Friday

October 9, 2015
Total # Posts: 34,448

**Math**

No way to tell the number of grams, since we know nothing about the solute. But in any case, the mass of solute is not changed by adding some water.
*September 27, 2015*

**algebra**

If the tens digit is 2x, the units is 3x. Then we have 10(3x)+2x = 10(2x)+3x + 27 x=3 The n umber is 69 96 = 69+27
*September 27, 2015*

**Physics, math**

well, just plug in the values of the trig functions, and you have 1.2 = 4.6*1.192 - 4.9*21.16/(0.413x^2) Now just collect the constants and solve for x.
*September 27, 2015*

**math**

well what's 25% of 500,000 mg?
*September 27, 2015*

**Calculus**

the chain rule is always necessary. It just happen s that dx/dx = 1, so it doesn't enter into the complexity. Suppose you had x^3 + y^3 + u^2 = uv^2 Then you'd have 3x^2 + 3y^2 y' + 2u u' = u' v^2 = 2uv v' Whenever you take a derivative, you have to ...
*September 27, 2015*

**Calculus**

Your second line should be (via the chain rule!) y" = [(y^2)(-2x)-(-x^2)(2yy')]/y^4 Now plug in -x^2/y^2 for y' and you should get the right result.
*September 27, 2015*

**Tertiary**

(a+b)^2e^-2x=a^2-b^2 divide both sides by a+b: (a+b) e^-2x = a-b (a+b)/(a-b) = e^2x a+b = ce^x a-b = ce^-x and the rest follows.
*September 27, 2015*

**Tertiary**

sinh x = (e^x - e^-x)/2 So, now you have e^x - e^-x = 2tan y e^2x - 1 = e^x * 2tan y e^2x - 2tany e^x - 1 = 0 Now use the quadratic formula to get e^x = [2tany ±√(4tan^2y+4)]/2 = tany±√(tan^2y+1) = tany±secy x = ln(tany±secy) Pick the ...
*September 27, 2015*

**fundamentals math**

without a Z table there is no way to do this stuff. Not unless you can calculate the normal distribution stuff by hand. There may be a chance that they will provide a few Z scores at test time, and if so, then you can interpolate. Otherwise, check your class materials and ...
*September 27, 2015*

**fundamentals math**

you can play around with Z table stuff here: http://davidmlane.com/hyperstat/z_table.html
*September 27, 2015*

**Math**

make sure you know what the general form is. Then expand this to get x^2-10x+25 = 5 Now just rearrange terms to place in general form.
*September 27, 2015*

**college algebra**

Or, reason like this: after 1 hour, the freight train is 60 miles ahead. Since the passenger train goes 20 mi/hr faster, how long will it take to make up the 60 miles?
*September 27, 2015*

**college algebra**

since distance = speed * time, 60(t+1) = 80t Now just find t. That's the time traveled by the faster train.
*September 27, 2015*

**Math**

x + .75x = 1425 x is the larger paycheck.
*September 27, 2015*

**Math**

just turn all those words into algebra: If there are x mg of vitamin C in a glass of apple juice y mg in a glass of orange juice then consider the amount of vitamin C as described above: x+y = 180 4x+3y = 637.4 now just find x and y It could have been worse; the glasses might ...
*September 27, 2015*

**Precalculus**

If y = ax^2+bx+c, then we can plug in the points and get 0a+0b+c = 5 a+b+c = 2 9a+3b+c = 2 y = x^2-4x+5 Or, noting the symmetry about x=2, we know that y = a(x-2)^2 + k y(0) = 5, so 4a+k = 5 y(1) = a+k = 2 so, a=1,k=1 y = (x-2)^2+1
*September 27, 2015*

**calculus**

recall that if u = secx, u' = secx tanx You have ∫ secx dx Turn that into a fraction by multiplying by (secx + tanx) and you have ∫ secx(secx+tanx)/(secx+tanx) dx Now, if u = secx+tanx, du = secx tanx + sec^2 x and your integral now becomes ∫ du/u = lnu...
*September 27, 2015*

**Math- Please help**

#1 g(x) = f(x-3) = x-3 #2 g(x): stretch y by 5: 5f(x) down 3: 5f(x)-3 x reflect: -(5f(x)-3) = 3 - 5f(x) g(x) = 3 - 5x^2 #3 g(x): shrink y by 4: (1/4)f(x) right 1: (1/4)f(x-1) up 2: (1/4)f(x-1)+2 g(x) = (1/4)|x-1|+2 #4 g(x): y stretch 3: 3f(x) up 2: 3f(x)+2 right 8: 3f(x-8)+2 g...
*September 27, 2015*

**Math**

that would be 2.46 std below the mean, or 78-2.46(4.6)
*September 27, 2015*

**Physics**

Maximum range is achieved at a 45° angle of elevation. Just use your equation of motion to get the range. If you have forgotten the relevant formulas, read a nice discussion here. https://en.wikipedia.org/wiki/Trajectory Then add a term of 250 to adjust the equation. Hmmm...
*September 27, 2015*

**Math**

assuming a 360-day year, as is often the case, then 18220(1+.052/360)^175 = 18686.40
*September 27, 2015*

**Math**

um, you might check when y=5/2
*September 27, 2015*

**math**

3g = g+24 g = 12 You can take it from there, I hope...
*September 27, 2015*

**precalc**

would you have trouble solving 1/2 = 1/x + 1/3 ? Probably not. So, follow the same steps here: 1/r = 1/r1 + 1/r2 1/r1 = 1/r - 1/r2 1/r1 = (r2-r)/(r*r2) r1 = (r*r2)/(r2-r) The other one is even easier: F = GMm/r^2 = (GM/r^2)m m = F(r^2/GM) = Fr^2/GM
*September 27, 2015*

**precalculus**

you are correct.
*September 27, 2015*

**pre-calc**

It might help to substitute u for √x. That gets rid of all those pesky fractional exponents. 3/u + 4u + u^3 (3+4u+u^4)/u (u+1)^2 (u^2-2u+3)/u (√x+1)^2 (x^3/2 - 2√x + 3/√x) The hard part here is factoring u^4+4u+3. Try synthetic division, knowing that ...
*September 27, 2015*

**MATH**

c'mon - don't forget your handy difference of cubes formula: x^3-y^3 = (x-y)(x^2+xy+y^2) You have x=a, y=b^2 So, plug and chug.
*September 27, 2015*

**Algebra II**

Just graph each piece over the indicated domain. Take some graph paper, and draw dark vertical lines at the boundaries in the domain. Then graph each function as a dotted line. Make the lines solid where the part of the domain applies. The solid lines are your final graph. For...
*September 27, 2015*

**Calculus**

Think about this: u^2 = r^2 2u u' = 2r r' u^2 = ∑ xj^2 2u du = 2∑ xj
*September 27, 2015*

**science**

as they say, one measurement is worth a thousand expert opinions. Go to a malt shop and order a smoothie. Watch what they do. or, remember that google is your friend.
*September 27, 2015*

**Geometry**

Given: r is perpendicular to s, t is perpendicular to s prove:r is parallel to t
*September 27, 2015*

**Geometry**

sorry parallel
*September 27, 2015*

**Geometry**

A carpenter cut the top section of a window frame with a 37-degree angle on each end. the side pieces each have a 50 degree single cut at their top sides. Will the side pieces of the frame be ?
*September 27, 2015*

**math**

what's all this ratio stuff? 16% better mileage means the current value times 1.16
*September 27, 2015*

**Math**

every 36 minutes they are in synch again. So, ... Of course, not knowing the length of the route, there's no way to tell when they will both arrive at that same stop again.
*September 27, 2015*

**Math**

well, since the standard form is Ax+By=C with A positive just work with it till that's what you have. 8y-16x=24 -16x+8y=24 16x-8y = -24 That looks ok, but A,B,C should have no common factors. So, dividing out the 8, we have 2x-y = -3
*September 27, 2015*

**Calculus**

along x=y, the expression is 2x^2/4x^2 = 1/2 along x=2y, we have 5y^2/9y^2 = 5/9 In other words, as we approach (0,0) along different paths, the limit varies, so cannot be said to exist as a single number.
*September 27, 2015*

**Maths: Sequences need help**

I cannot parse your syntax for (1) If Vn = 6*2^n, then clearly this is just a geometric sequence, where a = 12 r = 2 Finding its sum is now easy, right?
*September 26, 2015*

**Mathematics in Science**

Since 13.0 only has 3 sd's, I expect you need to round your answer to 3 sd's as well.
*September 26, 2015*

**trig**

(a) well, there are 2pi radians or 360 degrees per revolution. (b) the circumference of the wheel is 2pi*2.08 inches. That's how far it moves on each revolution.
*September 26, 2015*

**Taalnet**

2x+3y=200 2xy=1400 2x+3(700/x) = 200 x=88.08 or 11.92 So, the area is 23.84 x 58.72 or 176.16 x 7.94
*September 26, 2015*

**algebra**

if the three numbers are x-1,x,x+1, then (x-1)(x)(x+1) = x^3+33 x^3-x = x^3+33 x = -33 (-34)(-33)(-32) = -35904 = -33^3 + 33
*September 26, 2015*

**math**

If you subtract the bottom from the top, you eliminate y, leaving -2x = -1 Now you have x, and you can use that value to find y.
*September 26, 2015*

**Functions**

no. Because , if it had a period, say k > 0, then that would mean that e^(x+k) = e^x e^x e^k = e^x e^k = 1 k=0 But, we specified k > 0. I mean, just look at the graph. Surely it is not periodic! Now, if we use a complex number z, then it is true that e^z is periodic.
*September 26, 2015*

**MATH**

since each lb makes 4 burgers, just multiply by 4.
*September 26, 2015*

**math**

well, each lb makes 4 burgers, so just multiply 16 3/4 * 4
*September 26, 2015*

**math conversions**

12200cal/68.1g = 179.1 cal/g
*September 26, 2015*

**Math**

start doing the conversion from chickens to time. Its easy if you watch the units. I'll use c for chicken and f for feather. Thus, we have 5157c * 4904f/c * 1.9s/69.8f * 1hr/3600s = 191.2 hr
*September 26, 2015*

**Test**

well, I'd work faster. That becomes easier if you have studied before the exam, so you don't have to waste time figuring out how to solve the problems, and can just spend time writing your answers.
*September 26, 2015*

**analytic geometry**

well, you know that a parabola's equation with vertex at (0,0) is x^2 = 4py The length of the latus rectum is 4p, and the distance from the focus to the vertex is p. So, tan θ/2 = 2p/p = 2
*September 26, 2015*

**Physics**

three crests span two complete waves. Think of a sine wave. max-max is one wavelength, so max-max-max is two wavelengths. So, the wavelength is 7.5m Now use your formula: speed = wavelength * frequency
*September 26, 2015*

**Maths area**

8+10+8+10
*September 26, 2015*

**math**

.06x = 59.00
*September 26, 2015*

**math**

x(2)+x(100) = 2x+100x = 102x or x(2+100) x(102) 102x
*September 26, 2015*

**Algebra**

I'll take a guess at just what you mean: 5 - 13/(x-2) ---------------------- 6/(x-2) - 7 In both the numerator and denominator, put everything over a common denominator [5(x-2)-13]/(x-2) ----------------------- [6-7(x-2)]/(x-2) Since the denominators are the same, they can...
*September 26, 2015*

**Math**

just keep track of the amount of solute present. The amounts must add up to the total in the final solution. Remember to watch the units; a pint is 473mL. .38x + .82(473) = .50(x+473)
*September 25, 2015*

**animals**

you appear to want breeds, not kinds. Kinds of dogs are working dogs, sporting dogs, hunting dogs, terriers, toy dogs, etc. Anyway, it would have been much faster to google dog breeds -- you'll get many many hits. I'm sure you've heard of poodle chow chow beagle ...
*September 25, 2015*

**Z table**

play around with Z stuff at http://davidmlane.com/hyperstat/z_table.html
*September 25, 2015*

**Z table**

or, you can play around with Z values and areas at http://davidmlane.com/hyperstat/z_table.html
*September 25, 2015*

**7th grade algebra**

in 45 minutes, plane 1 has gone 450 miles. Plane 2 goes 200 mi/hr faster, so it takes 450/200 = 2.25 hours to catch up. Or, since distance = speed * time, 600(t+.75) = 800t
*September 25, 2015*

**Math (Discrete Math)**

well, is f(5) = 5? No. So, f^-1(5) is not 5. y = x^2-4x+2 = (x-2)^2 - 2 The inverse function, restricted to the domain above, is f^-1(x) = 2+√(x+2) so, f^-1(5) = 2+√7
*September 25, 2015*

**algebra 2**

it allows you to look for expressions that can easily be substituted or evaluated.
*September 25, 2015*

**Math**

irrational no others
*September 25, 2015*

**Indices**

Come on, guy. Add the powers of 2 for one answer; add the powers of 4 for the other. I was just showing how each number could be expressed either as a power of 2 or a power of 4. Sheesh.
*September 25, 2015*

**Indices**

p = 2^-12 = 4^-6 q = 2^-(4/3) = 4^(-2/3) r = 8*2^(1/2) = 2^(7/2) = 4^(7/4) Now just add up the powers for the product.
*September 25, 2015*

**Maths - coordinate geometry**

remember the point-slope form? Your line has slope 1/2, so the line parallel is y-2 = 1/2 (x+1)
*September 25, 2015*

**Math**

well, geez - just plug in the values! 2(3^-2)(-2)^-2 2(1/3^2)(1/(-2)^2) 2(1/9)(1/4) 1/18
*September 25, 2015*

**Calculus**

If I read your weird syntax correctly, you have y = r/√(r^2+1) Using the quotient rule, if u and v are functions of r, y = u/v y' = (u'v-uv')/v^2 We have u=r and v=√(r^2+1) u' = 1 and v' = r/√(r^2+1) y' = [(1)√(r^2+1)-r(r/√...
*September 25, 2015*

**math**

a = 4 pi r^2 da = 8 pi r dr You have dr = 0.05 and r=4, so da = 8 pi * 2 * 0.05 = 0.8 pi cm^2
*September 25, 2015*

**math - take two**

sorry. Naturally, an area of zero will be a minimum. So, pick sides of 0 and 20. That's technically not a triangle, but you van pick any tiny value h and make the sides h and √(400-h^2) and the area will be as close to zero as you like.
*September 25, 2015*

**math**

half of a square will max area.
*September 25, 2015*

**calculus**

the distance from (x,x^3) to (4,0) is z = √((x-4)^2+(x^3-0)^2) = √(x^6+x^2-8x+16) so, dz/dx = (6x^5+2x-8) / 2√(x^6+x^2-8x+16) Now, dz/dx=0 when the numerator is zero. That is when 6x^5+2x-8=0 x=1 So, the point (1,1) is closes to (4,0) Or, you could reason ...
*September 25, 2015*

**calculus**

we have 4x^2 + 9y^2 = 72 8x + 18y y' = 0 y' = -4x/9y So, the line through (h,k) tangent to the curve is y-k = (-4h/9k) (x-h) That line has x-intercept at (-4h/9k)x + 4h^2/9k + k = 0 x=(4h^2+9k^2)/(9k) * (9k/4h) = (4h^2+9k^2)/(4h) But, since 9k^2 = 72-4h^2, the x-...
*September 25, 2015*

**calculus**

If the side parallel to the river has length x, and the other two sides have length y, we know that the cost is 6x+3*2y = 600 x+y=100 the area is a = xy = x(100-x) That has a maximum at x=50. So, the area is 50 by 50
*September 25, 2015*

**math**

a square uses the least fence.
*September 25, 2015*

**calculus**

if there are x decreases of 100, then price = 900-100x demand = 5000+1500x so, the revenue r is r = (900-100x)(5000+1500x) So, just find where dr/dx = 0 for the maximum revenue. You know it is a maximum since the parabola opens downward. Note that x is not the answer to the ...
*September 25, 2015*

**math**

x+y=k p = xy^2 = (k-y)y^2 = ky^2 - y^3 dp/dy = 2ky - 3y^2 dp/dy=0 when y = 2k/3
*September 25, 2015*

**algebra**

480(1+.15/4)^(4*7)
*September 25, 2015*

**math**

h = 65tan(x) dh = 65 sec^2(x) dx Now plug in your values for x and dx (in radians!)
*September 25, 2015*

**algebra 2**

clearly, d(t) = 0.5t ft
*September 25, 2015*

**geometry**

42 km
*September 25, 2015*

**Math/solving two-step equatios(distributive proper**

step 1: remove the parentheses, by applying the distributive property step2: collect all the variable stuff on one side, by adding/subtracting the constants step3: divide by the coefficient to isolate the variable value 3(c+5) = 12 1:3c+15 = 12 2:3c = 12-15 = -3 3: c = -1 3/4...
*September 25, 2015*

**P6 Maths @!**

Hmmm. I get a=150 m=80 check: 40% of 150 = 60 75% of 80 = 60 80-20 = 60 150 = 60+90 Extra credit: where did Reiny go wrong?
*September 25, 2015*

**P6 maths**

.4a = .75m .75m = a-90 Now just find a and m, and thus a+m
*September 25, 2015*

**Math**

j=s+72, so s = j-72 t=s s=k+50, so k=s-50=j-122 j+k+s+t <= 502 j+k+2s <= 502 j+j-122+j-72 <= 502 3j-194 <= 502 3j <= 696 j <= 232
*September 25, 2015*

**Physics**

wow - what a lot of words. Just specify stuff with symbols, ok? r(t) = (3t^3-2t)i + (5-2t^4)j v(t) = (9t^2-1)i -8t^3 j a(t) = 18t i - 24t^2 j (d) at t=3, dr/dt = v(3) = 26i-216j so, tanθ = -216/26
*September 25, 2015*

**Algebra**

For m minutes, we want A >= B. So 13+0.06m >= 0+0.08m
*September 25, 2015*

**f5 math**

80/(x+2) = 80/x - 2
*September 25, 2015*

**Calculus 1**

well, if x>=0, |x|=x, so we have y = x/√(5-x^2) y' = 5/(5-x^2)^(3/2) At x=2, y'=5 So, the line through (2,2) with slope=5 is y-2 = 5(x-2) See this at http://www.wolframalpha.com/input/?i=plot+y%3D|x|%2F%E2%88%9A%285-+x^2%29%2C+y%3D5%28x-2%29%2B2+for+0%3C%3Dx%...
*September 25, 2015*

**Algebra**

(1200-500)/24
*September 25, 2015*

**algebra**

Looks the same to me :-)
*September 24, 2015*

**math**

after 24 minutes, they synch up.
*September 24, 2015*

**College Algebra**

solve for t years in 5000(1+.075/4)^(4t) = 7900
*September 24, 2015*

**College Algebra**

what is the half-life? If it is N years, then you need to solve for t in (1/2)^(t/N) = 0.25 Expect the answer to be just a bit over one half-life...
*September 24, 2015*

**Algebra**

you know that the amount remaining after t minutes is f(t) = 13 e^(-kt) Now you know that 13 e^(-20k) = 4.5 k = 0.053, so f(t) = 13 e^(-0.053t) Now you want the alarm to sound when p(t) = 2. So, just find t where 13 e^(-0.053t) = 2.0
*September 24, 2015*

**Pre Calculus**

Note that 80 minutes is 8 doubling periods, for a growth of 2^8 = 256 times. So, initially there were 50000/256 bacteria. I think you can take it from there, no?
*September 24, 2015*

**Math**

(3/4)/8 = 3/32 (1/3)/4 = 1/12 LCD(32,12) = 96 3/32 + 1/12 = 9/96 + 8/96 = 17/96
*September 24, 2015*

**Geometry**

G = 180-F = 180-(90-E) = 90+E = 90+(90-D) = 180-D = 180-(180-C) = C
*September 24, 2015*

**Math**

well, just multiply each ingredient by 5 1/2. For the granola, that's (1 1/2)(5 1/2) = 3/2 * 11/2 = 33/4 = 8 1/4 and so on
*September 24, 2015*

**math for managers**

and it is the line through (-5,2) with slope 2/3
*September 24, 2015*