Wednesday
February 10, 2016

# Posts by Steve

Total # Posts: 37,527

Math
Hmmm. does 34 = 32?
January 11, 2016

Math
multiply the top one by 2, and you have 3x+4y=22 3x+6y=22 Now what do you think?
January 11, 2016

Math
whatever you do to one side, you must also do to the other side, if they are to remain equal. You subtracted x in your first step, but only on the left. If you had tried a value for x and y, you would have seen that your solution was wrong. y = -x+7, so let x=1, and y is -6. ...
January 11, 2016

algebra 1
multiply the 2nd equation by 5 and you have 3x-5y = 21 10x+5y = 5 Now you can eliminate y and get x, then figure y.
January 11, 2016

Math
The water level rose 2 cm. So, the volume of the stones is 2*20*15=600 cm^3 This assumes that the stones were completely covered by water.
January 11, 2016

Math- steve? reiny?
Does f^-1(x) even exist? f'(x) = 5x^4+6x^2+1 That is always positive, which means that the graph of f(x) does not change direction, so it passes the horizontal-line test. where is f(x) = 3? x^5+2x^3+x-1 = 3 x^5+2x^3+x-4 = 0 a little synthetic division shows that x=1 is a ...
January 11, 2016

Math
divide into 5 equal parts. Then use 1 part and 4 parts for the lengths.
January 11, 2016

Algebra
s = 3d m+1 = 6d m+10 = 14+(s+10)+(d+10) solve to find m. I get non-integer values for s and d. If "three times older" means d+3d=4d, then I get integer values, but the man is 149. Not likely.
January 10, 2016

If the width is w, the length must be 50-w. So, the area is a = w(50-w) The maximum area is achieved when x=25. You can find what it is. Note that the max area is when the rectangle is a square.
January 10, 2016

maths
If you mean 6x^2-x+3 < 5x^2+5x-5 then just collect terms on one side, and you get x^2-6x+8 < 0 (x-2)(x-4) < 0 This is a parabola which opens upward, so it is negative between the roots. Thus 2 < x < 4 A product is negative if exactly one of the factors is negative.
January 10, 2016

Mathematics
If you are using A for θ, then clearly θ=π/4 is a straight line with slope 1, so that is just y = x r = a sin2θ r = 2a sinθ cosθ r^3 = 2a rsinθ rcosθ (x^2+y^2)^(3/2) = axy But that only gives half of the graph, where xy is positive.
January 10, 2016

Calculus
surely you jest! The critical points are where f' = 0. f'(x) = -3sin3x You know that sin(u)=0 when u is a multiple of pi. So, f'(x) = 0 when 3x is a multiple of pi: x= 0, pi/3, 2pi/3, ...
January 10, 2016

this doesn't look easy. I'd attack it like this: 10sinx cosx + 3sinx - 1 = 0 sinx(10cosx+3) = 1 sinx = 1/(10cosx+3) sin^2x = 1/(100cos^2x + 60cosx + 9) (1-cos^2x)(100cos^2x+60cosx+9) - 1 = 0 Expand that out, and you have a 4th-degree polynomial in cosx. Guaranteed not ...
January 10, 2016

maths
we see that both pipes together can fill the the tank in 120/7 minutes: 1/t = 1/40 + 1/30 t = 7/120 So, after 5 minutes, they have filled 35/120 = 7/24 of the tank. So, it will take A 7/24*40 = 35/3 minutes to fill the rest. Total time: 5 + 35/3 = 16 2/3 minutes.
January 10, 2016

Calculus
while f" = 1/x, f is not defined for x<=0. So, f is concave up for all x>0. f = 2^(x/2) f' = ln2/2 2^(x/2) f" = (ln2/2)^2 2^(x/2) This is just e^kx in disguise. It is concave up everywhere. There are no critical points. f' = x√(9-x^2) f'=0 at ...
January 10, 2016

Math
If the calorie content of the pies are p and h, respectively, then we have (1/2)p + (3/4)h = 765 (1/4)p + h = 745 Now just solve for p and h. It might be less cumbersome to clear the fractions: 2p + 3h = 3060 p + 4h = 2980
January 10, 2016

Algebra
OHH! Thank you very much, that would have been a pretty frustrating error if I continued without noticing! Thank you, Damon. Have a great night!
January 9, 2016

Algebra
so it would then turn into 9y+12y+15y-45=243 36y-45=243 ( add the y's together) 36y = 288 (add 45 to 243) y = 8? (288 divided by 36)
January 9, 2016

Algebra
If someone could just show me how to set up a formula that would be great!
January 9, 2016

Algebra
A stamp collection consists of 3¢, 12¢, and 15¢ stamps. The number of 3¢ stamps is three times the number of 12¢ stamps. The number of 15¢ stamps is three less than the number of 12¢ stamps. The total value of the stamps in the collection is...
January 9, 2016

Geometry
hard to say, without knowing T,U,V
January 9, 2016

MATH Precalculus
Draw a diagram! clearly, if f(t) is the distance in feet, for 0<=t<=6, f(t) = 15t for 6<=t<=12, f(t) = √(90^2+(15t)^2)
January 9, 2016

geometry
s = rθ = r(2π/12) = π/6 r
January 9, 2016

math
You know from eq #2 that y=x+4. So, plug that into eq #1 and you have x + 4(x+4) = 1 Now you can find x.
January 9, 2016

Math
the surface area is 2πr^2 + 2πrh = 2π(r^2+hr) Now it's clear that r^2+hr=16... Now, using h=r+4, you have 2πr(r+r+4) = 32π
January 9, 2016

physics
the circumference is 4π. SO, the angular velocity is 16m/s * 1rev/4πm * 2πrad/rev = 32π/4π = 8 rad/s
January 9, 2016

Direct variation algebra 2
since V = kG, V/G=k, a constant. So, you want to find V such that V/11 = 36/4
January 9, 2016

math
What GP's are possible? If the 3 numbers are chosen independently, then we have 1,1,1 1,2,4 1,3,9 1,4,16 1,5,25 1,6,36 1,7,49 2,2,2 2,4,8 2,6,18 2,8,32 2,10,50 3,3,3 3,6,12 3,9,27 3,12,48 4,4,4 4,8,16 4,12,36 5,5,5 5,10,20 5,15,45 6,6,6 6,12,24 and so on. If the three ...
January 9, 2016

math
area of a circle is pi r^2 So, how far could the bear have walked in 4 hours? 4*2=8. use that for the radius. Then use 5*2 for the radius in the 2nd part, then subtract.
January 8, 2016

Calculus @ Henry
I worked some on this earlier, and botched it a bit, so here goes again. A water tank is made by rotating f(x)=2^x-1 between [0,2] about the y-axis. The water tank is initially full, when a hole is opened at the bottom tip so that the water drains at a rate of 4 unit^3/second...
January 8, 2016

Geometry
The first problem is discussed here: http://www.algebra.com/algebra/homework/Triangles/The-line-segment-joining-the-midpoints-of-two-sides-of-a-triangle.lesson Google is your friend. Most problems posted here have been discussed many times on the web. For #2, if you draw a ...
January 8, 2016

Algebra
The sum of two numbers is fourteen. Using x to represent the larger of the two numbers, translate "the difference between five more than the larger number and three times the smaller number" into a variable expression. Then simplify.
January 8, 2016

Calculus
hint: since a = s^2, da = 2s ds
January 8, 2016

apex geometry
too many typos to proceed. No diagram, but then none needed, since all circles are similar.
January 8, 2016

maths
x+19 = 48 x = 48-19 ...
January 8, 2016

calculus
If the radius of the circle is x, the side of the triangle is y, and the side of the square is z, then we have 2πx+3y+4z = 1 a = πx^2 + √3/4 y^2 + z^2 da/dx = 2πx da/dy = √3/2 y = √3/2 (1-2πx-4z) da/dz = 2z a will have a maximum where all ...
January 8, 2016

maths
At any point (x, 3/2 x) on the line, the distance from the origin is d^2 = x^2 + 9/4 x^2 = 13/4 x^2 If the circle's center is at (h,3h/2), then, we have (x-h)^2 + (y-(3h/2))^2 = 13/4 h^2 (5/2-h)^2 + (1/2-(3h/2))^2 = 13/4 h^2 h=1 So, the circle is (x-1)^2 + (y-3/2)^2 = 13/4...
January 8, 2016

calc
what's with all the words? s(t) = -t^3/3 + 13t^2/2 - 30t when the particle is mofing to the right, s(t) is increasing, so ds/dt > 0 -t^2 + 13t - 30 > 0 3 < t < 10 Since our domain is 0<t<9, our interval is thus 3<t<9
January 8, 2016

maths
2s^2 = 98 s = 7
January 8, 2016

Calculus
When the height of the water is y, then the radius of the surface is x=log_2(y+1) Thus, the volume of the water when the depth is h is ∫[0,h] πx^2 dy Now, ∫π(log_2(y+1))^2 dy = π(y+1)(ln^2(y+1)-2ln(y+1)+2)/ln^2(2) That gives me ∫[0,3]π(...
January 8, 2016

Geometry
since consecutive angles add to 180, we have 8x+1 + 12x+19 = 180 Now find x, and then the angle measure.
January 7, 2016

Geometry
Assume the following is a true statement. If it is raining, I will carry an umbrella. Which form of the original statement must also be true? a- converse b-- inverse c- contrapositive d- biconditional My answer is c contrapositive
January 7, 2016

Math
#1. The geese eat m, 2m-1, 4m-3, 8m-7, 16m-15, 32m-21 Sum: 63m-47 Typo in answers? #2. T - (T/2-6) - (T/3-2) = T/6 + 8 #3. 3x(x+4) if x=3, that's 63 #4. -3^2 + 24/2*3 + 6*2 + 3^0 = -9 + 36 + 12 + 1 = 40 Maybe this will help
January 7, 2016

Algebra
The number of hours, h <= 4 So, the charges c <= 85*8 + 50
January 7, 2016

math geometry
Heck, just draw the line AB. Then pick a point X close to the line and Y far away from the line. While XY is the pb of AB, AB is not necessarily the pb of XY.
January 7, 2016

Math
The Pythagorean Theorem tells you that the exact length of lighting is √(8^2+14^2) = 16.12 feet So, now, what's the answer you need?
January 7, 2016

MATH
no idea what you're after. Permuting 5 numbers will not ever produce a sixth number.
January 7, 2016

Math
compare A:12.00*5 vs B:0.08*125*5 As you see, the 5-day period is useless. The better deal for 1 day is the better deal for any number of days, if the same number of minutes is used.
January 7, 2016

Mathematics
4π/3 x^3 = 2100 x^3 = 1575/π a = 4πx^2 = ? 2π/3 r^3 = 2π/3*15^3 = 2250π for the cylinder, then πr^2 45/2 = 2250π r = 10
January 7, 2016

Math
using the remainder theorem, f(a) is the remainder when dividing by (x-a), we have f(1) = 0 f(-1) = 2 f(2) = 6 So, now you have three equations to use: a+b+c = 0 a-b+c = 2 4a+2b+c = 6 7/3 x^2 - x - 4/3 check it to be sure.
January 7, 2016

Math
Hmm. Seems pretty clear to me. When you bring up the page, there are various buttons. One of them is labeled between. Enter your two Z values, and it will show the area. Play around there for a while, and it will become clear how it all fits together. You can enter Z vales, or...
January 7, 2016

Math
3D is correct. #4 is misleading, since it appears that the 1st two terms are 3 and 888. Lose the comma and things are clearer. There is a common ratio of 1/18, so B
January 7, 2016

Math
They look good to me.
January 7, 2016

Precalculus
or, just draw the triangle and label the sides. The missing side is √(49-9) = √40 Then you can read off all the trig functions just by looking at the sides and using the proper ones.
January 7, 2016

maths
clearly the sphere has diameter 14. So, just subtract to get the wasted metal: 14^2 * 20 - 4π/3 * 7^3
January 7, 2016

math
assuming they both show the correct time now, then since the fast clock gains 8 minutes per hour, it will gain an hour every 7.5 hours, and the minute hands will be aligned. It will gain 2 hours in 15 hours. Thus, after 6*15=90 hours, it will have gained 12 hours, and the ...
January 7, 2016

Maths
(2x+1)(x-1)
January 7, 2016

math
the volume of the metal is π(5^2 - 4^2)(35) cm^3 Now you can find the weight.
January 7, 2016

math
(m-5) = (s-5)^2 m+10 = 2(s+10) Now you can find m and s. You will get two answers, but only one is possible, given the conditions above.
January 7, 2016

Math
10/2 (2a+9d) = 220 Now, the odd terms are a, a+2d, a+4d, ... So they form a 5-term AP whose common difference is 2d, and whose sum is 5/2 (2a+4(2d)) = 100 Now you can find a and d.
January 7, 2016

math
The ellipse is degenerate, since the foci are at the vertices.
January 7, 2016

Math
with a 50% markup, the selling price is 1.50 times the cost. So, the cost is 200.
January 7, 2016

Math
the slope of the line through the two points is 5/-10 = -1/2. So, what is the line through the origin with that slope?
January 7, 2016

Math
clearly the line is y = 4/3 x - 5 So, just rearrange that to the general form ax+by+c = 0
January 7, 2016

Math
P=kQR, so P/QR is constant. Thus, you want P where P/2 = 420/21
January 7, 2016

Math
Inverse variation means that yz = k, a constant. No matter which values you have, their product stays the same. So, you want to find z such that 4*25 = 10z
January 7, 2016

Math
2/5 + 1/4 = 13/20 hr * 60 min/hr = 39 min
January 7, 2016

math
it is the distance between the two opposite vertices. Just use your distance formula.
January 6, 2016

Math
If the current speed is c, then the boat's speed is 5c. Since time = distance/speed, 48/(5c-c) + 48/(5c+c) = 5 12/c + 8/c = 5 ...
January 6, 2016

Math
Recall that (x-a)^2 = x^2-2ax+a^2 k^2-18k+50 = 0 k^2-18k = -50 Now, you want half of the coefficient of k and square it, so you have a perfect square. Then, to keep things equal, you have to add it to the right side as well. k^2-18k+81 = -50+81 (k-9)^2 = 31 k-9 = ±&#...
January 6, 2016

Math
what? no calculator? wrong! Just type 47*1330 into google's search box; it is also a mean calculator.
January 6, 2016

Math!!!
Clearly that would be 0.3 + 0.15 + 0.05 = 0.5 Makes sense, since both the intervals and the probabilities are symmetric. Extra credit: what is the probability that Y=0?
January 6, 2016

Math
cos(x) = sin(pi/2 - x) That's what the co- in cosine means: sine of the co-mplementary angle.
January 6, 2016

Geometry
sounds like a cylinder. 2πr^2 + 2πrh = 12π 2πrh = 8π, so 2πr^2 + 8π = 12π 2πr^2 = 4π r^2 = 2 r = √2 and r = √6
January 6, 2016

math
p = 6*4
January 6, 2016

Maths
If C is the right angle, then AB=5. Drop an altitude from D to BC, meeting it at E. Then, if DE=x, CD=2x and EB = 3/4 x. So, (3 - 3x/4)^2 + x^2 = (2x)^2 x = (16√3-12)/13 and CD=2x.
January 6, 2016

math
just subtract 2.5 twice from each dimension, since the border is on both sides and top&bottom. Although as you typed it, the problem is poorly expressed. Maybe I got it wrong.
January 6, 2016

geometry
this is just a 3-4-5 triangle scaled up by a factor of 16.
January 6, 2016

Algebra 2
a = 16*3 = 48 r = 1/2 So, what is S4?
January 6, 2016

Math
If the height of the building (above S) is h, and the distance from ST to the building is x, then we have h/x = tan60° (h-10)/x = tan 30° Rearrange things a bit and you have h cot30° = (h-10) cot60° Now just solve for h.
January 6, 2016

Word problem
The given ratios indicate that the block weighs 1.6 times as much as earth. So, if the block weighs b lbs, then we have b + 1.6b = 390 Now just find b. I don't see what the ton of water filling the box has to do with anything. Especially since it weighs less than the earth...
January 6, 2016

I'd use Heron's formula. Here, if c is the length of AB, s = (34+c)/2 = 17 + c/2 so we have (17+c/2)(4+c/2)(-4+c/2)(17-c/2) = 126^2 It looks messy, but expands into a nice simple quadratic in c^2. c=20
January 6, 2016

Math - eh?
solve what? d is just the definition of a function.
January 6, 2016

Minimum and maximum value
since f is decreasing, 2a^2+a+1 >= 3a^2-4a+1 a^2-5a <= 0 a(a-5) <= 0 0 <= a <= 5
January 6, 2016

Maths
if the roots are equal, then the discriminant is zero. So, (k-2)^2 - 4(1)(k+1) = 0 k^2 - 4k + 4 - 4k - 4 = 0 k^2 - 8k = 0 k = 0 or 8 you really should check to make sure that those two values of k cause the polynomial to have equal roots. That is, it will be a perfect square.
January 6, 2016

Trigonomentery Maths to difficult help me
if cos = L, then sin = √(1-L^2) csc=1/√(1-L^2) sec = 1/L tan = √(1-L^2)/L cot = L/√(1-L^2) so you have L/√(1-L^2) - 1/√(1-L^2) -------------------------- 1/L - √(1-L^2)/L (L-1)/√(1-L^2) ------------------- (1 - √(1-L^2))/L ...
January 6, 2016

Plz My Maths
This is just like the cloth problem. If there are m people and each one received n, then mn = 6500 (m+15)(n-30) = 6500 Now just solve for m and n. Why Do You Capitalize Every Word? It Is Rather Distracting. BUT NOT QUITE AS MUCH AS ALL CAPS, EH?
January 6, 2016

MATH
or, just start with what you are given: a point and a slope. Ding ding - use the point-slope form of the line: y+2 = -3/2 (x-3) now just rearrange stuff, and you will get Reiny's equation.
January 6, 2016

math
a = 3c b = a-6 b = 4d a+b+c+d = 39 (a,b,c,d) = (18,12,6,3)
January 6, 2016

math
if the figure is a parallelopiped, the bases have the same area. So, if the dimensions given are x,y,z, I'd say each base has area 2*6 = 12. your presentation is rather cryptic...
January 6, 2016

math
well, 1/4 = 2/8, so what do you think?
January 6, 2016

Maths
since cost is unitprice(p) times length (q), pq = 200 (p-2)(q+5) = 200 p = 10 Birr/m q = 20 m
January 6, 2016

Math of Investment
(1+.55/2)^(2n) = 2 I guess. Not sure of what your notation means.
January 6, 2016

math
what does "decreased by one of its one fourth" mean? decreased by 1/4, or decreased by 1/4 of its value? either n = d+5 or n = d-5 so, the new value is either (d+5)/(d+10) or (d-5)/(d+5) now equate that to whatever your weird statement implies.
January 6, 2016

math
cone: 1/3 πr^2 h hemisphere: 2/3 πr^3 sum: πr^2/3 (h+2r) Now just plug in your values.
January 6, 2016

Math
since the slope of the line is 1/2, tanθ = 1/2 = y/x. Now draw that triangle in QIII and you can see that cosθ = x/r = -2/√5
January 6, 2016

Math
since the median is the center value, at most half of the numbers can be positive.
January 6, 2016

Algebra 1
clearly it is not a whole number. Now you should note that the fraction is the ratio of two integers.
January 5, 2016

Geometry
5/x the enlargement ratio is newsize / oldsize
January 5, 2016

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