ask.
*August 29, 2015*

**Calculus**

(f'(π/3) = (-π/3 * √3/2 - 1/2)/(π/3)^2 = -(9π-3√3)/(2π^2) If we call that slope m, then the tangent line is y-1 = m(x-π/3)
*August 29, 2015*

**alegbra 2**

Or, knowing that the equation of a parabola with focus at y=(0,0) and focus at y = -p is x^2 = 4py we have a shifted parabola with p=-3, so the equation is (x-6)^2 = 4(-3)(y-4) x^2-12x+36 = -12y+48 x^2-12x+84 = -12y Verify at http://www.wolframalpha.com/input/?i=parabola+%28x-...
*August 29, 2015*

**Math**

I think you mean ∛(-27 x^4 a^5) = ∛-27 ∛x^4 ∛a^5 = -3 x∛x a∛a^2 = -3ax∛(xa^2) you could have typed cbrt(-27 x^4 a^5) or 4throot, 5throot, etc.
*August 29, 2015*

**calculus**

simple enough. You want ∫[0,b] (2x+b) dx = 288 Now just solve for b. You can check by just finding the area of the trapezoid: b(b + 2b+b)/2 = 288
*August 29, 2015*

**Algebra**

you are correct in your solutions and your simplifications. Good work.
*August 29, 2015*

**Geometry**

thank you
*August 29, 2015*

**Geometry**

since <rpb = <tpb, x+2 = 2x-6 So, just solve for x and then you can find the angle measures.
*August 29, 2015*

**Geometry**

ray pb bisects < rpt so that < rpb = x+2 and < tpb = 2x-6. What is < rpt =
*August 29, 2015*

**calc**

It would appear so, but you make it hard to tell, being so sloppy with parentheses. Much better would have been 3x-2y=7 8x=(y-1)/2 4x+(2/3)y=8
*August 29, 2015*

**calculus**

well, clearly each cross-section has a base of side length y, so its area is y^2 The volume is thus ∫[-2,1] y^2 dx = ∫[-2,1] (x+2) dx I'm sure you can take it from here, no?
*August 29, 2015*

**Math**

yes
*August 29, 2015*

**Precalc**

well, you want 3/4 x - 1 = 3 3/4 x = 4 x = 4(4/3) = 16/3
*August 29, 2015*

**calculus**

if you mean dx/dy = (1/2) x, then dy/dx = 2/x dy = 2/x dx y = 2 lnx + c domain: x>0 I'm sure you can find c. I'm surprised that you give dx/dy when looking for y(x)...
*August 29, 2015*

**Math**

well, then we have y-4 = 4x+3y 2y = -4x-4 y = -2x-2 y-4 = -(9-x) y-4 = x-9 y = x-5 So, -2x-2 = x-5 x = 1 and thus y = -4 xy = -4
*August 29, 2015*

**Math**

what are we to make of the two = signs?
*August 29, 2015*

**word problem**

x+y=12 z = x^2 y^(1/4) = (12-y)^2 y^1/4 = 144y^1/4 - 24 y^5/4 + y^9/4 dz/dy = 36/y^3/4 - 30y^1/4 + 9/4 y^5/4 = (36 - 30y + 9/4 y^2) / y^3/4 dz/dy=0 when 9y^2-120y+144 = 0 3(3y-4)(y-12) = 0 clearly, y=12 gives z=0, a minimum y=3/4 gives x=45/4 and z=(1024/9) 4throot(4/3)
*August 29, 2015*

**integral calculus**

5(cos3x)^2 but you need a siny to form the full derivative cos^2 u = (1+cos 2u)/2 so, we have 5/2 (cos6x+1) Now you have 5/2 (1/6 sin6x + x) + C
*August 29, 2015*

**maths**

you recall that the sum of the interior angles of a pentagon is 540.
*August 29, 2015*

**Algebra**

t = 7u-8 10u+t = 10t+u-9 I don't get integer values. I suspect a typo.
*August 29, 2015*

**physics**

It takes 3.7 seconds to fall 67.7 meters. So, since time = distance/speed, So, 3.7 + 67.7/v = 3.91
*August 29, 2015*

**Physics**

the normal MKS units, of course.
*August 29, 2015*

**Math**

let's clear fractions and see what we have 5x+3y=3c 4x+2y=c x+y=6 If we subtract the 2nd from the 1st we have x+y=2c x+y=6 that help?
*August 29, 2015*

**Calculus**

(a) might be true (sin(0)/0 not defined) (b) might be true (f(0) might not be defined) (c) must be true (d) must be true - that's the definition of f'
*August 28, 2015*

**Math**

no there are 7 chances for, and 1 against, so 8 chances in all So, p = 7/8 1:7 are the odds against 1/8 is the probability against
*August 28, 2015*

**Maths**

1/6 + 1/5 + 1/4.5 = 53/90 So, their output is in the ratios 15:18:20 20/53 * 750 = 283
*August 28, 2015*

**maths - incomplete**

I don't see any = sign there.
*August 28, 2015*

**Geometry**

no way to tell. If the base is 2, the sides are 17 If the base is 10, the sides are 13. If the base is x, and the sides are y, you know that x + 2y = 36 And, you know that x < 2y or the base is so long that the sides won't reach the ends.
*August 28, 2015*

**good Samaritan school**

918/1030 = 89.12% That means that 10.88% of the berg is showing. so, 224 = 0.1088v
*August 28, 2015*

**math**

(1) 60 is just a number, not a percentage P = 2000 + 60t (2) P is increasing, so you want P = 2000 * 1.05^t 0.95^t means that each year the population decreases by 5%
*August 28, 2015*

**Math**

since 100 is divisible by 4, only the last two digits need to be considered. So, what 2-digit numbers beginning with 4 are divisible by 4? Actually, since 40 is divisible by 4, only the final digit matters. What values less than 10 are multiples of 4?
*August 28, 2015*

**heith**

x + 2x = 30 solve for x; that is the smaller volume.
*August 28, 2015*

**math**

well, you know that density is measured in mass/volume. You are given very little information, so expect the solution to be relatively uncomplicated: 500g/2500cm^3 = 0.2 g/cm^3
*August 28, 2015*

**How many milliliters of a stock solution of 6.00 M**

0.0155L * 1000mL/L = 15.5mL
*August 28, 2015*

**Math**

50 @ SE = <35.36, -35.36> You want a direction θ such that 500 sinθ-35.36 = 0 sinθ = 35.36/500 θ = E 4.05° N
*August 28, 2015*

**Geometry/Steve**

78.5 = 25π, so r=5 (2-2)^2 + (-9-4)^2 = 13^2, so D is wrong (A) (-6-2)^2 + (4-4)^2 = 64, so nope (B) (2-2)^2 + (-1-4)^2 = 25 we have a winner you can check (C) if you want.
*August 27, 2015*

**probability**

0.3 * (1-x) = 0.06 x = 0.80
*August 27, 2015*

**Geometry - eh?**

You said: 14 visited the zoo but not the museum, ... 2 visited the zoo but not the museum. So, which is it?
*August 27, 2015*

**C++**

write a prompt, then read in a real, an integer, and a real
*August 27, 2015*

**Geometry**

the length is correct. But the midpoint is -2+7 = 5. 5 = -2+7 = 12-7
*August 27, 2015*

**Geometry**

Line pb is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint. My answer would be the total length pf pb is 14 units so the midpoint would be 7.
*August 27, 2015*

**Geometry**

explain how you can use a straight edge and a compass to construct an angle that is both congruent and adjacent to a given angle.
*August 27, 2015*

**Geometry**

If we call the vertices A,B,C and the opposite sides a,b,c then we have (A): a=3, b=4, c=5 (B): a=6, b=√85 stop right there (C): a=13, b=10√2 stop right there (D): a=8, b=10, c=6 we have a winner!
*August 27, 2015*

**Chemistry**

The total masses of S and O are approximately equal, so since O has half the mass/mole of S, that means the empirical formula is probably SO2
*August 27, 2015*

**Geometry**

thank you
*August 27, 2015*

**Geometry**

What is the circumference of a circle in terms of pi with a radius of 2.2? I know that c = 2 pi * r c = 2 pi * 2.2 c = 2 * 2.2 my answer is 4.4 pi
*August 27, 2015*

**Algebra**

actually, that's x ≠ -3y, but it does not affect the final answer. Just sayin' ...
*August 27, 2015*

**Equation - oops. go with Damon**

Hmmm. I seem to have disregarded the distributive property ...
*August 27, 2015*

**Equation**

just use the quadratic formula: x^2 - bx + b-1 = 0 x = [b±√(b^2-4(b-1))]/2 = [b±√(b^2-4b+1)]/2 If you want an integer solution for b, then clearly b=2 and you have x^2-2x+1 = (x-1)^2 = 0 For a real solution, you need b^2-4b+1 >= 0 or b >= 2+&#...
*August 27, 2015*

**Math**

how many even numbers are there? 9 So, P(even) = 9/19 P(4) = 1/19 Now just add 'em up
*August 27, 2015*

**Mathematics**

well, 25kg = 25000 = 250*100 g
*August 27, 2015*

**geometry**

the 3' border on each side increases each dimension by 6. So, the outside dimensions are 18 by 22 Now you can figure the perimeter, right?
*August 27, 2015*

**Math 10**

3^x + 3^-x = 82/9 3^x + 1/3^x = 82/9 (3^2x + 1)/3^x = 82/9 clearly, x=2, but let's go on. 9(3^2x + 1) = 82*3^x 9*3^2x - 82*3^x + 9 = 0 think of this as 9u^2-82u+9, and you get (9*3^x - 1)(3^x - 9) = 0 3^x = 9 or 1/9 x = 2 or -2 aha. an unexpected solution!
*August 27, 2015*

**problem solving.**

j-10 = 4(b-10) j = 2b now it's a cinch, right?
*August 27, 2015*

**math - eh?**

If you mean 2*(1/2)^(4y) = 1/8, then (1/2)^(4y) = 1/16 (1/2)^1 = 1/2 y = 1 well, that didn't work. As written, you have (sort of) (5/2)^(4y) = 1/8 4y log(5/2) = -log8 That's not getting us anywhere. So, just what did you mean? what's the (2 1/2) doing there?
*August 27, 2015*

**nyakasura school**

s = 1/2 at^2, so 1/2 a*64 = 40 a = 80/64 m/s the mass does not matter.
*August 27, 2015*

**math**

for any x, x^2 >= 0 so, y >= 9 for all real x. x can, of course, be any real number. D: (-∞,+∞) R: [9,+∞)
*August 27, 2015*

**algebra**

Where did the 6 yards come from? If the temperature is constant from 6 to 15 yards, then we have to modify things. We then have at x=18 ft (6 yds), t(x) = 52. t(x) = 70-(2/3)x for x in [0,18] t(x) = 52 for x in [18,45] t(x) = 40+3x for x in [45,60] #5. Clearly you meant (x+3)/...
*August 27, 2015*

**algebra**

#4. -8/2 + 4 (____) - 2 -4 + 4x - 2 -6 + 4x that will always be even, so you just want -6 + 4x > 0 4x > 6 x > 6/4 So, any integer greater than 2 will work. #5-7 can be done similarly #8. yes. -16/4 = -4 #9. surely you could easily find out that 3 ft = 1 yd. Geez. So, ...
*August 27, 2015*

**algebra**

what's wrong with -6/9? It's just a fraction. Deal with it 3 - 2(4 - 7) ÷ 9 3 - 2(-3) ÷ 9 3 - (-6)÷9 3 - (-2/3) 3 + 2/3 11/3
*August 27, 2015*

**Calculus 1**

if tanθ = x, then cosθ = 1/√(1+x^2) cos2θ = 2cos^2θ - 1 = 2/(1+x^2)-1 = (1-x^2)/(1+x^2)
*August 27, 2015*

**Calculus 1**

that it is.
*August 27, 2015*

**Calculus 1**

come on. don't forget your trig now that you're taking calculus! You surely recognize cotθ = √3 No? How about tanθ = 1/√3
*August 27, 2015*

**Calculus 1**

for these, always draw the right triangle! for example, sin(arctan 17/8) = 15/17 Draw the triangle, fill in the missing side, and take the needed trig function. Then, as in the second problem here, remember your double-angle formula: sin2θ = 2sinθcosθ
*August 27, 2015*

**Math (functions)**

I believe you are correct.
*August 26, 2015*

**Algebra**

5s + 8(19-s) = 116
*August 26, 2015*

**Algebra**

(1 1/2 - 1 1/8)/2 = (3/2 - 9/8)/2 = (12/8 - 9/8)/2 = (3/8)/2 = 3/16
*August 26, 2015*

**Algebra**

if there are n jr high students, then we have n/(n+100) = 7/9 9n = 7(n+100) 2n = 700 n = 350
*August 26, 2015*

**Ap algebra**

since a function maps values in its domain to values in the range, if the y-value is undefined, the x-value cannot be in the domain. Surely the minimum value of a function is the least y-value in the range. For continuous functions, that is no problem. But, if there are point ...
*August 26, 2015*

**precalc**

y = -4x+1 has slope -4 so do all parallel lines perp. lines therefor have slope 1/4 Now use your point-slope form for the line: parallel line is y-3 = -4(x+2) change the slope to 1/4 for the perpendicular line.
*August 26, 2015*

**Math**

domain is all reals, but since x^2 >= 0 for all x, y >= 9 for all x. That is the range. D: (-∞,+∞) R: [9,∞)
*August 26, 2015*

**Algebra 2**

The angles are 2x,3x,3x. The sum is 180, so x=22.5 C-A = 3x-2x = x
*August 26, 2015*

**Precalc**

check the graph of x^3+1. No horizontal line crosses it more than once, so its inverse is a function. 4^x = (1/2)^(x-3) 4 = 2^2 = (1/2)^-2, so (1/2)^(-2x) = (1/2)^(x-3) -2x = x-3 x = 1
*August 26, 2015*

**Algebra**

15^3
*August 26, 2015*

**AP Calculus**

recall the definition of |u|. It is u for u>=0, and -u for u<0. So, your function f(x) = (x-2)/(x-2) for x >= 2 (x-2)/(-x-2) for x < 2 Now you can easily find the necessary limits. Then, peek at the graph below to verify your calculations.
*August 26, 2015*

**Math**

correct. you can also note that a constant function y(x)=k is the same as y=kx^0, and since 0 is an even power, kx^0 is an even function, and thus symmetric about the y-axis.
*August 26, 2015*

**Precalc**

5x^3 y^-1 z^-5 = 5x^3 / yz^5 take the -3 power of that and you have y^3z^15/125x^9 x^2 y^0 z^-6 = x^2/z^6 square that and you have x^4/z^12 Now just multiply the two fractions and you have y^3z^3 / 125x^5
*August 26, 2015*

**Math**

k is 1000, as in kg, km, etc. 2.0*10^3kcal/day * 1day/86400s * 1000cal/kcal = 23.15 cal/s
*August 26, 2015*

**Math**

.6carat * 200mg/carat * 1kg/10^6mg * 2.205lb/kg * 16oz/lb = 0.00423 oz
*August 26, 2015*

**Geometry**

well, you know that AC+CB=AB, so 3x+55+2x = 65 Now just solve for x and AC=3x
*August 26, 2015*

**math**

divide 36 into 4+5=9 parts. Each part is 4. so, the bikes are 16:20
*August 26, 2015*

**Logs**

well, it is easy enough with a calculator; there's an e^x button. can you use Taylor Series? e^x = 1 + x + 1/2 x^2 + 1/6 x^3 + ... 1 + (-.6) = 0.4 1 + (-.6) + (-.6)^2/2 = 0.58 ...+(-0.6)^3/3!+(-0.6)^4/4! = 0.5494 ...+(-0.6)^5/5!+(-0.6)^6/6! = 0.5488 what other ...
*August 26, 2015*

**geometry**

(-3+x)/2 = -3/2 -3+x = -3 x = 0 Think about it. Starting at -3, x grows by 3/2 to -3/2 at B. It grows by another 3/2 to be 0 at C. (4+y)/2 = 1 4+y = 2 y = -2 Had you plotted these points, you would have seen that your C point was way off. And what's with the "over&...
*August 26, 2015*

**Algebra 1**

I sense a question in there somewhere... x+y=50 20x+30y=1200 so, ...
*August 26, 2015*

**vector**

I see you are not about to do anything more than repost your question. IT'S 90 DEGREES!
*August 26, 2015*

**Math**

D=L D-26 = 2(L-38)
*August 26, 2015*