Wednesday

September 17, 2014

September 17, 2014

Total # Posts: 25,003

**Math**

Nope. Forgot the 60 degree angle. In that case, recall that cos 60 = 1/2
*September 17, 2014*

**Math**

Hint: Think of the ubiquitous 3-4-5 right triangle, scaled up to 6-8-10.
*September 17, 2014*

**n2maths**

50^2 + x^2 = (x+10)^2
*September 17, 2014*

**Math**

It appears that the two boys are less than 10, since adding up all the ages gives only 83 Granny cannot be less than 83-17=66 66+8+9=83 67+7+9=83 68+6+9=68+7+8=83 69+5+9=69+6+8=83 71+5+7=83 72+4+7=72+3+8=72+2+9=83 73+3+7=83 WE HAVE A WINNER!
*September 17, 2014*

**maths**

having what as 5000m?
*September 17, 2014*

**Algebra**

correct both times. In general, for a given set of problems, U is the Universe. Any subsets being discussed will always be subsets of U, or things are poorly set up.
*September 17, 2014*

**Algebra**

so, use one. wolframalpha.com does a good job
*September 17, 2014*

**math**

We have two lines, with slopes (-5-b)/10 and (-3)/(-6-a) If the lines are perpendicular, then (-5-b)/10 * (-3)/(-6-a) = -1 (b+5) = 10/3 (a+6) b = 5/3 (2a+9)
*September 17, 2014*

**Math**

We have a=7 d=12 So, when does Tn exceed 1000? Tn = 7+12(n-1) = 12n-5 12n-5 < 1000 12n < 1005 n < 83.75 So, the first 83 terms are less than 1000 Similarly for 2000
*September 16, 2014*

**Math**

clearly, a = 28 r = 1/6 So, S = a/(1-r) = 28/(5/6) = 33.6
*September 16, 2014*

**Math**

since x has an unspecified value, there is no way to round it. So, I assume you want to solve the equation, and round the answer to two decimals. 2x^4+3x-4 = 0 There are only two real roots, x = -1.43 or 0.90 The graph is at http://www.wolframalpha.com/input/?i=2x^4%2B3x-4 Or...
*September 16, 2014*

**math**

16/10 is the same as 1.6
*September 16, 2014*

**math**

probably because you have learned by heart some simple results, like sums totaling 10, or 5, etc. The mechanics never change, so if some are easier, it just means that you have learned some patterns that you can recognize.
*September 16, 2014*

**math**

The language is very confusing in its use of present and past tenses. When is "now"? The end of the year? If girls joined the band, how come there are now fewer students than at the beginning? I cannot believe the question was posed as you state. If so, the problem ...
*September 16, 2014*

**trigo**

First, vessels travel on headings, not bearings. 200 @ 245° = (-181.262,-84.524) 50 @ 320° = (-32.134,38.302) add them up to get (-213.396,-46.222) = 218 @ 258°
*September 16, 2014*

**Algebra**

correct.
*September 16, 2014*

**Calculus**

f(a) = 3a^2-2a f(a+h) = 3(a+h)^2 - 2(a+h) = 3a^2 + 6ah + 3h^2 - 2a - 2h f(a+h)-f(a) = 6ah + 3h^2 + 2h So, (f(a+h)-f(a))/h = 6a + 3h + 2 So, with various values of h, f(a+1) = 6a+3+2 f(a+0.1) = 6a + 0.3 + 2 = 6a + 2.03 and so on. Nothing difficult, just algebra I.
*September 16, 2014*

**Math**

That's a lot of work. Just think about it a bit. You start with 1 gram. 3 days later the amount left is 0.1 gram If the half life is k days, then (1/2)^3k = 1/10 3k = log(.1)/log(.5) = 3.32 So, k = 1.11 R(t) = (1/2)^(1.11t) But, since we like things base e for our ...
*September 16, 2014*

**Math**

just solve for x in the equation −0.01x2 + 130x − 180,000 = 174900
*September 16, 2014*

**math**

The expression factors as (3x-1)(x+2) However, there are lots of other ways to divide things up. For example, if x=3, the area is 8*5 = 40, but those are not the only two ways to get two numbers which multiply to 40.
*September 16, 2014*

**math help**

Just plug in the value: (4x+8)(x+2)(2x+4) / 2((4x+8)(x+2)+(4x+8)(2x+4)+(x+2)(2x+4)) = 8(x+2)^3 / 28(x+2)^2 = 2(x+2)/7
*September 16, 2014*

**Math**

steps to what?
*September 16, 2014*

**math**

The answer is r^2-5 + 5/(r^2-2) See the details when you enter your polynomials at calc101.com. Click on the long division button.
*September 16, 2014*

**Math**

after n hours, the length is 3*3^(n-1) = 3^n Now just plug in n=3
*September 16, 2014*

**math**

since the circumference is 8*3.14, the diameter is 8
*September 16, 2014*

**math**

f = m+5 f+5 = 2m m+5 + 5 = 2m m = 5
*September 16, 2014*

**math**

the first car went 20 miles before the 2nd car started out. So, it made up 20mi/(5/3 hr) = 12 mi/hr That is, car 2 was going 12 mi/hr faster than car 1, or 72 mi/hr Check: car 1 went 120 miles in 2 hours car 2 went 72(5/3) = 120 miles in 1 hr 40 min
*September 16, 2014*

**Algebra**

g(f(x)) = {g(8),g(5),g(-5),g(3)} = {10,9,3} g(3) is undefined
*September 16, 2014*

**Algebra 2**

y = 2x-1 + 3/5
*September 16, 2014*

**Algebra 1**

your solution is correct. To check on (180,-30), plug it in 8(180)+5(-30) =?= 900 But, how do you sell -30 student tickets?
*September 16, 2014*

**Math**

(a) max height occurs at t = -87/-32 (b) just solve for t when h=0
*September 16, 2014*

**Trig**

if the wind speed is w and the plane's speed is s, then (w cos-135°,w sin-135°)+(s cos63°, s sin63°) = (550 cos64°,550 sin64°) -.707w + .454s = 241.104 -.707w + .891s = 494.337 w = 31.089
*September 16, 2014*

**c**

or, 1/4 + 1/(x+9) = 1/x x = 3 so, the 2nd hose takes 12 hours check: in 1 hour, the two hoses fill 1/4 + 1/12 = 1/3 of the pool.
*September 16, 2014*

**college algebra**

If you mean the increase occurs only for those in excess of 3000, then you have (20)(3000) + (20+0.01)(x-3000) = 153525
*September 16, 2014*

**Coordinate Algebra**

In point-slope form, we have y-4 = -3(x-5)
*September 16, 2014*

**Math**

what, you don't know how to do any of those steps?
*September 16, 2014*

**Calculus**

Well, let's see what they have said. dL = k dT L0 so, L = k*L0*T + C Now you can plug in initial conditions or boundary conditions to determine k and C
*September 16, 2014*

**Math Proof:**

Looks to me like you just have to write the definition of inf and sup. a is not in E, but is greater than any other number less than any element of E.
*September 16, 2014*

**physics**

Looks like 600N/m^2 assuming it is lying flat on one face
*September 16, 2014*

**math**

1 = 1^3 8 = 2^3 27 = 3^3 so, what do you think?
*September 16, 2014*

**Math quadratic word problem**

Your very first line is off. For a triangle, A = bh/2
*September 16, 2014*

**Trigo**

Draw a diagram. If the pole has height h, and the tip of the shadow is x horizontally away from the pole, then (82 sin8° + h)/x = tan28° x/82 = cos8° Now, eliminate x to get (82 sin8° + h)cot28° = 82 cos8° Now just solve for h
*September 16, 2014*

**math**

2/5 + 1/3 = 6/15 + 5/15 = 11/15 That leaves 4/15 as woodwinds. So, 2/15 are clarinets 2/5 * 240 * 1/8 = 12 are tubas
*September 16, 2014*

**Plural of economix?**

.
*September 16, 2014*

**math**

0.9 x 5.2 / 0.2 x 25 = 585 (0.9 x 5.2) / (0.2 x 25) = 0.936 Pick the one you mean and then subtract 120 to find the missing value.
*September 16, 2014*

**physics**

distance = speed * time so, plug and chug
*September 16, 2014*

**math**

the only purpose I can see is readability. The math is identical, regardless of representation.
*September 16, 2014*

**Calculus**

It is not always possible to find such a tangent line. Consider the graph of y=x^2. No tangent line will pass through the point (0,1), since it lies inside the parabola. However, assuming that the point is properly placed, we need to find a point (x,y) on the graph such that ...
*September 16, 2014*

**Math Problem (please help)**

wolframalpha is your friend: http://www.wolframalpha.com/input/?i=6x^4+%E2%88%92+13x^3+%E2%88%92+144x^2+%2B+325x+%E2%88%92+150
*September 15, 2014*

**Calculus-Math**

Rolle's Theorem says that since C(2)=C(15), there is some value 2<c<15 such that C'(c) = 0. dC/dx = 12(2x^2-6x-9)/(x(x+3))^2 dC/dx=0 when 2x^2-6x-9=0, or x = 3/2 (1±√3) or, x = -1.1, 4.1 So, your answer of 4 is correct. The graph at http://www....
*September 15, 2014*

**math**

since 1/7 does not evenly divide 9/10, the answer is no.
*September 15, 2014*

**math**

#1 -14.8 + 22.6 = 7.8 #2 (x - 16) + 5 = -15 x-16+5 = -15 x-11 = -15 x = -4 #3 5 = –(–z + 3) 5 = z-3 8 = z #4 t - 17 = -11 Your choice is the situation where the temperature started at 17° and then decreased by t°.
*September 15, 2014*

**Math**

The number is negative, so it is -2.78 Its absolute value is +2.78 So, the distance between the two is 5.56 They are equal distances from 0, but in opposite directions.
*September 15, 2014*

**pre-calculus**

If there are x lamps, then 54x = 3564 So, there are 66 lamps sold If they cost c each, then 66c + 396 = 3564 So, the cost is 48. So, for 145 lamps, the profit is 145*(54-48) - 396 = 474
*September 15, 2014*

**Grade 11 Math functions**

All polynomials have domain xeR. All reals. Your domain makes no sense. xeR includes all values, including 2<x<3. Since y = (x - 5/2)^2 - 1/4, its minimum is at y = -1/4. So, the range is all reals y >= -1/4.
*September 15, 2014*

**geometry**

since the median is the middle value, the probability is 1/2 that a random value is above or below the median.
*September 15, 2014*

**math**

how long does it take to land? 9.8 - 4.9t^2 = 0 Now, with that t, how far does he go at 15.2 m/s? That would be 15.2 t
*September 15, 2014*

**algibra1**

If the 2nd side is x, then 2x + x + x+4 = 24 Now just find x, which is the 2nd side. Then it is easy to figure the other two sides.
*September 15, 2014*

**Pre-Calculus/Trigonometry**

correct
*September 15, 2014*

**Math**

use the law of cosines: d^2 = 18^2 + 11^2 - 2(18)(11)cos 70°
*September 15, 2014*

**Math**

actually, 711,311 is the only answer. If the hundreds digit is 3, then the remaining 4 digits must add to 4. They must all be 1's.
*September 15, 2014*

**dav**

the area scales as the square of the sides, so the sides are in the ratio √15/√25
*September 15, 2014*

**Math**

B clearly not, since 1+1=2, which is not in B T clearly, since adding any two multiples of 4 yields another multiple of 4. F yes, since adding any two integers yields another integer greater than 4. No idea. What is W?
*September 15, 2014*

**algebra**

If x is invested at 9%, then .068(4600) + .09(x) = .08(4600+x)
*September 15, 2014*

**algebra**

If x is drained, then .25(6-x) + 1.00(x) = .33(6)
*September 15, 2014*

**algebra**

if we call x the flying time for the 2nd plane, then since distance = speed * time, 660x + 540(x+1) = 1800 x = 1.05 hours So, how far did the first plane travel in 2.05 hours?
*September 15, 2014*

**Math 221**

(a) looks to me like it will be (30/110)(29/109)(28/108) Do (b) similarly. This is just like the problems involving drawing from a deck of cards.
*September 15, 2014*

**Math**

do the graphs at wolframalpha.com match your own? There, the two lines are clearly reflections in the x-axis.
*September 15, 2014*

**Math**

to reflect over the x-axis, y values change sign. So, f(x) -> -f(x), so it is -f(x) = 3x-5 Note that -f(-x) = -(-3(-x)+5) = -(3x+5) = -3x-5 See the reflection at http://www.wolframalpha.com/input/?i=plot+y%3D-3x%2B5%2C+y%3D3x-5
*September 15, 2014*

**algebra**

No sweat. Getting from the words to the algebra is half the battle. Do lots of word problems. They help you think mathematically.
*September 15, 2014*

**algebra**

If the cost is x, then x/4 = x/3 - 4000
*September 15, 2014*

**algebra**

I'll do one; you try the others. If you get stuck, come on back and show where. 5/13 t = -9 multiply by 13/5 to cancel the 5/13: t = -9(13/5) t = -117/5 I suspect #3 has a typo
*September 15, 2014*

**Algebra**

I think the easiest way is to use the point-slope form of the equation, since they gave you a point and a slope. Recall that the equation for a line through (h,k) with slope m is y-k = m(x-h) So, you have y+3 = -2(x+1) Now work with that: y+3 = -2x-2 y = -2x-5
*September 15, 2014*

**calculus**

(a) the period of sin(kt) is 2π/k, so we have period 2π/π = 2 seconds. (b) since the minimum of sin(kt) = -1, our minimum is -3/5 (c) since the length of the rod is 1, x^2+y^2 = 1 That means that y^2 = 1/25 (16 + 9cos^2(πt)) when x = 3/10, t=1/6, y = √...
*September 15, 2014*

**Maths**

since most bridges are level, I find the term questionable. I expect that in such problems, we're talking about the apex of the supporting structure, which is often a parabola. That would then be the vertex of the parabola.
*September 15, 2014*

**pre calc**

If x oz. of gold, we have 6000x + 50(1-x) = 200
*September 15, 2014*

**Pre Calc**

If normally the speed is x, then 90/x = 1 + 90/(x+3)
*September 15, 2014*

**Pre Calculus**

If the speed is x, then since time = distance/speed, 48/(x+4) = 32/(x-4)
*September 15, 2014*

**math**

Hint: Draw a diagram. You should recall that a common right triangle with integer sides is 7-24-25.
*September 14, 2014*

**AP Calculus**

You have y' = (2x-y)/(x-2y) at x = -2, y = -1±√13, so there will be two lines tangent to the ellipse at x = -2. for y = -1+√13, y' = (-4+1-√13)/(-2-2(-1+√13)) = (-3-√13)/(-2√13) = (13+3√13)/26 So, the line is y = (13+3&#...
*September 14, 2014*

**Algebra**

c+7 <= 3 c <= -4 So, plot a dot at -4 and shade everything to the left.
*September 14, 2014*

**Math**

since there are 10 choices for each digit, that would mean there are 10^7 possible numbers. Actually, SS numbers have 9 digits.
*September 14, 2014*

**Math**

Since there are 2 choices for each answer, there are 2^6 = 64 ways to answer all the questions. If some may be left unanswered, then we have 2^6 * 6C6 ways to select and answer all 6 2^5 * 6C5 ways to select and answer 5 2^4 * 6C4 ways to select and answer 4 and so on. Adding ...
*September 14, 2014*

**algebra**

just plug in either of the points. They must satisfy the equation, so if we pick (-8,-10), (-8+1.5)^2 + (-10+7)^2 = r^2
*September 14, 2014*

**algebra**

We need to rearrange terms into the standard equation: 5x^2−6x+5y^2+8y−9=0 5(x^2 - 6/5 x) + 5(y^2 + 8/5 y) = 9 (x^2 - 6/5 x + 9/25) + (y^2 + 8/5 y + 16/25) = 9/5 + 9/25 + 16/25 (x - 3/5)^2 + (y + 4/5)^2 = 70/25 Now you can read off the desired data.
*September 14, 2014*

**algebra**

domain: x >= 0 range: y >= 16
*September 14, 2014*

**Math**

If the original width is x length is 2x With a=2, our new box has volume (a)(x-2a)(2x-2a) = 32 2(x-4)(2x-4) = 32 2(x-4)(2x-4) - 32 = 0 4x(x-6) = 0 x = 6 So a sheet 6x12 will be cut to a box 2x2x8 with volume = 32
*September 14, 2014*

**Physics !!!!!!!!!!!!!!!!**

v(t) = Vo + at where a is negative, in this case. s(t) = Xo + Vot + 1/2 at^2 where a is negative If all you wanted was the formulas, why not just look in your text book? They are presented there. I'm sure.
*September 14, 2014*

**Limits**

1/(3+x) -> 1/3 1/(3x) -> ∞ clearly the sum is ∞ However, the left and right limits have opposite signs.
*September 14, 2014*

**PLEASE HELP! Math**

Liz is going 6 mi/hr faster than Mandy. By the time she starts, Mandy has gone (1/3)(30) = 10 miles So, at 6 mi/hr, it will take 10/6 = 1 hr 40 min to catch up with Liz. So, that will be 2 hours after Mandy started, or 1:00 pm. Or, you can plot both cyclists' positions as ...
*September 14, 2014*

**Math**

since each card has a 1/52 chance of being drawn, that would be (1/52)^12
*September 14, 2014*

**math**

75*42*(1/3) ft^3 * 7.5gal/ft^3 = 7875 gal
*September 14, 2014*

**Geography?**

Don't see much geometry in that ...
*September 14, 2014*

**Algebra 1**

start off with the point-slope form, since that is what they gave you: y+3 = -2(x+1) and rearrange things to fit the slope-intercept form.
*September 14, 2014*

**math**

well, just solve for x in -0.01x^2 + 130x - 180000 = 174900 x = 3900 or 9100
*September 14, 2014*

**AP CALC. AB**

#1: when is the denominator zero? When 1+sinx = 0 sinx = -1 x = 3π/2 + 2kπ Since f(-5) > 0 and f(-1) < 0, f(x)=0 only for a single value of x between -5 and -1. I assume the given choices included such a number.
*September 14, 2014*

**math**

2000000cm / (65π cm/rev) = 979.4 rev
*September 14, 2014*

**algebra**

Assuming you want to solve for x, x^2+x-1 = 0 looks like you need the quadratic formula. See http://www.wolframalpha.com/input/?i=x2+%3D+%E2%88%92x+%2B+1
*September 14, 2014*

**algebra**

(z-1)^2 = -4 z-1 = ±2i z = 1±2i
*September 14, 2014*

**algebra**

just solve -16t^2 + 200t = 380 -16t^2 + 200t - 380 = 0 Now just use the quadratic formula to find the roots.
*September 14, 2014*

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