Friday

May 27, 2016
Total # Posts: 40,851

**Physics Volume question!!!**

since the range is proportional to the square of the initial velocity, if it has increased by a factor 4, the initial velocity has doubled. Since the volume of water stays the same, that means that the area of the opening has been halved.
*April 27, 2016*

**Pre-Calculus**

y = kx 6 = 4k, so k = 3/2 y = 3/2 x
*April 27, 2016*

**PreCalc**

Reiny is right: 42.5, not 37.5 but I'm sure you caught my error. Note how he offset his function by using a phase shift, which has the same effect as changing the sign as I did, since shifting by 1/2 period does that flip: cos(x+pi) = -cos(x)
*April 27, 2016*

**PreCalc**

the max-min value is 50-35=15, so the amplitude is 7.5. The center line is (35+50)/2 = 37.5 y = 7.5 sin(x) + 37.5 y has a max at t=12, and the period is 24 hours, so the minimum k is a t t=0. cos(x) has a max at x=0, so we have -cos(x) and thus y = -7.5 cos(π/12 x) + 37.5...
*April 27, 2016*

**math**

2":4ft = 2":48" = 1:24
*April 27, 2016*

**Math **

lose the apostrophe in one's, unless you also write event's and coin's and cloud's... independent events do not affect each other. So, I'd choose A,D,E
*April 27, 2016*

**Math **

4/35 = .114 = 11.4% However, the sum of your listed colors (and one color is missing and one is duplicated) does not equal 35.
*April 27, 2016*

**prealgebra**

If you mean 6P2 (permutations of 6 things, 2 at a time), then yes, the answer is 6*5 = 30
*April 27, 2016*

**prealgebra**

could be, depending in the value of P. and what does P2 mean?
*April 27, 2016*

**Trig**

since sin^2θ is never more than 1, you need cos^2θ = 0 so, θ = π/2 or 3π/2 or, solving algebraically, sin^2θ = cos^2θ + 1 cos^2θ - sin^2θ = -1 cos(2θ) = -1 θ = π/2 or 3π/2
*April 27, 2016*

**Geometry**

2πr(r+h) = 112π 8π(4+h) = 112π 4+h = 14 h = 10
*April 27, 2016*

**algebra**

slope = -13 now you can plug that into the point-slope form, using either point.
*April 27, 2016*

**Math**

if the length is L, then you know that 1.8L = 18900 so, divide by 1.8 to get L. If the width is in cm, then you will also get L in cm, so divide that by 100 to get L in meters.
*April 27, 2016*

**Math**

the area is 18900/100^2 = 1.89m^2 so, the length is 1.89/1.8 m
*April 27, 2016*

**Algebra**

2(x + 6x) = 420 x = 30
*April 27, 2016*

**Calculus**

just plug and chug f(x) = f(2) + f'(2)(x-2)/1! + ... f(2) = 1/2 f'(2) = -1/x^2 = -1/2^2 = -1/4 f"(2) = 2/x^3 = 1/4 f(3)(2) = -6/x^4 = -3/8 f(4)(2) = 24/x^4 = 3/4 f(x) = 1/2 + (-1/4)(x-2)/1! + (1/4)(x-2)^2/2! + (-3/8)(x-2)^3/3! + (3/4)(x-2)^4/4! + ... = 1/2 - 1/4 (...
*April 27, 2016*

**Calculus**

From 0 to π/2, 4cos(x) is above 8-4x/π, so the area would be ∫[0,π/2] (8-4x/π)-4cos(x) dx = 7π/2 - 4 But there is a second symmetric region between π/2 and π, so the area is double that, or 7π-8 see http://www.wolframalpha.com/...
*April 27, 2016*

**algebra**

Apparently you mean tn = 75^(5n) = (75^5)^n tn+1 = tn * 75^5
*April 27, 2016*

**Math(Radicals)**

2√6 (3√2 - 12) = 6√12 - 24√6 = 12√3 - 24√6
*April 27, 2016*

**maths**

come on - you have the formulas. plug in your numbers. We can check your results. and that's alpha, not alpher.
*April 27, 2016*

**Math**

log(y+3) = log(x^3/(x-2)) y+3 = x^3/(x-2) y = x^3/(x-2) - 3
*April 27, 2016*

**Logs**

assuming base 10, log(3x-13) = log100 - logx log(3x-13) = log(100/x) 3x-13 = 100/x 3x^2 - 13x - 100 = 0 (3x-25)(x+4) = 0 x = 25/3, since x = -4 is not allowed.
*April 26, 2016*

**math**

well, the extra 4 balls added 3.160-2.040 = 1.12g Now you know how much each ball weighs, so you can figure the mass of the box.
*April 26, 2016*

**math**

Since the tank has a cross-section area of 100π in^2, each in^3 of ball raises the water level by 1/(100π) in. So, figure the volume of the ball and multiply.
*April 26, 2016*

**Arithmetic sequence**

so, follow the hint. add them and multiply them.
*April 26, 2016*

**Geometric series**

apparently you have a = 1 r = -1/√2 S20 = a(1-r^20)/(1-r) = 1023/(512(2+√2))
*April 26, 2016*

**Pre-Calculus**

g(x) has two branches, so g^-1(x) = ±√(x-7) in either case, the domain is all x such that x-7 >= 0 just as the range of g(x) is [7,∞)
*April 26, 2016*

**trig**

34 mi/hr * 1hr/60min * 12*5280in/mi * 1rev/(14π in) = 816.33 rev/min
*April 26, 2016*

**math**

Reiny did this. See the related questions below.
*April 26, 2016*

**Math**

There are lots of solutions, such as 1/2*6+8*5*7/4+3*9 = 100 4/8*6+2*5*7/1+9*3 = 100 8/4*7+6*9*3/2+1*5 = 100
*April 26, 2016*

**Algebra Help me Please**

the y-intercept is the constant term the end behavior is y->∞ or y-> -∞, as with all polynomials. the only other features of interest are the x-intercepts. A little synthetic division will reveal those.
*April 26, 2016*

**math**

anyway, since 2/3 of the odd numbers on a regular die are primes, that means that a prime will come up 2/9 of the time.
*April 26, 2016*

**math**

since odds come up 1/3 of the time, I guess it depends on how many of the odd faces are primes. You haven't said how many faces are on the die.
*April 26, 2016*

**Logs**

since logs are only defined on positive numbers, we need x^2+14x > 0 x(x+14) > 0 You know that this parabola crosses the x-axis at -14 and 0, and since it opens up, it is positive everywhere except between the roots. So, the domain is (-∞,-14)U(0,∞)
*April 26, 2016*

**scte**

you forgot the frequency. anyway, once you have that, just plug in v = L di/dt and crank it out.
*April 26, 2016*

**Algebra**

2*6 = 12 (total length of pythons) 21-12 = 9 (amount left for the corn snakes) 9/3 = 3 feet per corn snake c = (21-2*6)/3
*April 26, 2016*

**Math/Precal**

(9^2x)/(27^x-2)=81^3x-4 since 9 = 3^2 and 27 = 3^3, this is 3^(4x) / 3^(3x-6) = 3^(12x-16) 4x-(3x-6) = 12x-16 x+6 = 12x-16 11x = 22 x = 2 check: 9^4/27^0 = 81^2 yep
*April 26, 2016*

**algebra**

if the steamboat's speed is s, then since time=distance/speed, 147/s = 120/(s-9)
*April 26, 2016*

**math**

I have no idea how many times she rolled the die to get the 12 twos, but since 2 only comes up on average 1/6 of the time, she can expect about 16 twos in 100 rolls.
*April 26, 2016*

**Math-check my answers!!!**

you can easily check your work by typing in your expressions at wolframalpha.com It will show how they can be simplified, and much other information as well.
*April 26, 2016*

**math**

0.10 (1+r)^(2016-1948) = 85 (1+r)^68 = 850 1+r = 1.104 r = .104 or 10.4%
*April 26, 2016*

**Math**

B = F+6 (B-22)+(F-22) = (B+F)/2 Try that. Your solution indicates that when they last met, they were 6 and 14. But 6+14 is not half the sum of their ages today.
*April 26, 2016*

**Math**

Two old friends meet. They hadn't seen each other in 22 years. Betty is 6 years older than France's, but neither is older than 50. The sum of their ages when they met is exactly half of their ages today. How old is Betty? B= F+6 B=50-22 =28 F =50 -22=28 B=28+6=34 Betty...
*April 26, 2016*

**Math**

stop guessing, and try the various functions! Just plug in a value for x and see whether the y also matches. -8*2 - 5 = -21 -8*5 - 5 = -45
*April 26, 2016*

**Math**

A? c? d? help meh
*April 26, 2016*

**Math**

nope. check again.
*April 26, 2016*

**Math**

The ordered pairs (2,-21) and (5,-45) are solutions to which of the following equations? y = -8x - 5 y = -8x + 5 <---- my answer y= 8x - 5 y= 8x + 5
*April 26, 2016*

**maths**

(2x+y+7) - (x-y) = (x-y)-2 (x-3y)-(2x+y+7) = (x-y)-2 x=2, y=-3 ...
*April 26, 2016*

**maths**

n/2 (2*2 + (n-1)(5/4)) = 204 n = 17
*April 26, 2016*

**maths**

Figure how many terms there are (n) Sn = n/2 (39+380)
*April 26, 2016*

**maths**

clearly the limit is -0.3
*April 26, 2016*

**maths**

Tn = 5 + 7(n-1) = 7n-2 S38 = 38/2 (2*5 + 37*7)
*April 26, 2016*

**maths**

do you recognize powers of 3?
*April 26, 2016*

**physics**

Let the speed of sound be s. Then the time taken for the splash to be heard is 45/s seconds. That means that the stone fell for 3.12 - 45/s seconds. You know that stone fell 45m, so 5(3.12-45/s)^2 = 45 s = 375 m/s not too close to the expected value of 343 m/s...
*April 26, 2016*

**Calc 2**

an+1/an = e^-3 (1 + 2/n + 1/n^2) that ratio is less than 1, so the series converges. see http://www.wolframalpha.com/input/?i=sum+n^2%2Fe^%283n%29
*April 26, 2016*

**Math**

44 - 0.95 * (54-34) = 25
*April 26, 2016*

**Math**

7+9=16 80/16 = 5 7:9 times 5 is 35:45
*April 26, 2016*

**math**

well, 3000 ml is 3 liters.
*April 26, 2016*

**College Algebra**

just find t where 15 e^(-0.051t) = 1
*April 25, 2016*

**algrea brs so hard**

your parentheses do not balance. is m7 m*7 or m^7 ? if all you want is to expand it, use the distributive property.
*April 25, 2016*

**math**

1/3 for each son. if each ate 1/2 of his share, then 1/2 of the pie was eaten, leaving 1/2 uneaten. You can see that the number of slices does not matter here.
*April 25, 2016*

**Maths Urgent please**

well, assuming you meant g(x) = (1/16 + x)^(-5/4) g'(x) = (-5/4)(1/16 + x)^(-9/4) using the chain rule for g(x) = u^n and u = (1/16 + x) do that again for g", and evaluate the fractions.
*April 25, 2016*

**Maths Urgent please**

so, what do you get for g'(x)?
*April 25, 2016*

**Calculus II**

Looks good to me.
*April 25, 2016*

**Calculus**

since the radius is 3/4 the height, The volume of the pile is thus v = π/3 r^2 h = π/3 (3h/4)^2 h = 3π/16 h^3 dv/dt = 9π/16 h^2 dh/dt now, plugging in your numbers, at t=3, v = 3/2, so 3π/16 h^3 = 3/2 h = 2/∛π so, 9π/16 4/∛π^...
*April 25, 2016*

**math**

huh? How much do you make on regular days? It will be 1.5 times that much.
*April 25, 2016*

**Math**

the given line has slope 1/3 so, perpendicular lines will have slope -3 The line you want is thus (using the point-slope form): y+2 = -3(x-6) or, if you prefer, y = -3x + 16
*April 25, 2016*

**Calculus II**

no, but x^(4n+2) will work. duh.
*April 25, 2016*

**Calculus II**

squaring the entire series would be (sin x)^2, not sin(x^2) Just replace all the x's with x^2. ∑(-1)^n[(x^2)^(2n+1)]/(2n+1)!
*April 25, 2016*

**Length of similar shapes**

25/10 = 5/2 all of the other dimensions are multiplied by that same ratio.
*April 25, 2016*

**Calculus**

the separation distance z after t hours is found using z^2 = (200t)^2 + (150t)^2 so, find dz/dt when t=2
*April 25, 2016*

**Math**

The medians of the triangle all pass through the center of the circle. The medians intersect 2/3 of the way to the opposite side. The altitude of the triangle is also one of the medians, and it has length 10√3. So, r = (2/3)10√3 = 20/√3 For an equilateral ...
*April 25, 2016*

**Roots, complex numbers**

huh? negatives are just numbers, like positives. z^5 = -1 = 1 cisπ z = 1^(1/5) cis(π/5) but since cisπ = cis3π = cis5π, etc., to get all the values from 0 to 2π, z = 1 cis(π/5 k) where k = 1,3,5,7,9 Reiny went over this with you. There are 5 ...
*April 25, 2016*

**Math/Precal**

sorry. I meant logy(8y-7)
*April 25, 2016*

**Math/Precal**

depends on what you mean by "solve" It is log7(8y-7)
*April 25, 2016*

**math**

depends on the table.
*April 25, 2016*

**Math**

Does 34 mean 3/4? How can Ava give 920 cranes, when she only made 100? anyway, start writing down the amounts, adding and subtracting as required. At the end, subtract Ava's from Brittany's.
*April 25, 2016*

**Math**

yep
*April 25, 2016*

**Calculus**

v = 4π/3 r^3 dv/dt = 4πr^2 dr/dt Now just plug in your numbers.
*April 25, 2016*

**Calculus**

plug and chug x^2+y^2 = 25 2x dx/dt + 2y dy/dt = 0 Now you have x, y, dx/dt, so find dy/dt
*April 25, 2016*

**Calculus**

If his distance from the pole is x and the length of the shadow is s, then s/2 = (s+x)/10 1/2 ds/dt = 1/10 (ds/dt + dx/dt) 4 ds/dt = dx/dt So, the length of the shadow is growing 1/4 as fast as the man's speed. But that's not how fast the tip of the shadow is moving. ...
*April 25, 2016*

**PHYSICS! HELIUM BALLON**

the balloon weighs 277*9.8 = 2714.6 N add to that the weight of the helium enclosed. (volume * density * 9.8) so, the volume of air displaced must weigh the same amount. Now just plug in the numbers and crank it out.
*April 25, 2016*

**Calculus**

see the other problams - they are all the same thing.
*April 25, 2016*

**Calculus**

No, they said that the radius is increasing at a constant rate of 2 cm per minute That means dr/dt = 2. dv/dt = 4πr^2 dr/dt da/dt = 8πr dr/dt You have r and dr/dt, so crank it out.
*April 25, 2016*

**Calculus**

the separation distance z after t hours is found using z^2 = (200t)^2 + (150t)^2 so, find dz/dt when t=2
*April 25, 2016*

**Trig**

for Lions, assuming that all points lie on the curve, k + Asin(0+C) = 1272 k + Asin(2B+C) = 1523 k + Asin(4B+C) = 1152 k + Asin(6B+C) = 891 I'd start by noting that sin(C) = (1272-k)/A Now you can find cos(C) and then use the sum formulas to expand the other sines.
*April 25, 2016*

**O.D.E**

If someone can help me with this ODE I would greatly appreciate it. Thank you in advance! ------ Consider the differential equation dx/dt = 1/2x This is a separable O.D.E., so we know how to find all of its solutions: they are of the form x(t) = sqrt(t+c) where C is a constant...
*April 25, 2016*

**CALCULUS**

the small tank has a volume of 96π ft^3 its depth decreases at a rate of (1/2)/(16π) = 1/(32π) ft/s So, A: v(t) = 96π - 1/2 t B: duh C: the large tank's area is 4 times as big, so its depth increases 1/4 as fast, or 1/8 ft/s. D: 6/(192π)
*April 25, 2016*

**Brokport**

If the amounts invested are x,y,z then they have told us that x+y+z = 180000 .08x + .06y + .09z = 8520 .08x = 6 * .06y I suspect a typo, since even if the whole amount were invested at 6%, the interest would be 10,800. In other words, there's no way to solve these ...
*April 25, 2016*

**Algebra SOLVING LINEAR EQUATIONS AND INEQUALITIES**

#1 you can solve for 1/x and 1/y in the usual ways: elimination: double the 1st and subtract 6/x - 4/y = 28 6/x + 3/y = 7 ------------------- 7/y = -21 1/y = -3 then, 1/x = 8/3 or, y = -1/3 and x = 3/8 using substitution, 3/x = 14+2/y 2(14+2/y) + 3/y = 7 28 + 4/y + 3/y = 7 7/y...
*April 25, 2016*

**Math**

(2)(33)(19)[2(33)(19)-33-19] (2)(33)(19)[1254-33-19] (2)(33)(19)[1202] 1,507,308
*April 25, 2016*

**geometry**

Find the volume in terms of pi of a sphere with a surface area of 9 pi sq ft
*April 24, 2016*

**Math2**

f(x) = 3x^2 - 12x + 2 the y-intercept is clearly at 2. x-intercepts? where y=0. Use the quadratic formula to get x = 2±√(10/3)
*April 24, 2016*

**Math**

3 : 2 = 1 : 2/3 = 5 : 10/3
*April 24, 2016*

**Algebra**

slope = 15/9 = 5/3 y-4 = 5/3 (x-6) y = 5/3 x - 6 The lines are not perpendicular, because the slopes are not negative reciprocals. The line through the points is perpendicular to y = -3/5 x - 6 However, they do both have a y-intercept of -6.
*April 24, 2016*

**Math**

using the vertex form, y = a(x-3)^2 - 6 using the point given, 10 = a(-1-3)^2 - 6 10 = 16a-6 a = 1 y = (x-3)^2 - 6 = x^2-6x+3
*April 24, 2016*

**math**

clearly getting a 44 (lower than any of her scores so far) will not raise her grade!! Add up the total points she has so far. A "B" average for 7 tests needs at least 80*7 = 560 points. So, how many does she need to get there?
*April 24, 2016*

**Math**

The sequence is not geometric! 17111/19 = 900.5789 1539121/17111 = 89.9492 the ratio is not constant. Fix it, find the common ratio r, and then a6 = 19*r^5
*April 24, 2016*