Tuesday

September 30, 2014

September 30, 2014

Total # Posts: 25,371

**math**

1000(1+.06/2)^2t <= 800(1+.08/12)^12t t >= 10.8 years
*August 4, 2014*

**Math**

since sin(x) = cos(90-x) sin^2 0° + sin^2 90° = 1 sin^2 5° + sin^2 85° = 1 ... sin^2 45° + sin^2 45° = 1 Now, you have excluded sin^2 0, but since that's zero anyway. You have 9 pairs, plus a single 45, so the sum is 9.5
*August 4, 2014*

**algebra**

since the shadow:height ratio is the same, 25.2/8.4 = x/20.7
*August 4, 2014*

**General knowledge**

What is google, and what does google do?
*August 4, 2014*

**Algebra**

we know that sum 9/3^n is just a geometric series, which converges. 9/(n*3^n) has terms which are even smaller, so it also converges
*August 3, 2014*

**physics**

so, if we name the takeoff point as (0,0) we want the vertex of the parabola to be at (5,4.5) The parabola can thus be written as y = -0.18(x-5)^2 + 4.5 so, at x=0, y' = 1.8 That means the initial angle is θ=60.9° Now you should be able to work out the velocity ...
*August 3, 2014*

**math**

the slope is 1/9, so the point-slope form tells us that y-2 = 1/9 (x+3) now just put that into standard form
*August 3, 2014*

**math**

the line is horizontal, so the y-value does not change. What function stays at -8 for any value of x?
*August 3, 2014*

**math**

using discs, of thickness dx v = ∫[-1,1] πr^2 dx where r = y = 1-x^2 So, v = π∫[-1,1] (1-x^2)^2 dx = 16/15 π Using shells, of thickness dy, we have to account for the two branches of the parabola, so it's easier just to use symmetry and get v = 2...
*August 3, 2014*

**Geometry**

you could draw a semicircle, then draw a tangent line for the stem of the J. Note that the tangent to the circle is perpendicular to the radius.
*August 3, 2014*

**geometry**

(18+2w)(15+2w)-18*15 = 234 w=3 since the frame is 3" wide, you can now determine its dimensions.
*August 3, 2014*

**math**

not much to sketch. Linear functions are just straight lines. So, draw the line through those two points. Done. The only problem is, y is not a function of x. Why not?
*August 3, 2014*

**Grammar**

"I" is singular. So, you need a singular noun.
*August 3, 2014*

**College math**

5logT+2logW+logZ
*August 2, 2014*

**Algebra**

what don't you get? Divide by x+k is the same as divide by x-(-k), so the remainder is p(-k). Same for p(3k). They said the remainders are equal. So, equate the two expressions and solve for k. To check, just evaluate p(x). p(-3/2) = p(9/2) = 47/4
*August 2, 2014*

**geometry**

how about a line, and then a semicircle? Just draw a short perpendicular to the line (don't actually draw it), and then, using that as the radius, draw a semicircle touching the end of the line.
*August 2, 2014*

**geometry**

You drew a line through two points? That's certainly the first step, but it's not the letter E. You still need to draw three perpendicular lines; two at the ends of your line, and one in the middle.
*August 2, 2014*

**math**

(60 / 12^3)*60 = 2.08 But then, we already knew that, since "a pint's a pound, the world around."
*August 2, 2014*

**Math**

You need to review the methods of expressing complex numbers as a+bi and r cisθ. Surely your text has a discussion of the topic. Also, a simple google on "complex numbers polar" will turn up may explanations and examples. √3-i can be plotted as the point...
*August 2, 2014*

**Math**

Tell you what -- why don't you simplify them and we'll check your answers. To get started on (a) √3-i = 2cis -π/6 so, (√3-i)^4 = 16cis -2π/3 now just convert that back to rectangular values.
*August 2, 2014*

**Trigonometry**

Label the two observation points A,B and the rock R. Drop a vertical from R and draw horizontals from A,B to intersect it at M,N. So, AM and BN are horizontal lines. Let RN intersect the slope at P. Drop a vertical from B to intersect AM at C. We want the distances RN and RM ...
*August 2, 2014*

**algebra**

If the speeds are a and b, then under suitable assumptions, since distance = speed*time, 15a+150 = 15b a+b = 150 now just solve for a and b.
*August 2, 2014*

**math - need glasses**

My bad. There are seven consonants. Guess I need to go back to counting school.
*August 2, 2014*

**math**

Since there are 6 consonants, the E can be in any of seven positions.
*August 2, 2014*

**Hard Geometry Problem**

So, did you get 11/27?
*August 1, 2014*

**Hard Geometry Problem**

a negative scale factor changes size, and reflects through the dilation center. If it were positive, the whole reduced triangle would of course remain within ABC. But, by flipping through G as well as scaling, some of A'B'C' will lie outside of ABC.
*August 1, 2014*

**algebra**

c = p+37 i = 2p-38 c+p+i = 447 Now just solve for c,p,i using your favorite method.
*August 1, 2014*

**mat/117**

since the discriminant is negative, there are no real solutions.
*August 1, 2014*

**mat/117**

just start substituting for n: a1 = 2*1 = 2 a2 = 2*2 = 4 ...
*August 1, 2014*

**math**

what do we know? c = 2/3 p r = 1/2 c t = 100 = r-90 So, what is p? p = 3/2 c = 3/2 (2r) = 3r = 3(t+90) = 3(190) = 570
*August 1, 2014*

**math**

well, how many cubic yards in a single post? Expressing the dimensions in yards, the volume is (9/36)(9/36)(6/3) yd^3
*August 1, 2014*

**math**

Clearly that would be (5.75+8.2)-(6.2+9.4)
*August 1, 2014*

**math**

That would total up to 0.75 + 0.50 + 0.45 km
*August 1, 2014*

**Logarithms**

If the fraction is a/b c then you'd have +logc If, as I suspect, it is a/(bc) then it is indeed loga - (logb+logc) = loga - logb - logc
*August 1, 2014*

**Chemestry**

just look up element #50 on the periodic table. Protons determine the atomic number. It's short two electrons, so the charge will be +2.
*August 1, 2014*

**first chemistry**

just look up the formula for aspirin (acetylsalicylic acid) and add up the weights of all the atoms involved.
*August 1, 2014*

**chem**

Since the required amounts of the two reagents have almost the same mass, H2S will be the limiting one, since twice as many moles of that are required. So, it will be the limiting reagent. So, figure how many moles of H2S are in 87.1g, and calculate the mass of 3/16 that many ...
*August 1, 2014*

**Geometry**

Since the vertices are 36° apart, and X and R are 4 positions apart, it is indeed a central rotation of 144°. However, we want to rotate about U, not the center of the decagon. If you draw the figure, and if we call the center of the decagon A, then you can see that &...
*July 31, 2014*

**physics**

The horizontal speed does not change. It remains at 7.5 cos51° = 4.72 m/s The vertical speed is given by v = Vo -9.8t, so it ends up at 7.5 sin51° - 9.8*1.5 = -8.87 m/s So, the final speed is √(4.72^2 + 8.87^2) = 10.05 m/s
*July 31, 2014*

**Math**

use the two-point form of a line and you can see that (y-5)/(x+1) = (5+1)/(-1-2) y-5 = -2(x+1) y = -2(x+1)+5 So, y(x+1) = -2((x+1)+1)+5 = -2(x+2)+5 = -2x-4+5 = -2x+1
*July 31, 2014*

**Maths**

I'd say that would be 8*6 = 48
*July 31, 2014*

**Calculus**

Using the comparison test, the series diverges.
*July 31, 2014*

**AP Calc**

let the center of the cable be at (0,220). That becomes the vertex of the parabola, so the equation is y = ax^2+220 Since y(2100) = 750, that means that a*2100^2 + 220 = 750 a = 530/2100^2 = 0.00012 So, we now know that the height y = 0.00012x^2 + 220 Now, we know y' = 0....
*July 31, 2014*

**Translations**

what do you mean by "that's not right?" What calculation did you do? Without loss of generality, we can take the distances to be measured along the x-axis. We have two points, P and Q on the x-axis, where OQ = 4(OP) because of the dilation. Since PQ=18, that ...
*July 31, 2014*

**Translations**

all distances also scale by a factor of 4.
*July 31, 2014*

**Physics**

The trains approach at 260km/hr The distance to cover is 285km. So, it takes 285/260 hrs to meet. In that time, the train from Calgary covers 285/260 * 140 = 153 km
*July 31, 2014*

**geometry help!! answer all questions!! please**

Posting a whole homework assignment with no evidence of any attempt on your part will get you scant help here. Surely you have covered the relevant material, so you must have some ideas on at least some of the problems... The hints I posted earlier should get you started on ...
*July 31, 2014*

**Geometry**

P(x,y) -> P'(x+3,y-3) reflection over y=x is (x,y) -> (y,x) reflection over the y-axis is (x,y) -> (-x,y) reflection over the x-axis is (x,y) -> (x,-y) and so on. Where do you get stuck?
*July 31, 2014*

**Math**

distance is just the integral of velocity. So, just integrate, and evaluate at the ends of the interval.
*July 31, 2014*

**Math**

y = -(x-1)(x-4) so you want to integrate between the roots, in the interval [1,4] a = ∫[1,4] -x^2+5x-4 dx = -1/3 x^3 + 5/2 x^2 - 4x [1,4] Now just evaluate at the ends and subtract.
*July 31, 2014*

**trigonometry**

The problem states: Find the formula of the trigonometric function that models the height H of the weight t seconds after it reached its maximum height. Your function is supposed to model the height starting when it is at its maximum. So, let that be t=0.
*July 31, 2014*

**prealgebra**

you know that for such a triangle, the sides are in the ratio 1:√3:2 So, the short side is 41 The long side is 41√3 The hypotenuse is 41*2 The functions of 30° are standard values, which it would be well to learn.
*July 31, 2014*

**math**

All you want is the number of permutations for 3 out of 4: 4P3 = 4*3*2 = 24 You can pick the first in 4 ways. Now there are 3 choices for the 2nd, and 2 left for the 3rd.
*July 31, 2014*

**math(precalculus)**

You don't need any c. It can be absorbed into a and b. Actually, you have solved the problem. Pick any value for c, and plug it in. As long as a=c and b=-4c, R(x) will work. So, make things easy. Let c=1. As I worked it out, R(x) = ???/(x+1)(x-2) Since y=0 is the asymptote...
*July 31, 2014*

**Math**

heads: r+c = 35 feet: 4r+2c = 94 Now just solve for r and c, in any of several ways.
*July 31, 2014*

**Science/Physics**

weight (force) = mg Look up g if you don't know it. Now, divide that by the relative gravity of the moon. For example, if the moon has 1/2 the gravity of earth, you will need double the mass for the same weight.
*July 31, 2014*

**Physics**

The resultant velocity is v = (106,106) + (0,20) = (106,126) |v| = 164.7 The angle x obeys tan(x) = 126/106 The time taken is 500,000/164.7 seconds
*July 31, 2014*

**Math**

surely you can see that A=3 B=pi/20 C=0 D=7 I mean, just read it off. Now employ your skills to convert your cos(x) to sin(pi/2-x) A and D stay the same.
*July 30, 2014*

**Math**

since y is a max when t=0, we want a cosine function, since cos(0) = 1. y = 7+3cos(pi/20 t) because the period is 40 seconds, and the level varies between 7+3 and 7-3 feet.. C=0 because cosine is a max at t=0, so there is no offset. Naturally, you can now write the sine ...
*July 30, 2014*

**Alegbra1**

depends. How much of all that is under the radical sign? Once you specify that, just remember that the domain of √u is u>=0.
*July 30, 2014*

**Math**

20% + 15% = 35% given away. That leaves 65%, so .65x = 520 Now just solve for x.
*July 30, 2014*

**math - huh?**

I see several problems. who the heck is Mary? Is Mary really male?
*July 30, 2014*

**math**

f+l = 80 2/3 f = l-10 so, 2/3(80-l) = l - 10 160-2l = 3l-30 190 = 5l l = 38 check: initially there were 38 local and 42 foreign after removing 10 local and 14 foreign, there were 28 of each.
*July 30, 2014*

**PreCalculus**

just make the usual substitution. y = rsinθ x = rcosθ so, that means r^2sin^2θ/25 - r^2cos^2θ/9 = 1 r^2(9sin^2θ-25cos^2θ) = 225 r^2 = 225/(9sin^2θ-25cos^2θ) see the expected vertical hyperbola at http://www.wolframalpha.com/input/?i=plot...
*July 30, 2014*

**statistics**

Since there are 10 choices, I'd just use the nth digit of 3 numbers chosen from the random number table. which n depends on how many digits in each entry; just make sure all use the same n. Or maybe add up the digits and take the last digit of the sum.
*July 30, 2014*

**Maths**

1+2+4=7, so if we divide the sum into 7 equal parts of size x, 7x = 126 x = 18 So, the shares are 18,36,72
*July 30, 2014*

**Math**

find the distance between the two points, as usual. Now, since the area of a square is a = d^2/2, just figure that.
*July 30, 2014*

**math**

clearly, if the angle is x, tan(x) = 7.15/10.1
*July 30, 2014*

**Math - grrr.**

all that anti-derivative stuff is too much for me that early. Thanks for the fix. I'm sure Tim caught the error and fixed it though. . . . Right, buddy?
*July 29, 2014*

**Math**

since y" = 6x y' = 6x+a y = 3x^2+ax+b we know the slope is y'(1) = -3, so 6(1) + a = -3 a = -9 so, y = 3x^2-9x+b since 5-3x=2 at x=1, y(1) = 2, and we have 3-9+b = 2 b = 8 and y = 3x^2-9x+8 See the graphs at http://www.wolframalpha.com/input/?i=plot+y%3D3x^2-9x%...
*July 29, 2014*

**PreCalculus**

sin(x)sec(x) - 2sin(x) = 0 sin(x)(sec(x)-2) = 0 sin(x) = 0 sec(x) = 2 Those are pretty standard angles, so listing the solutions should be easy.
*July 29, 2014*

**geometry**

The diagonals cross in the center, so the acute angle is the vertex of an isosceles triangle with height=24 base=14 so the acute angle x obeys tan(x/2) = 7/24
*July 29, 2014*

**Geometry**

If the dimensions are x,y,z then we have 2xy+2xz+2yz = 22 4x+4y+4z = 24 xy+xz+yz = 11 x+y+z = 6 How about 1,2,3 diagonal is √14
*July 29, 2014*

**algebra**

I'd do it by taking the log of the values, and using a normal linear best-fit on the log values. Where log(15500/v) = log4, that's the number of years you want.
*July 29, 2014*

**math**

4 = 2^2 4/(2^x) = (2^2)/(2^x) = 2^(2-x) Now, just solve the equation. Hint: 2^(x-2) = 2^x / 4
*July 29, 2014*

**Trigonometry**

The individual displacements are 150 @ 220° = (-96.4,-114.9) 130 @ 130° = (99.6,-83.6) So, the final location is at (3.2,-198.5) Just find the distance from there to the origin.
*July 29, 2014*

**math**

On the other hand, if you meant 27√3, that makes b=7/2
*July 29, 2014*

**Finite Math**

clearly it's 500-x
*July 29, 2014*

**Math**

just start by listing the facts: width=w length=w+6 height=2 area is the 4 sides + bottom = 2(width*height)+2(length*height)+(length*width) = 2(2w)+2(2(w+6))+w(w+6) = 4w + 4w+24 + w^2+6w = w^2 + 14w + 24 So, now we know that w^2+14w+24 = 280 w^2+14w-256 = 0 Solve that for w, ...
*July 28, 2014*

**math**

after 1/8 were purchased, 7/8 were left. So, now we have 7/8 x + 10 = 52 7/8 x = 42 x = 48
*July 28, 2014*

**math**

a/p = 3/5 (2/5 a)/(p-40) = 2/5 a=60 p=100 so, she paid 60(.30)+100(.45) = $63.00
*July 28, 2014*

**math**

3278164781246
*July 28, 2014*

**math**

9/180 = 0.05 = 5%
*July 28, 2014*

**chemistry**

32 days is 4 half-lives. So, the mass is reduced to 1/2^4 = 1/16 of 40mg, or 2.5mg
*July 28, 2014*

**Math**

so far so good. Now just solve for b and plug that into your formula. Then check that (-3,-8) satisfies the equation.
*July 28, 2014*

**Math**

plot the point. Since the slope is 2/3, go right 3 and up 2 and plot another point. Draw the line connecting the two points.
*July 28, 2014*

**physics**

the difference is 4.9µC. So, move half that, or 2.45µC. Now just convert that to no. electrons.
*July 28, 2014*

**math/help**

4 1/6 = 25/6 1 1/6 = 7/6 so, (25/6)/(7/6) = 25/7 3 3/1 ??? fix that and work it as in the above one.
*July 28, 2014*

**math**

just as usual. Where is y" positive? e^-3t is always positive, so all you need is 2t-3 > 0 t > 3/2 e^3/2 = 4.48, and you can see from the graph that it is concave upward for x > 4.48 http://www.wolframalpha.com/input/?i=plot+x+%3D+e^t%2C+y+%3D+te^-t+for+1%3C%3Dt%...
*July 28, 2014*

**math**

x = e^t y = te^-t dy/dx = y'/x' = (1-t)e^-t/e^t = (1-t)e^-2t d^2/dx^2 = (x'y"-x"y')/x'^3 = ((e^t)(t-2)e^-t - (e^t)(1-t)e^-t)/e^3t = (2t-3)e^-3t or, do it directly x = e^t, so y = lnx/x y' = (1-lnx)/x^2 = (1-t)e^-2t y" = (2lnx-3)/x^3 = (2t...
*July 28, 2014*

**Science**

why do you include a third dimension? The taxi cannot travel vertically. The total displacements are 20+6=26 blocks south 15 blocks east. So, √(15^2+26^2) = √901 = 30.0
*July 28, 2014*

**physics**

15.7 + 17.5
*July 28, 2014*

**math**

1/2 * 1/2 * 1/6
*July 28, 2014*

**Algebra**

Start by expanding the parentheses: 3(x-1) -2(x^2+3x+4)-5(x+9) 3x - 3 - 2x^2 - 6x - 8 - 5x - 45 Then collect terms of like degree: -2x^2 + (3-6-5)x + (-3-8-45) -2x^2 - 8x - 56
*July 27, 2014*

**Math**

If their heights are k and r, then k/375 = sin 32° r/375 = sin 38° So, the difference is r-k = 375(sin38°-sin32°)
*July 27, 2014*

**math**

that's because you mixed up dollars and cents. It asked for only dollars.
*July 27, 2014*

**math**

3:40 to 6:20 is just 2 hours and 40 minutes. That should get you going.
*July 27, 2014*

**Math**

Assuming you mean "I" and not "O", just pick any two values for x and calculate the y: x=0: y=4 x=4: y=5 So, the points (0,4) and (4,5) are on the line. Plot them, and draw a line between the two points.
*July 27, 2014*

**math**

There are only 3 colors. Any group of more than 3 cards will have to have a duplicate color.
*July 27, 2014*

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