Monday

July 6, 2015

July 6, 2015

Total # Posts: 32,134

**math**

If the apparent heading of the plane is (65+θ)°, and the plane's speed is v, then 60+v*sin65° = 750 sin(65+θ)° 750 cos(65+θ)° = v cos65° v = 695 and θ=1.6° So, the plane needs to fly at N66.6°W and the plane's ground ...
*June 3, 2015*

**Math 7**

draw a diagram. Using similar triangles, you can see that if the tree has height h, h/25 = 10/6 The ratio of height:shadow is the same for both pole and tree.
*June 3, 2015*

**Consumer math**

^ and log are inverse operations x+8 - 8 = x x/8 * 8 = x (√x)^2 = x log88x = x 8log8x = x The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier. The definition of log8x is that power ...
*June 3, 2015*

**Astronomy**

If you are talking about the time when the planets are on the same side of the sun, then only the planets outside Mars' orbit would exhibit retrograde motion, since Mars travels faster in its orbit.
*June 3, 2015*

**Algebra**

If the width, length, height are x,y,z then you know that 2(xy+xz+yz) = 160 y = 2x y = z-4 Now just make some substitutions, and you will find that z=9
*June 3, 2015*

**math**

if there are x 6d nails, and y 10d nails, then you have been told that x+y = 8 x = y+2
*June 3, 2015*

**Algebra**

apparent to whom? measured in what units? The shuttle does not orbit on the surface of the earth, so at what altitude?
*June 3, 2015*

**math help**

Don't know what's missing, but since you have a - sign, I'll sssume your + key is malfunctioning. If we go with x-3+2y=0 then x = 3-2y Plug that into the other equation and you have 2y^2-3(3-2y)^2-4(3-2y)y=9 or, 2y^2-24y+36 = 0 Then, using the quadratic formula, y...
*June 3, 2015*

**Math**

maximize p=3x+6y subject to 6x+9y <= 300 5x+4y <= 180 Now just draw the lines and find the vertices. There are many helpful online sites to verify your work. One is at http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html
*June 3, 2015*

**Geometry**

The solution to the last one didn't take? Take another look at it, and try your hand on this one.
*June 3, 2015*

**physics**

since velocity involves final displacement, not total distance covered, you have 3km/25.5min = 0.1176 km/min in the direction from start to finish.
*June 3, 2015*

**Geometry**

180(n-2) = 10800
*June 3, 2015*

**Math**

15: 9*7 x 10^(6+5) do #16 in like wise.
*June 3, 2015*

**physics**

f1 = <-31.82,31.82> f2 = <44.55,44.55> r = <-8.49,8.49> f3 = <x,y> where -31.82+44.55+x = -8.49 31.82+44.44+y = 8.49 Now just find x and y.
*June 3, 2015*

**math**

The differences are 4,6,8,10,12,... The 2nd differences are 2,2,2,... That means it's a quadratic. a+b+c = 1 4a+2b+c = 5 9a+3b+c = 11 Looks like An = n^2+n-1 So, when is n^2-n-1 = 2549 n^2-n-2550 = 0 (n+50)(n-51) = 0 Looks like A51 = 2549
*June 3, 2015*

**Geometry**

Alas? All was good up till there. The standard equation desired is indeed x^2 + (y-2)^2 =4
*June 3, 2015*

**Geometry**

(x-0)^2 + (y-2)^2 = 2^2
*June 3, 2015*

**math**

Sorry. 3x^2 kx-k makes no sense. Is it 3x^2+kx-k or 3x^2-kx-k ? As it stands, since a b means a*b, you have 3x^2*kx-k = 3k 3kx^3-k = 3x 3kx^3-3x-k = 0 which clearly does not work.
*June 3, 2015*

**math**

You are missing a + or - sign in there.
*June 3, 2015*

**Algebra 1**

221-150 = 71, which is 43 std above the mean!!! Look that up in your Z table! I suspect a typo.
*June 3, 2015*

**Math**

You have 2^3 x^-9 y^12 ----------------------- 4^2 x^2 y^2 which is y^10 / 2x^11
*June 3, 2015*

**Geometry.**

Hmm. Looks to me like ∠D corresponds to ∠A = 24°
*June 3, 2015*

**sat math**

99+99 = 198 B+C = 17 The only way you could get more than that would be if the number ended in 99. But NR+RN = 11(R+N) so R+N would have to end in 99. I think you can see why that cannot be so.
*June 3, 2015*

**Math**

since distance = speed * time, he went 8(1/2) + 55(24/60) miles
*June 3, 2015*

**math**

42
*June 3, 2015*

**Math**

The height changed by -0.5m in one hour. That means that it was 1.71m slightly before it fell to 1.7m. Its rate of change between 9 and 10 am was -0.5 m/hr. So, it was .01 hours before 10 am when the height was 1.71m. .01 hrs = 0.6 minutes, or 36 seconds. So, the height was 1....
*June 3, 2015*

**Derivatives Instantaneous rate of change**

another way to write that is E = Kr^-2 so, using the power rule, dE/dr = K(-2r^-3) = -2K/r^3
*June 3, 2015*

**Math**

As you figured, 19 January starts 66 hours from x=0. So, you want values of x between 66 and 90 (midnight on Jan 19) You can see that there are two periods during that time when y >= 1.7 http://www.wolframalpha.com/input/?i=plot+y+%3D1.05+sin%282pi%2F11.72+x%29+%2B+1.55%2C+...
*June 2, 2015*

**Math**

however, if you are solving an equation, such as -x^2 - 5x + 4 = 0 you can multiply both sides by -1 to get rid of the leading minus sign: x^2 + 5x - 4 = 0 since -0 = 0.
*June 2, 2015*

**Maths**

assuming a 360-day year, that would be 598 * 0.0775/360 * 186
*June 2, 2015*

**Math**

You have y= 3(-4x-2)^2 + 5 = 3(16x^2+16x+4)+5 = 48x^2+48x+17 Now, f = x^2, so x = √f That makes y = 48f + 48√f + 17
*June 2, 2015*

**Math**

looks good to me.
*June 2, 2015*

**Math**

you have f for 0,1,2,3,4 Clearly, since g(x) = -f(2x+3) g(-3/2) = -f(0) = 0 so (-3/2,0) g(-1) = -f(1) = -4 so (-1,-4) and so on
*June 2, 2015*

**math**

Nope. When dividing, subtract powers. What you have is x^14/x^2 That is the same as x x x x x x x x x x x x x x --------------------------------- x x Two of the x's cancel, leaving 12 in the numerator: x^12
*June 2, 2015*

**Pre-Algebra**

2x^2+8-4x+3x-6x^2+7 Collect the coefficients of like powers: (2-6)x^2 + (-4+3)x + (8+7) -4x^2 - x + 15
*June 2, 2015*

**Math help please**

input|1| 2| 3| 4|5 output|9|15|21|27|33 Note that y increases by 6 for each increase of 1 in x. So, your rule will look like y = 6x But, using x=1, 6x=6, but y=9. So, we're too low by 3. That means y = 3+6x You can easily verify that this rule works for the other entries ...
*June 2, 2015*

**Math**

q = d+8 n = 5q 5n+10d+25q = 700 Now just plug and play!
*June 2, 2015*

**calculus**

Well geez. Try amazon.com They will list dozens of calculus books, most of which will be for first-year calculus classes. Or just visit your nearest used-book store. They will surely have several.
*June 2, 2015*

**algebra A055,**

so, how many times you gonna post the same flaming problem?
*June 2, 2015*

**algebra A055,**

you just need t where -0.075t + 3.85 < 3.5 0.075t > 0.35 t > 4.67 So, any year after 1935
*June 2, 2015*

**Math**

8 * 180/pi = 458.4 Even without knowing that, you know that 8 > 2pi, so 360 is the closest of the choices.
*June 2, 2015*

**Math**

you are correct, since (-4,6) is in QII. Recall that cosine is x/r. r^2 = 4^2+6^2 = 42 r = √42 = 2√13 so, your cos is -4/2√13 = -2/√13 Or, as they clumsily put it, -2√13/13
*June 2, 2015*

**algebra Please help**

the max height is at the vertex of the parabola. You know that for at^2+bt+c, the vertex is at t = -b/2a. Then use that to find h of the vertex.
*June 2, 2015*

**algebra**

you just need t where -0.075t + 3.85 < 3.5 0.075t > 0.35 t > 4.67 So, any year after 1935
*June 2, 2015*

**AlgebraII**

You do have some signs mixed up, all right... (2x+3)(3x-2) = 6x^2+5x-6 so, -(2x+3)(3x-2) = -(6x^2+5x-6) = -6x^2-5x+6
*June 1, 2015*

**Calculus**

convert headings (not bearings!) to x-y coordinates and add them up: 724@30° = (362,627) 32@90° = (32,0) addthem up and you have (394,627) √(394^2+627^2) = 740.5 90-arctan(627/394) = 32.2° Note that the proposed solution of 57.9° is measured from the x-...
*June 1, 2015*

**math**

#1 Nope (9-5)m+(6-6) = 4m+0 = 4m #2 ok #3 Nope (6-9)h+(1+4) = -3h+5 #4 Nope (-7-(-5))w^2 + (-2-3)w + (-1-(-2)) = -2w^2-5w+1 You have a problem with subtraction?
*June 1, 2015*

**Math**

4" = 1 /3 ft 4" x 4" = (1/3 ft)(1/3 ft) = 1/9 ft^2
*June 1, 2015*

**MATH URGENT**

that would be (f(-1)-f(-4))/(-1 - -4) = (-9-0)/3 = -3 See the graphs at http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2%2B2x-8%2Cy%3D-3x+-+12+for+-5+%3C%3D+x+%3C%3D+0
*June 1, 2015*

**Math: 5th Grade**

after the sale, she had r-624 red and r yellows, so r = 4(r-624) 3r = 2496 r = 832 check: 832-624 = 208 832 = 4*208
*June 1, 2015*

**Math**

I think the question is poorly posed. Surely there is no largest number which is not divisible by 7,11 or 30. Just take any huge product of powers of those numbers and add 1, such as 7^3 11^5 30^4 + 1
*June 1, 2015*

**math**

how many mcg/min? And is that micro or milli grams? mg = milli ug = micro
*June 1, 2015*

**physics**

Many times greater. You have the two equations. Plug in the numbers. The ratio of electric to gravitational force is Kq^2/Gm^2 = 4.1x10^48 That's quite a difference!
*June 1, 2015*

**Math**

can't draw a state machine here, but you should include states such as 0: outputs an F and loops back unless an a is received, when it transitions to state 1: outputs an F and goes back to 0 unless a b is received, when it outputs a T. You haven't said what it does ...
*June 1, 2015*

**DISCRETE MATH**

clearly B is the set of positive multiples of 52.
*June 1, 2015*

**algebra**

if $x in A, then x+3000 was in B. .08x + .05(x+3000) = 1320
*June 1, 2015*

**Math - Thanks, Reiny**

Good job. I should have seen that the vertices would be where to divide the lines. My bad!
*June 1, 2015*

**Math**

not sure what you mean by "gets to advanced." Not sure why you used slashes ? instead of the real symbol |. so, we have s(x) = |x-2| + |x-3| + |x+1| Since you asked no questions about it, nor provided the division of the domain among the parts, I'll just present ...
*June 1, 2015*

**DISCRETE MATH**

(a) clearly 2R4 and 2R6. for a function, the each m must be related to a single n (b) A is the set of factors of 52. I'm sure you can list them. (c) B is the set of all multiples of 52. (d) A ∩ B = {52}
*May 31, 2015*

**Physics**

since we cannot see the diagram, you will have to describe the series/parallel connections. Also, you have not asked a question. I assume you want the voltage drop across r.
*May 31, 2015*

**Math**

1600-1500 = 100 So, that is 100/150 = 0.67 std above the mean.
*May 31, 2015*

**Math**

enter your numbers on this web page and you can see that the answer is 82% http://davidmlane.com/hyperstat/z_table.html If you play around with things a bit, it should make things clearer.
*May 31, 2015*

**geometry**

we want AD parallel to BC, so D will have to be (x,-1). Since (10,-1) is 2 units to the right of B, D will have to be 2 units to the left of C: (-3,-1)
*May 31, 2015*

**Algebra**

since time = distance/speed, if the wind has speed w, 600/(100+w) = 400/(100-w) Now just find w.
*May 31, 2015*

**Sequences**

Find the ratio of the 1st two terms: (4/27) / (8/81) = 4/27 * 81/8 = 3/2 You can easily verify that each term is 3/2 the previous one. So, So, a10 = 8/81 * (3/2)^9 = 2^3/3^4 * 3^9/2^9 = 3^5/2^6 = 243/64
*May 31, 2015*

**Math**

if there are a lbs of A, then the rest (174-a) is B. So, 5.85a + 4.40(174-a) = 906.25
*May 31, 2015*

**Math**

if we set the wave with its vertex at (0,30) and it has height 0 at x=-20 and 20. y = 30-ax^2 y(20) = 0, so 30/400 = a = 0.075 y = 30 - .075x^2 Now we want to know where y > 10: 30 - .075x^2 > 10 20 > .075x^2 -16.32 < x < 16.32 So, to travel a distance of 32.64m...
*May 31, 2015*

**DISCRETE MATH**

because 3*4 = 12 = 2 (mod 5)
*May 31, 2015*

**Math**

as usual, draw a diagram. You will see that tanθ = 120/313
*May 31, 2015*

**Logs**

I assume sqrt4(n) means 4th root. So, log 4throot(x^16/y^4) = log(x^4/y) = 4logx - logy = 4*8 - 1 = 31 Of course, you could have worked it without extracting the 4th root: log 4throot(x^16/y^4) = 1/4 log(x^16/y^4) = 1/4 (16logx - 4logy) = 1/4 (16*8-4*1) = 1/4 (128-4) = 1/4 * ...
*May 31, 2015*

**Trigonometry**

sinθ = 20/130
*May 31, 2015*

**math**

the mean of two values lies between them. So, (√2+√3)/2 does the job. Or, just note that √2 = 1.414... √3 = 1.732... Now pick any value in between them.
*May 31, 2015*

**math**

I assume you want to solve for a and b in (√2+√3)/(3√2-2√3) = a+b√6 get rid of the radicals in the bottom by recalling that (x-y)(x+y) = x^2-y^2. So, multiply top and bottom by 3√2+2√3 and you have (√2+√3)(3√2+2√...
*May 31, 2015*

**Calculus**

just use the power rule: A' = 2x - 128/x^2 A" = 2 + 256/x^3
*May 31, 2015*

**physics**

you want mass. So, since density = g/cm^3, you need to multiply density times volume to get mass. So, do the math...
*May 31, 2015*

**geometry**

on the vertical line x=7, you could have (7+55,-2) or (7-58,-2) On the horizontal line y = -2, you could have (7,-2+59) or (7,-2-51) Of course, you could pick any points on the circle (x-7)^2 + (y+2)^2 = r^2 where r is between 50 and 60.
*May 31, 2015*

**Math**

a sphere has area 4πr^2. You have half a sphere, so just solve for r in 2πr^2 = 1062 r^2 = 1062/2π ...
*May 31, 2015*

**Maths**

4b+4c=4 3b = 2c, so substitute that into the first equation 4b+6b=4 10b=4 b=$0.40 3b= $1.20, so 2c=$1.20, and c=$0.60
*May 31, 2015*

**Math**

note that each term is 6 less than the previous one. So, the 100th term is 6*99 less than the 1st term. . . .
*May 30, 2015*

**Math**

start listing the powers of 7. Just the last digits are important: 7 49 343 ...1 ...7 Every 4th power starts a new cycle of digits. 40 = 4*10, so the final digit of 7^40 is 1. Now you know how to get the final digit of 7^42.
*May 30, 2015*

**algebra**

4p^3 + 20p^2 - 9p - 45 = 0 4p^2(p+5) - 9(p+5) = 0 (4p^2-9)(p+5) = 0 (2p+3)(2p-3)(p+5) = 0
*May 30, 2015*

**maths - eh?**

is there a question in there somewhere?
*May 30, 2015*

**Physics**

s = v^2/2a, so 4.2^2/2a = 2.1 a = 4.2 m/s^2 F=ma, so 100 = (20+m)(4.2) m = 3.8 kg
*May 30, 2015*

**Math please help!!**

as always, draw a diagram. Note that if the tower's height is h, you have h cot45° - h cot55° = 40 Now just solve for h.
*May 30, 2015*

**Math - eh?**

I guess that would depend on the table, no?
*May 30, 2015*

**math**

if the price is p, then the price for all 5 items is 3p. So, each costs 3/5 p, or 60% of the original price, regardless of what it was.
*May 30, 2015*

**Math**

the two diagonals d1 and d2 can be found using the law of cosines: d1^2 = 78^2 + 90^2 - 2(78)(90)cos35° d2^2 = 78^2 + 90^2 - 2(78)(90)cos145° = 78^2 + 90^2 + 2(78)(90)cos35°
*May 30, 2015*

**math**

what is ^x ? square root? If so, we have (√x - 1/x)^2 = x - 2/√x + 1/x^2 3+2^2 = 3+4 = 7, so we have 7 - 2/√7 + 1/49 That's kind of strange, so maybe you can clarify the notation and the grouping. Some parentheses would be helpful in that regard.
*May 30, 2015*

**math**

(2n+5) > 1 2n > -4 n > -2 -(2n+5) > 1 2n+5 < -1 2n < -6 n < -3 Think of the shape of |x| -- it is a V-shape. So, if |x| > n, it will be where the graph is above the line y=n. That means there will be two intervals, not one. See http://www.wolframalpha....
*May 29, 2015*

**Algebra**

f(x) = 4|x-7| To get f(x+1), just replace every x with x+1: f(x+1) = 4|(x+1)-7| = 4|x-6|
*May 29, 2015*

**math**

Are you asking us or telling us? In any event, B is correct.
*May 29, 2015*

**math**

s = b/2 s+7 = 2/3(b+7) now just solve for s and b. You should get Sam is 7 years old now.
*May 29, 2015*

**Math**

(42,42)
*May 29, 2015*

**polar form precalculus**

r sinθ = rcosθ r(sinθ-cosθ) = 1 r = 1/(sinθ-cosθ) or, r = 1/(√2 sin(θ-π/4)) = 1/√2 csc(θ-π/4)
*May 29, 2015*

**precal**

9x^2+36=y^2+36x+6y 9x^2-36x -y^2-6y = -36 9(x^2-4x) - (y^2+6y) = -36 9(x^2-4x+4) - (y^2+6y+9) = -36 + 9*4 - 9 9(x-2)^2 - (y+3)^2 = -9 (y+3)^2 - 9(x-2)^2 = 9 (y+3)^2/9 - (x-2)^2 = 1 That's a standard form, so you should be able to provide its description now.
*May 29, 2015*

**algebra**

just add like terms: 5x^8 -5z^4+5z^2+3 +3z^6+4z^4-9z ----------------------------- 5x^8 + 3z^6 - z^4 + 5z^2 - 9z + 3 I suspect you meant z^8 and not x^8.
*May 29, 2015*

**geometry**

the desired locus is the perpendicular bisector of the line segment. So, its slope is -1 and it passes through (5/2,7/2) y - 7/2 = -1(x - 5/2)
*May 29, 2015*

**Maths**

ahhhh. I did the solution, but I failed to notice the three-day time difference. So you'll have to analyze the graph several periods later.
*May 29, 2015*

**English**

Which pf the following, would not always require a citation in a research paper? a- quotation of a phrase b- quotation of a sentence c- thesis statement d- sentence paraphrased from a book
*May 29, 2015*

**English**

in which of the following resides the irony in the short stories the gift of the magi and the necklace
*May 29, 2015*