Wednesday

July 23, 2014

July 23, 2014

Total # Posts: 23,930

**Algebra**

correct

**Math**

supply the missing width (?) and solve for x, where 2(? + x) = 354

**maths Arthmetic**

well, since 4 is half of 8, 4/3 is half of 8/3 so, what number is 22 half of? 44 you are correct

**physics**

greater than 10+15

**physics**

hmmm... If θ is the angle between p+q and p, cosθ = 4/5 If Ø is the angle between p+q and q, then the angle between p and q is θ+Ø Let's let |q| = a, so |p| = a+1 p•q = a(a+1)cos(θ+Ø) (p+q)•p = |p+q|*|p| cosθ = (4/5)(...

**physics**

The two forces clearly have magnitudes 6 and 10. So, use the law of cosines to get r^2 = 100+36-120(-1/2) = 196 r = 14

**physics**

recall that the electric force F = 9.0*10^9 (q1*q2)/r^2 So, plug in your values, remembering how many electrons are in a Coulomb, and you have only 1 electron at each pole. r must be in meters, of course, not km.

**math**

The supplementary angle is always 90° more than the complementary angle.

**Algebra**

(B) the slope is not a constant. Every value is possible for the slope at some point on the curve. you are correct.

**Algebra**

y = a(x-3)^2 + 1 10 = a(0-3)^2+1, so a = 1 Looks like (C) to me

**physics**

looks like 25 mph West to me

**Algebra**

dang typo: y=40

**Algebra**

write down the data. If there are x footballs and y baseballs, then we have p = 6x + 5.5y 35 <= x <= 45 40 <= y <= 55 x+y <= 80 we want to maximize p. Using your favorite linear optimization calculator, you find that x=40 y=50 profit = 460

**Algebra**

that's the ticket.

**Algebra**

evidently 46.5% per time period

**Algebra**

There's no algebraic way to do it. A numeric method or a graphical analysis will be required. See http://www.wolframalpha.com/input/?i=solve+3x^2%2B4lnx%2B4%3D0

**Chemistry**

When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...

**arithmetic**

After the first 1/8 died, only 7/8 were left 3/5 of those died, meaning 3/5 * 7/8 of the original number died 1/8 = 5/40 3/5 * 7/8 = 21/40 So, 26/40 = 13/20 of the fish died

**Chemistry**

When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...

**math**

nope. Just because two numbers multiply together to make 1, you still know nothing about the numbers. If nothing else, try your idea. If x=1, 2x+1=3, and 1*3≠1 However, if two numbers multiply to be zero, then one or the other must be zero. So, let's set things equal...

**Math**

well, 45g = 0.045 kg. So, you will have 0.365 kg +.045 kg ------------- 0.410 kg

**Algebra**

cmon, guy. I posted an update to the first one, using substitution, and also showed elimination. What don't you get? Have you looked at them?

**Algebra**

another way is called elimination. You have 5x - 9y = 7 7y - 3x = -5 Rearrange terms a bit to get 5x - 9y = 7 -3x + 7y = -5 To get rid of the x values, find the LCM of 5 and 3: 15. Now multiply things a bit to get 15x - 27y = 21 -15x + 35y = -25 Now you can add the two equatio...

**algebra**

sure. the first equation 5x - 9y = 7 tells us that x = (9y+7)/5 Just plug that into the 2nd equation, and you get 7y-3(9y+7)/5 = -5 fractions are a nuisance, so multiply through by 5: 35y - 3(9y+7) = -25 35y - 27y - 21 = -25 8y = -4 y = -1/2 Now plug that value into either equ...

**algebra**

7y-3(9y+7)/5 = -5 y = -1/2 so, x = 1/2

**Algebra**

v + (4+2v) = 16 v = 4 so, 4 oz vinegar and 12 oz oil.

**Math**

that would be (0.365 + 45.000) kg That's some loaded pizza. I suspect a typo. Just fix that and add the two numbers.

**geometry - incomplete**

That depends. Is DE the arc length, or the chord length? Then, you have also left out the radius or the subtended angle.

**Inequalities & Absolute value**

oops - a typo. should be x > -13/2 so, the solution to the first one is -13/2 < x <= 1/2

**Inequalities & Absolute value**

OK. To solve absolute-value problems, you really have to do them twice. Recall the definition of |z|: |z| = -z if z < 0 |z| = z if z >= 0 So, you have |2x+4|<5 That means that If 2x+4 < 0, (or, x < -2)you have -(2x+4) < 5 -2x-8 < 5 -2x < 13 x > 13/2 ...

**Inequalities & Absolute value**

I get -4/3 < x < 1/2, so only (ii) works. In this case, it's easy enough just to substitute in each of the values to see which works in both cases. Always keep in mind the V shape of absolute value graphs. See http://www.wolframalpha.com/input/?i=plot+y+%3D+|2x%2B4|%...

**Math**

Since you are adding 20 to each number, just add 20*21 to the total. Or, thinking of the values as an arithmetic progression, recall that the sum of n terms is Sn = n/2 (T1+Tn) With a=40,d=1, S21 = 21/2 (40+60) = 1050 With a=60,d=1, S21 = 21/2 (60+80) = 1470 Note that 1470 = 1...

**algebra**

figure the common denominator. Then, using that, add/subtract the values: 1/3 + 3/7 21 = 3*7, so you really have (1*7)/(3*7) + (3*3)/(3*7) = (7+9)/21 = 16/21

**algebra**

I'd guess that depends on the size of the tank.

**math**

The smallest such number is 3*5*7 = 105 Since 64 <= 105 < 128 or 2^6 <= 105 < 2^7 That will require 7 digits: 1101001

**algebra**

complex zeros come in conjugate pairs. Just as in the first problem above. So, what do you think?

**algebra**

(x-7i)(x+7i) = x^2+49

**algebra**

(12-2x)(10-2x) = 80 Solve that for x, or just note that 80 = 10x8, so both dimensions are reduced by 2", making a 1" margin all around.

**math**

A1/A2 = (s1/s2)^2 = (2/√2)^2 = (√2)^2 = 2 (B)

**math**

in each suit of 13 cards, there are 5 even cards. That means, there are 8 others. So, P(~even) = 8/13

**Algebra**

just recall that a^2-b^2 = (a-b)(a+b) So, first, make sure that both terms are perfect squares. In this case, they are not. However, if you factor out a 2, you have 2(49-4w^2) 49 is 7^2 and 4w^2 = (2w)^2. So, we now have 2(7-2w)(7+2w)

**math**

look up you standard form for ∫√(u^2-a^2) du Now, if you let u = 2x, you have u^2 = 4x^2 du = 2 dx, so dx = du/2 Also, let a = √3 So, now your integral is 15/2 ∫√(u^2-a^2) du and just go for it.

**math**

a+b+c+d+e = 35 (mean=7) c = 7 (median) e = a+7 (range) a+b+7+d+a+7 = 35 2a+b+d = 21 If a=1, b+d=19 But b<=7 and e=8 1,b,7,d,8 But, if b<=7, and d<=8, no go If a=2, b+d=17 2,b,7,d,9 same problem as above If a=3, b+d=15 d<=10, so b>=5 so we can have 3,b,7,d,10 as ...

**Math**

all the prime factors of c are less than p, so n has 4 unique prime factors. n^2 does not have any new prime factors, so it also has 4.

**algebra**

3.14 * 1/1000 and you can massage that as you will.

**Math**

just replace each expression in parentheses, and you will see that the values are the same. An illustration of the associative property of addition.

**algebra**

mary's age 5 years ago is x-5 1/3 of that is (x-5)/3 3 less than that is (x-5)/3 - 3 Now, that may not be the answer, since it's difficult to parse just who's how old when, with your unusual verb tenses.

**math**

If there are t tourists and r rooms, t = 6r-9 t = 3(r+4) 6r-9 = 3r+12 3r = 21 r = 7 so, t=33

**math**

(ab)^2 = abab If abab = aabb then the middle ba = ab

**math**

y" + 9y = cos2x+sin2x You know that y"+9y=0 has solutions y = a cos3x + b sin3x so the solution here is y = a cos 3x + b sin 3x + (cos2x+sin2x)/5

**Algebra**

first step: expand the polynomial. You will see that x^3 goes away, leaving you with just 3x^2+2x = 85 Now just solve as you normally would: 3x^2 + 2x - 85 = 0 (3x+17)(x-5) = 0

**104B**

500*2.5*r = 40 r = 0.032

**math**

19/3x - 20

**Math**

if x at 7%, then .07x + .08(x+6000) = 7.80 Fix the interest amount and solve for x. And pay more attention to what you type.

**Math**

4c + 5m = 25.50 2m = c+1.75 Now just solve the two equations, using your favorite method. I get (A) assuming a missing decimal point.

**Math - incomplete**

some data missing here. Read what got posted and fill in what got omitted.

**physics 1**

if the initial velocity was v, v - 3.55*2.13 = 4.90 v = 12.46 m/s the displacement s is thus s = 12.46*2.13 - 3.55/2 * 2.13^2 s = 18.49 m

**math**

we want to approximate ∫[0,4] e^(3√t) sin 3t dt So, divide the interval[0,4] into 8 pieces, each of width 0.5 Now apply each Rule named above, calculating f(x) for each value from 0 to 4, and add up the areas of all the rectangles or trapezoids. There are online ca...

**Heron's formula**

anything to do with the area of triangles. Just look around your home and see what triangles you might be interested in. Painting gables, carpeting a corner of a room, etc.

**Math - bzzzt**

Sorry. If PQ joins the midpoints of AB and AC, then it is parallel to BC and half its length. You cannot have PQ=2 and BC=3.

**Chem**

You have: .0286*.169 = 0.004833 moles of Na3PO4 .0397*.255 = 0.010124 moles of Ca(NO3)2 If the reaction is 2Na3PO4 + Ca(NO3)2 = 2NaNO3 + Ca(PO4)2 then you need 2 moles of Na for each mole of Ca. Since there is extra Ca, you will wind up with .09666 moles of Ca(PO4)2 Just multi...

**algebra 1**

well, the triangle obviously has area = 12 So, the whole outfit has area 6x+12. So, 6x+12 = 150 6x = 138 x = 23

**math**

surely you can count days on a calendar...

**Math**

If you subtract the 2nd equation from the first, you get 4x-3y-4 = 0 4x+2y+5 = 0 ---------------- -5y-9 = 0 now add 9 to both sides: -5y = 9 now divide by -5: y = -9/5 Knowing that y = -9/5, just plug it into either of the original equations and then solve for x. The work is s...

**algebra**

20m

**math**

Just think about it. Every second it travels 1 meter. So, 5 seconds ago it was down 5 meters. now think forward in time for 120 meters above.

**math**

if now is time t=0, then the temperature at any time t is -2t. So, we want -2(-3) and -2(5)

**Math**

that would be 420/12 = ?

**math**

If they were laid out flat, they'd each be 4.8 units long. So, they must be more than that, and since 4.8 is not an acceptable answer, 4.9 is what we have to go with.

**math**

The midpoint of two points is (6,2). One of the points is (3,5). Since the two ends must be equidistant from the midpoint, 3 = 6-3, 9 = 6+3 5 = 2+3, -1 = 2-3 So, (9,-1) is at the other end.

**Physics**

it gained (18-12)=6 m/s in (4-2)=2 seconds, so that is 6/2 = 3 m/s^2 In the first 2 seconds, then, it gained 6 m/s, so it started at 6 m/s.

**geometry**

hmmm. you have the formula. What's the trouble? The same formula applies for ym: (y1+y2)/2 A value midway between two others is just their average: the sum/2.

**10 gr math**

ok. plug in the data and evaluate: the distance between (1,3) and (7,2) is √((7-1)^2 + (2-3)^2)

**Chemistry**

When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...

**algebra**

A. No - the decrease in intensity is not a constant, but depends on the previous intensity. The intensity I of x meters of cable is I = 1500 * 0.964^x C yes you can probably write that one on your own.

**Math**

if there are 8x tools, then there are 3x shovels and 5x rakes. So, 5x = 3x+10 x=5 so, there are 15 shovels and 25 rakes

**Math**

If you can find the midpoint of a line segment know that the slope of the perpendicular is -1/(slope of line segment) remember the point-slope form of a line then all of these problems are straighforward. Review those topics, give it a try, show where you get stuck, if you do.

**Non**

just a note: that's mu sub-k, not "muse of k" µk

**Volume**

Just figure the tank's volume (66.75*132*10) and divide it by 231 in^3, the volume of a gallon.

**algebra**

x^2+8x = x(x+8) Pick any positive value for x and you get a rectangle.

**math**

take a look at the graph of (1+.10/n)^(n) It shows the effective yield of 10% compounded n times per year. It approaches continuous compounding, e^.1 http://www.wolframalpha.com/input/?i=plot+y%3D%281%2B.1%2Fn%29^n+for+n+%3D+1..40%2C+y%3De^.1

**algebra**

solve it just as you would an equation: 42 = -6d -7 = d However, multiplying and dividing by negative values changes the direction of the inequality. So, you have 42 < -6d 7 < -d -7 > d or d < -7 Since you can always add and subtract without changing the direction,...

**science**

I may have messed up the sign change, so double check my math.

**science**

the position falling from a height of h feet is y = h - 16t^2 After t seconds, y=0, so h=16t^2 So, we have (h-16t^2) - (h-16(t-1)^2) = 11h/36 0 - (16t^2 - 16(t-1)^2) = 11(16t^2)/36 32t-16 = 44/9 t^2 11t^2 - 72t - 36 = 0 t = 7.01 So, h = 16t^2 = 786.24 ft

**calc**

first off, I'd use partial fractions: (x^3 -3x^2 -9)/(x^3 -3x^2) = 1 + 1/x + 3/x^2 - 1/(x-3) There are no discontinuities on [4,5], so it's straightforward. The integral is just x + logx - 3/x - log(x-3) so we get (5 + log5 - 3/5 - log2)-(4 + log4 - 3/4 - log1) = 23/20...

**Math**

54° is 3/20 of a full circle. SO, the whole circumference 3/20 c = 9 c = 60

**ALGEBRA - eh?**

cannot parse the "8n 12" part

**math**

The solution of this equation is so complex, I have to assume you're doing numerical methods or something. Take a peek at http://www.wolframalpha.com/input/?i=sin^6x+-sin^2+4x+%3D+sin2x+sin10x for further insight.

**trigonometry**

well, we have h/120 = tan 10°18' h = 21.8 ft

**Maths**

y = 1/x y' = -1/x^2 y'(1/4) = -1/(1/16) = -16 I think you lost a minus sign. And, of course, you have displayed the usual sloppiness with parentheses.

**math**

I don't see any way. Each odd number is of the form 2k+1 Add up 7 of those, and you have a sum of the form 2n+7 = 20 But 2n cannot be 13. The sum of an odd number of odd numbers cannot be even.

**Math**

well, ∫ lnx/x^2 dx = -(lnx + 1)/x recall that ln √x = 1/2 lnx let u = 3-5x^2 and du=-10x dx That gives you ∫ -1/10 2^u du which is just 2^u / ln u Now it's pretty straightforward

**Math**

well, we know that d/dx arccosh u = 1/√(u^2-1) du So just use the chain rule, and note that (2x-1)^2-1 = 4x^2-4x

**physics**

(i) the range for angle θ is R = v^2/g sin2θ (ii) Naturally max height is reached at θ = 45° (iii) given the range, and that horizontal velocity is constant, getting t is easy. So, what do you get?

**Algebra**

y(x) = 3*2^x y(x+1) = 3*2^(x+1) = 3*2*2^x = 2y(x) So, each year y doubles.

**Wood working**

Of course, if each stripe is that wide, there will be no space between them, so the board will just be solid white. Now you have to decide how much blank space to allocate between the stripes, and whether the end stripes will reach to the very ends of the board, or whether the...

**Math-Parabolas**

If you mean y = x^2+9 you can see that since x^2 can never be less than zero, the vertex is at x=0. Since y=9 there, the vertex is at (0,9) Or, recalling that the vertex of y = (x-h)^2 + k is at (h,k), note that we have h=0 and k=9.

**pre cal**

since complex roots come in pairs, we have (x-3)(x+13)(x-(5+4i))(x-(5-4i)) (x-3)(x+13)((x-5)-4i)((x-5)+4i) (x-3)(x+13)((x-5)^2+4^2) (x^2+10x-39)(x^2-10x+41) x^4 - 98x^2 + 800x - 1599

**Science**

Some of the CO2 was lost as a gas. Also, depending on how hot the mixture became, maybe some of the water was lost as steam.

**pre-cal**

However, assuming the chopper starts at (0,h) and the vehicle starts at (0,0), after t minutes the chopper and vehicle are at (2640t,h - 5/33 t) and (4224t,0) So, the line between them has slope (h-5/33 t)/(1584t) Now you have the angle tanθ = (h-5/33 t)/(1584t) so you ca...

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