Thursday

February 11, 2016
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*

**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*