Thursday
February 11, 2016

Posts by Steve

Total # Posts: 37,543

Calculus 1
by l'Hospital, (a) -> (1/x + 2)/(2x) -> 3/2 (b) -> 2x/e^x -> 2/e^x -> 0
November 19, 2015

Algebra I
all correct. good work
November 19, 2015

Maths
xy=800, so x == 800/y x+2y = 800/y+2y for minimum value, you need -800/y^2 + 2 = 0 y=20 This is just like the fencing problems where minimum fencing for 3 sides of a rectangle is desired. The amount is evenly divided between the x's and the y's
November 19, 2015

math
sounds like the response to a question on Jeopardy! Want to revise the syntax?
November 19, 2015

math
that would be correct, since then the sin curve is above the cos curve.
November 19, 2015

math
To get the algebraic (signed) area, just do ∫[-π/2,π/2] cos(t)-sin(t) dt = 2 But that value subtracts the area where cos < sin. If you want the physical area, you need to break up the region at π/4. http://www.wolframalpha.com/input/?i=%E2%88%AB[-%CF%80...
November 19, 2015

math
cost: 40 desired revenue: 40*1.10 = 44 now divide that by the 80 good bananas to get the price for each banana.
November 18, 2015

math
cost: (120 * 1/6) + (120 * 1/5) = 44 sales: (120+120)/4 = 60 profit: 60-44=16 % profit = 60/44 = 15/11 15/11 - 1 = 4/11 = .3636 = 36 4/11 % It makes it harder to arrive at the solution when you have typos in the problem...
November 18, 2015

Math
clearly, the extra 4 balls added 760 g now do the math.
November 18, 2015

Math
p=3q q = r-1.1 r = p-1.3 q = p-1.3-1.1 q = 3q-2.4 ...
November 18, 2015

Identities
cos2x/sin2x + sinx/cosx cos2x/sin2x + 2sin^2 x/(2sinx cosx) (cos2x + 2sin^2 x)/sin2x (1-2sin^2 x + 2sin^2 x)/sin2x 1/sin2x csc2x
November 18, 2015

Mathematics
this is explained here: http://socratic.org/questions/how-do-you-use-limit-to-prove-the-derivative-of-secx-secxtanx google is your friend. Use it.
November 18, 2015

trigonometry
parent is clearly sin(θ) -34sin(10θ+10π) = -34sin(10(θ+π)) period is 2π/10 phase shift is -π amplitude is 34 vertical shift is -14 midline is y = -14 see the graph at
November 18, 2015

Pure Mathematics
one way is Gaussian elimination, as shown here: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx Just enter your matrix of coefficients
November 18, 2015

Calculus III
The integral is easy enough, but I sure don't see where symmetry helps, especially in that region R.
November 18, 2015

Mathematics
nope. it cannot. Lose the 5
November 18, 2015

Math
Come on... 9.50 - 7.18 = 2.32
November 18, 2015

Math
well, did you actually do the subtraction? 50-18 ≠ 48
November 18, 2015

Math
ahem - you multiply by 100 to turn a number to a percentage: 1 = 100% 10 = 1000% 503,000,000 = 5.03x10^8 5.03x10^8 = 5.03x10^10 % But that's a different problem, eh?
November 18, 2015

Math
1.331
November 18, 2015

Math
The 15th term comes after 14 multiplications. So, 4n^14
November 18, 2015

Mathematics
tan2x = sin2x sin2x/cos2x = sin2x sin2x(cos2x-1) = 0 so, sin2x=0 or cos2x=1 That help?
November 18, 2015

Math
tanθ = sinθ sinθ/cosθ = sinθ sinθ = sinθ cosθ sinθ - sinθ cosθ = 0 sinθ(1-cosθ) = 0 No idea where the 5 came from.
November 18, 2015

Algebra 1- Just one question
4 shirts = 1 pants 8 shirts = 2 pants so, 2*18.98 = ?
November 18, 2015

Math
if 25f = 100 f = 25f/25 = 100/25 = 4 If I told you 2*f=10, would you have trouble finding f? Probably not. So, when confronted with uncomfortable numbers, try solving the same problem with easy numbers, and then follow the same steps.
November 18, 2015

Pre Calculus 1
the decay function after t years is 0.3^(t/4) You want the half-life, or 0.5^(t/k) 0.5^(t/k) = 0.3^(t/4) t/k log 0.5 = t/4 log 0.3 k = 4log.5/log.3 = 2.3 so, you have (1/2)^(t/2.3) and thus the half-life is 2.3 years for the other, the population is 40*1.03^t
November 18, 2015

Math Asap
no, it would be an integer :-)
November 18, 2015

Math Asap
sorry; √9 is a rational number. In fact, it is 3, an integer. Most of the time, a √ is irrational, but not always.
November 18, 2015

Math
the -ir prefix means "not"
November 18, 2015

math
2(x+y) = 3(x-y)+8 (x+y)/2 = (x-y)+1 The numbers are 7 and 3
November 18, 2015

math
(a) clearly, 20 * -2 (b) 10*4 - 8*2 + 2*0 (c) 4*c - 5*2 = 14 (d) 20-(c+5) using the value for c above
November 18, 2015

Analytic Geometry
Line Q has slope -1/5; so do all parallel lines Perpendicular lines P therefore have slope 5 So, just use the point-slope form of a line to write the needed equations. Now, what is the slope of a line 45° clockwise from P? If P makes an angle Ø with the x-axis, then...
November 18, 2015

math
If you mean r(t) = 3+t^2, then dr/dt = 2t If you really mean rt = 3+t^2, then r = 3/t + t dr/dt = -3/t^2 + 1
November 18, 2015

Algebra II
clearly the 1st step is to factor out 3x: 3x(2x^4-17x^2-9) Then you have a quadratic in x^2, which you can factor with a little work, to get 3x(x^2-9)(2x^2+1) The x^2-9 is easy, giving 3x(x-3)(x+3)(2x^2+1)
November 18, 2015

Scientific Calculus
if your constant is the k in e^-kt, then you have e^-0.000124t = 0.56 Now you can calculate the approximate age. If by constant of proportionality you mean that that fraction is lost each year, then you have 0.999876^t = 0.56
November 18, 2015

geometry
Not sure how he can turn from the horizontal, unless he goes uphill, but whatever the direction, just turning 30° in the opposite manner will put him on a course parallel to his original one.
November 17, 2015

Math
m = 3f 5m/6 = b 2/3 f = g b = g+121 So, solve all that and you get m/6 + f/3 = 77
November 17, 2015

Geometry
XY = √(4h^2+4h^2) XZ = 4h YZ = √(4h^2+4h^2) Now just see whether XY^2 + YZ^2 = XZ^2
November 17, 2015

PHYSICS

November 17, 2015

PHYSICS

November 17, 2015

Algebra 2
The total value is 355. You have just counted the bills, rather than adding their values. Clearly, n+f+t cannot be both 355 and 120! n+5f+10t = 355 n+f+t = 120 n = 2(f+t) The way you wrote the last equation, you indicated that adding the 5's and 10's you had twice as ...
November 17, 2015

Math
if A is 62, so is D If B is 13, so is E So, since D+E+F=180, just plug in your values for D and E.
November 17, 2015

Algebra 1
d = 40 + 65h
November 17, 2015

Radicals
fractional exponents are roots, where the radical index is the denominator. So, you have n^3/4 p^5/4 = (n^3 p^5)^1/4 = ∜(n^3 p^5) or, if you want proper fractions for the roots, = p∜(n^3 p)
November 17, 2015

Integer Exponents
minus powers swap between top and bottom in fractions. So, if you want all positive exponents, (6abc^2) / 15a^2 * (2bc / 3a)^-2 = (6abc^2) / 15a^2 * (3a / 2bc)^2 = (6abc^2 * 3a)/(15a^2 * 2bc) = 18a^2bc^2 / 30a^2bc = 3c/5 try the other one the same way. We can check your work.
November 17, 2015

Algebra - eh?
If the boards are h inches high, then the soil is (h-4)" deep. If the outside dimensions are x and y, with x<y, x=2h y=4h So, the inner dimensions are (x-8) and (y-12), and using the given volume, (h-4)(x-8)(y-12) = 3136 h(2h-8)(4h-12) = 3136 h = 11 inches. Check: The ...
November 17, 2015

Math
so, did you draw a diagram and see the similar triangles?
November 17, 2015

@Damon - typo
make that -4z... But I'm sure the student caught the typo.
November 17, 2015

Calculus
Fx = 3x^2 + 2y^3 Fy = 6xy^2 - 9 Fxx = 6x Fxy = 6y^2 = Fyx Fyy = 12x Now just plug in the numbers
November 17, 2015

ipc
well, v changes by +3.2 m/s every second. So, what is that after 6 seconds?
November 17, 2015

math plz help
like terms have the same variable. So, ...
November 17, 2015

Trigonometry
3 = 3 cis0 2+3i = √13 cis x where tan x = 3/2 now divide, and you get 3/√13 cis(0-x) = 3/√13 (cosx - i sinx) = 3/13 (2/√13 - 3/√13 i) = 6/13 - 9/13 i
November 17, 2015

Trigonometry
b^2 = a^2+c^2-2ac cosB So, plug in your numbers and solve for cos B Then B is cos^-1 of that number.
November 17, 2015

Trigonometry - eh?
planes fly on headings distant objects have bearings I thought you said the plane flew SW from C to A. Why then do you ask for it? Typo?
November 17, 2015

Calculus
Partials are easy. Just consider the extra variables as constants. Wx = 4xy-6yz Wy = 2x^2-6xz+10z^2 Wz = -6xy+20yz Now just plug in the numbers.
November 17, 2015

Calculus
∂R/∂x1 = 700 - 4x1 - 4x2 ∂R/∂x2 = 700 - 4x1 - 4x2
November 17, 2015

math
since 2 <= f(x) <= 3, and the width of the interval is 6, 2*6 <= ∫f(x) dx <= 3*6
November 17, 2015

math
oops: y=64
November 17, 2015

math
4x = 7y x-y = 48 x - 4x/7 = 48 3x = 7*48 x = 7*16 = 112 So, y = 4*16 = 56 check: 112-56 = 48
November 17, 2015

calculus
If the pen is x by y, then we have xy=720 p = 2x+y = 2x+720/x dp/dx = 2 - 720/x^2 x^2=360 x = 6√10 So, the pen is 6√10 by 12√10 As always, the area is max when the fence is divided equally among lengths and widths. clearly the cost per foot of the fence does ...
November 17, 2015

VERTEX,FOCUS AND DIRECTRIX
x^2+3y-9 = 0 x^2 = -3(y-3) now use what you know about the parabola x^2 = 4py to discover the properties. In this case, the vertex is at (0,3).
November 17, 2015

Math
f(x) = x^3(x^2+7) Now you can easily state the zeroes and their multiplicities.
November 16, 2015

math - linear programming
If there are x boxes of nuts and y boxes of fruit, you want to maximize p=7x+8y subject to 2x+4y <= 1000 2x <= 900 2y <= 400 Now use your favorite linear programming tool.
November 16, 2015

Calc
v = 1/3 πr^2 h = π/3 (d/2)^2 h = π/12 h^3 dv/dt = π/4 h^2 dh/dt Now just plug in your numbers.
November 16, 2015

Algebra 2
correct
November 16, 2015

Duplessiss primary
well, 97 = 6*16 + 1
November 16, 2015

Geometry
p>p'(-2,-6) for the glide reflection where the translation is (x,y)>(x,y-1) and the line of reflection is x=1. What are the coordinates of P? The answer is (4,-5) I'm looking for the steps of how to get to the answer. 69-year-old grandpa trying to help grandson
November 16, 2015

Algebra
if each value of y is the same multiple of x, it varies directly. If you can multiply each value of x by some number, k, and get the corresponding value of y, then k is the constant of variation, and y = kx
November 16, 2015

algebra
Parallel lines have the same slope. So, you want a line with slope = -1 Now you have a point and a slope. Use that to get y+2 = -1(x-2) y+2 = -x+2 y = -x Or, given y = -x-2, you know that any parallel line will be y = -x + b So, plug in x=2 into your equation, and you have y...
November 16, 2015

math
divide both sides by -13 what do you get?
November 16, 2015

Calculus
actually, that's a repeated linear. I get 1/(x+2) + 2/(x+2)^2 - (x-2)/(x^2+4)
November 15, 2015

College Algebra
just put the words into symbols. If the numbers are x,y,z, respectively, then we are told that y=z+5 x=2y x+y+z=87 Now just solve the equations.
November 15, 2015

math
|6-4| = |6|-|4| = 6-4 = 2 |4-6| ≠ |4|-|6| = 4-6 = -2 -b is the additive inverse of b, so the statement is always true.
November 15, 2015

Quadratic Functions Applications
#1 -4t-4.9t^2 = -1750 #2 (w+2*3)((w+6)+2*3)-(w)(w+6) = 288 #3 If Mary Beth takes x hours, 1/x + 1/(x+6) = 1/4 #4 clearly a 9x9 square fits the bill Since a square has maximum area for a given perimeter, no other rectangle can do the job.
November 15, 2015

pre calculus
you gotta use the tan^-1 button on your calculator Or, the 2ndtan or invtan sequence Or go to any online calculator and evaluate arctan(.6524)
November 15, 2015

Trigonometry
expanding things a bit, we have 4cos^2x - 4sin^2x + 6sinx cosx = 2 2cos^2x + 3sinx cosx - 2sin^2x = 1 (2cosx-sinx)(2sinx+cosx) = 1 Now divide by cos^2x and you have (2-tanx)(2tanx+1) = sec^2x 4tanx - 2tan^2x + 2 - tanx = 1 + tan^2x 3tan^2x - 3tanx - 1 = 0 tanx = (3±&#...
November 15, 2015

Math
You have the expression. The value can be discovered as below: 8[(20-4)-6] 8[-16-6] 8[-22] -176
November 15, 2015

maths plz help
1/a + 1/b = 1/3 1/b + 1/c = 1/5 1/a + 1/c = 1/7 add them all up and you get 2/a + 2/b + 2/c = 1/3 + 1/5 + 1/7 = 71/105 1/a + 1/b + 1/c = 71/210 So, it takes 210/71 ≈ 2.95 hours for all three to do the job. That's rather surprising, isn't it?
November 15, 2015

Geometry
no idea. Where are B and C?
November 15, 2015

math(quadratic equation)
t+k=30 (t-6)(k-6)=80 (t-6)((30-t)-6) = 80 (t-6)(24-t) = 80 24t-t^2-144+6t = 80 t^2 - 30t + 224 = 0 (t-14)(t-16) = 0 ...
November 15, 2015

math
The building is 10 times as far away, so it is 10 times as tall as the tree.
November 15, 2015

math
the larger the divisor, the smaller the quotient. So, as x gets incredibly large, 1/x gets incredibly small. So, as x gets infinitely large, 1/x gets infinitely small, or zero. So, yes, all reciprocal functions have y=0 as their horizontal asymptote. (depending on just what ...
November 15, 2015

math
a^2+ab-ac-bc = a(a+b)-c(a+b) = (a-c)(a+b) (a^2-c^2)/(a-b) = (a-c)(a+c)/(a-b) Now do the division (multiply by the reciprocal) and the (a-c) factors cancel, leaving (a+b)(a-b)/(a+c) = (a^2-b^2)/(a+c)
November 15, 2015

math
(p-2q)/(p+2) = 3q p-2q = 3q(p+2) p = 2q+(3p+6)q p = (3p+8)q q = p/(3p+8)
November 15, 2015

math
(1+.04/4)^(4t) = 5 Now solve for t
November 15, 2015

college algebra
1/30 + 1/45 = 1/x x = 18 minutes
November 15, 2015

Maths
Ariel is a person's name An aerial is an antenna recall the definition of tan(x) and you will see that the aerial's height is 200tan58° - 200tan56°
November 15, 2015

College algebra
in 2h the 1st pipe has filled 1/3 of the pool. 1/6+1/8 = 7/24 That's how much the two pipes together can fill in an hour. So, to fill the remaining 2/3 of the pool takes (2/3)/(7/24) = 16/7 hours
November 15, 2015

Calculus 1
f = x^2/(x-4)^2 f' = -8x/(x-4)^3 f" = 16(x+2)/(x-4)^4 f is concave up where f" > 0, or x > -2 concave down then, is everywhere else, or x < -2 Unfortunately, there is an asymptote at x=4, so f is concave up on (-2,4)U(4,∞). The graph is concave up ...
November 15, 2015

calc 2
The curves intersect at π/6, not π/4. The leaves of the rosette return to (0,0) at multiples of π/4, but that's not where the circle intersects the rosette. Using the 8-way symmetry, I'd just integrate over [0,π/6], so a = 8∫[0,π/6] 1/2 (...
November 15, 2015

calc 2
I'd integrate from -a to a
November 15, 2015

Pre cal
use the law of cosines. The short diagonal is 7^2+4^2-2*7*4cos55° The longer diagonal lies opposite the supplementary angle, so it is 7^2+4^2+2*7*4cos55°
November 15, 2015

Algebra
looks good to me
November 15, 2015

Precalculus
9 ∑ 20-1.5n n=0 9 ∑ 40(-1/4)^n n=0
November 14, 2015

Calculus 1
f'(t) = -16sin(t) + 16cos(t) f'=0 when sin(t)=cos(t) t = π/4 f(0) = 16 f(π/4) = 16/√2 + 8 = 8(1+√2) > 16 f(π/2) = 0 So, it looks like max = 8(1+√2) min = 0 Let's check the graph: http://www.wolframalpha.com/input/?i=16+cos+t+%2B+...
November 14, 2015

Advanced Functions
co-sine means sine of co-mplimentary angle. so, cos(90-x) = sin(x) and your function is just -sin(x) Or, you can apply the difference formula, but that is done before the negative -[cos(90-x)] = -[cos90cosx+sin90sinx] = -sinx
November 14, 2015

Math: Word Problem
well, 450 = 30*15, and 15+30+15=60
November 14, 2015

algebra
since distance=speed*time, if the boat's speed is x, we have 3(x+6) = 5(x-6)
November 14, 2015

further algebra
let us assume that the ball is at rest when it bounces less than 1mm. Starting at 30,000 mm, we find that on the 12th bounce it has "stopped" bouncing. So, with r=0.4, and noting that 12 bounces involve a round trip (up and down), we have the sum of a geometric ...
November 14, 2015

Algebra
if the digits are x and y, the value is 10x+y 10x+y = 3(x+y) 10x+y+45 = 10y+x The number is thus 27 check: 27 = 3*(2+7) 27+45=72
November 14, 2015

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