Thursday
September 3, 2015

Posts by Steve


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

math
42
August 27, 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

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