Saturday
July 30, 2016

Posts by Steve

Total # Posts: 42,193

matg
first step is usually to get rid of the nasty fractions. I see there's a typo in the first equation. I'll just assume 9/4 x. If wrong, fix it and follow the same steps to solution. 18x + 3y = -18 -4x + 45y = 4 or 6x + y = -6 -4x + 45y = 4 multiply to get rid of x: 12x...
July 30, 2016

AHOOGAAH! Homework Dump
no ideas on any of these?
July 30, 2016

Calculus AB
did you do the sketch? It should be clear that l/5.5 = (x+l)/12 no crank it out. Algebra I, babe.
July 30, 2016

Calculus AB
see similar previous problem. Just express r as a function of h and plug it in.
July 30, 2016

Geometri euclid
If the two circles have radii r and R, then the area between the circles is π(R^2-r^2) If a circle has AB as a diameter, then BC is its radius, since AB = AC + BC BC^2 + r^2 = R^2 so, BC^2 = R^2-r^2 That means the area of the circle with BC as its radius (AB as its ...
July 30, 2016

Calculus AB
v = 1/3 pi r^2 h But the dimension of the tank indicate that at any time, r/h = 4/10 So, use that to eliminate r.
July 30, 2016

Calculus AB
You know where the roots are. You know that if the root is of odd order, the graph crosses the x-axis there. And, if the root is of even order, the graph is just tangent there. So, knowing what you do about the general shape of polynomials, since this one is of even order, The...
July 30, 2016

Math
ratio test says no
July 30, 2016

Math
the two graphs are x^2 + y^2 = 1 (x-2)^2 + (y-3)^2 = 16 x^2-4x+4 + y^2-6y+9 = 16 but, x^2+y^2 = 1, so that means -4x+4 + 1 -6y+9 = 16 4x+6y = -2 so the slope of the line is -2/3 No need to actually find the points.
July 30, 2016

Math
Oops. Not all of those are on the graph. You may be right.
July 30, 2016

Math
well, let's see n   x   y 23 94 -98 22 90 -95 ... -22 -86 37 -23 -90 40 -24 -94 43 -25 -98 46 Looks like a lot more than 9 to me.
July 30, 2016

Math
eliminate t: (30-x)/40 = (50+y)/30 30(30-x) = 40(50+y) 900-30x = 2000+40y 30x+40y = -1100 3x+4y = -110 x = 4n+2 y = -(3n+29) Now just work out how many values of n produce x and y in the desired interval.
July 30, 2016

Physics
google is your friend. Use it.
July 30, 2016

math
See joejoe's post below. Same problem, different letters.
July 30, 2016

Trigonometry
Just factor out sinx: sinx(6sinx-1) = 0 so, sinx = 0 or sinx = 1/6 each will provide two solutions.
July 30, 2016

Trigonometry
The ship turned 90 degrees. So, the distance from port is just the hypotenuse of a right triangle with legs 7 and 24. Look familiar?
July 30, 2016

math
Assuming you mean the ratio of areas, If BC = 2x, then AD = 2x ABD has area 1/2 * 2x * 2x = 2x^2 ABEF has area (2x)*(2x) = 4x^2
July 30, 2016

Math
Sn = a(1-r^n)/(1-r) so, S5 = a(1-r^5)/(1-r)
July 30, 2016

Algebra
Col. Mustard, of course!
July 30, 2016

Math
In the interval -pi/4 <= t <= pi/4, the graph is traced once. But on 0 <= t <= pi/2, only half the curve is completed. Try changing the domain on this plot at http://www.wolframalpha.com/input/?i=plot+x%3Dcos(4t),y%3Dsin(6t),+-pi%2F4+%3C%3D+t+%3C%3D+pi%2F4
July 30, 2016

math
it's not that b is the middle value, but that if we want to build a set of ratios, a:b:c we need to have a common value for b in the two ratios a:b and b:c We could not have placed a or c in the center spot, because we only had one ratio for each of those. But to join the ...
July 29, 2016

math
a:b = 2:3 c:b = 3:2 we want b in the middle, so b:c = 2:3 lcm(2,3) = 6, so now we can write a:b = 4:6 b:c = 6:9 a:b:c = 4:6:9 a:c = 4:9
July 29, 2016

Calculus
try using the ratio test. You should be able to show that the series converges for |x| < e
July 29, 2016

Calculus AB
well, you want cos x = -0.4 so, x will be an angle in QII or QIII Your reference angle is arccos(0.4) = 66.4° so, x will be 180±66.4°
July 29, 2016

math
looks good to me Make sure you specify mm^3 for volume. That's a dang small prism, to be sure...
July 29, 2016

math
A(1+.12*5) = 160000
July 29, 2016

Calculus AB
it's an even multiple of 2pi, so the functions are the same as for 0.
July 29, 2016

Calculus AB
recall that log_a(b) = ln(a)/ln(b) So, converting everything to natural logs (or any set of logs with a common base), ln3/ln25 x + ln7/ln2 y = ln27/ln5 ln8/ln7 x + ln5/ln3 y = ln2/ln49 Now just solve the system as usual. It's messy, but it's just numbers. If you don&#...
July 29, 2016

statitics
just list the cases: P(WL) = 0.60*0.25 P(LW) = 0.40*0.55 Since they are mutually exclusive, P(WL)+P(LW) = 0.37
July 29, 2016

math
Divide 32 by the number of colors. Then count over in the list the remainder. For example, your list has 5 colors 32/5 = 6 R2 So, there are six complete cycles, with 2 left over. The 32nd stripe is thus blue. If you only wanted 4 colors, the do that division instead. A zero ...
July 29, 2016

luderitz
not following instructions, as in the subject of your post.
July 29, 2016

Math
.85x +.60*150 = .80(150+x)
July 29, 2016

math
x = (90-x)-8
July 29, 2016

Math
35 m/s * 1km/1000m * 3600s/hr = ? km/hr
July 29, 2016

science
If the distance is x meters, then since time = distance/speed, x/55 + x/330 = 7 x = 330m Now, the problem is that the bullet will drop 176m in the 6 seconds spent in the air. So, now we have to include the angle of the trajectory, which complicates matters some.
July 29, 2016

Maths
Review your sine rule. It is then clear that sinθ = √(15^2-6^2)/15 It might have been easier to calculate using cosθ = 6/15
July 29, 2016

Accounts
2000(1+.06/2)^(2*6)
July 29, 2016

Stats
Your Z table tells you that about 97% of the population lies below the mean + 1.88 std. so, ...
July 29, 2016

Physics
If I can get by the sloppy typing, it is clear that h^2 + 2^2 = 9^2
July 29, 2016

math
the number who passed either or both is .80+.85-.75 = 0.90 So, 10% of x students failed both: 45 = 0.10x . . .
July 29, 2016

PACE INter Science Colldege
100km/hr * 1L/10km * 1hr/3600s * 1000cm^3/L = 27.77 cm^3/s
July 29, 2016

Math
the linear ratio is √25:64 = 5:8 the volume ratio is thus 5^3:8^3 = 125:512 or, 250:1024
July 28, 2016

math
If the dimensions are x and y, then we have √(x^2+y^2) = x+8 xy = 60 You can grind out the solution, but I think you can recognize which factors of 60 form a convenient right triangle that works, no?
July 28, 2016

Calculus
dang those typos, yeah? 64 works much better.
July 28, 2016

Calculus
x+y=64 z = xy^3 = (64-y)y^3 = 64y^3 - y^4 dz/dy = 192y^2 - 4y^3 = 4y^2(48-y) I think the way is now clear, right?
July 28, 2016

jeez - get it right, willya?
and stop posting it!
July 28, 2016

algebra - eh?
how's that again? The product of two consecutive integer is 5 three times the larger integer
July 28, 2016

Math
just remember that revenue = price * no.tickets.sold You can use that to answer all these questions. Give it a try, and come back if you get stuck. also, recall that the vertex of a parabola ax^2+bx+c is at x = -b/2a. For R(x), that is where the maximum revenue occurs.
July 28, 2016

physics
v = √(2as) = √(2*9.8*20) = 19.80 m/s Now use that to answer the other question.
July 28, 2016

math
can't see hwy you don't just write the fractions, like 1/3, 2/√5, etc. Anyway, since volume is length * width * height then if one or more of those dimensions are scaled by a factor of r,s,t respectively, then the new volume is (length*r)*(width*s)*(height*t) = (...
July 28, 2016

Algebra 1
After n years, v = c(1-r)^n = 20000 * 0.79^n no need to subtract from anything, unless you want to see how much its value has declined. 6154.11 is the value after 5 years.
July 28, 2016

Maths
try using the sum-to-product formulas. If you get stuck, come on back and I'll see what we can do with what you have so far. I see google has some good discussions.
July 28, 2016

Maths
cos3x = cosx(2cos2x - 1) similarly, cos6x = cos2x(2cos4x - 1) I think you can see where this is going, right?
July 28, 2016

Maths
google is your friend many proofs online
July 28, 2016

pre cal
the asymptotes mean y = ??? / (x+2)(x-1) y(0)=0, so y = ax / (x+2)(x-1) y(2) = 12, so 12 = 2a/4 a = 24 y = 24x / (x+2)(x-1)
July 28, 2016

pre cal
vertical asymptote at x=6 and a horizontal asymptote means y = a(x-b)/(x-6) + c y(5) = 0, so b=5 y = a(x-5)/(x-6) + c y(0) = -5/6 and y(∞) = -1, so 5/6 a + c = -5/6 a + c = -1 1/6 a = -1/6 a = -1 c = 0 y = (5-x)/(x-6)
July 28, 2016

math
2 + 2 sinθ = 3 cos^2θ 2 + 2sinθ = 3 - 3sin^2θ 3sin^2θ + 2sinθ - 1 = 0 (3sinθ-1)(sinθ+1) = 0 sinθ = 1/3 sinθ = -1 so, there are two solutions for sinθ = 1/3 (QI and QII) and one solution for sinθ = -1
July 28, 2016

basic maths trignometry
secx - tanx = 1/cosx - sinx/cosx = (1-sinx)/cosx now use the double angle formulas to make that 1 - 2sin x/2 cos x/2 ------------------------- 2 cos^2 x/2 - 1 divide by cos^2 x/2 to get sec^2 x/2 - 2tan x/2 ----------------------------- 2 - sec^2 x/2 1+tan^2 x/2 - 2tan x/2...
July 28, 2016

math
5*4/5 = 4
July 28, 2016

Math
45/9 = x/12 x = 60
July 28, 2016

math
Oops. r=16% I calculated with r as the 6-month interest rate.
July 28, 2016

math
6250(1+r/2)^2 = 6760 r = 8%
July 28, 2016

Maths
For ease of reading, I'll just use s for sinx and c for cosx (1+s-c)/(1+s+c) = (1+s-c)^2/[(1+s)^2-c^2) = (1+s-c-sc)/(s+s^2) = (1-c)(1+s)/(s(1+s)) = (1-c)/s That means that [(1+s-c)/(1+s+c)]^2 = (1-c)^2/s^2 = (1-c)(1-c) / (1+c)(1-c) = (1-c)/(1+c)
July 27, 2016

Maths
I assume you mean arctan(x)+arcsin(x)=3/4 π well, you know that π/4 + π/2 = 3/4 π so, x=1 the hard way: sin(arctan(x)+arcsin(x)) = 1/√2 sin(arctan(x))cos(arcsin(x)) + cos(arctan(x))sin(arcsin(x)) = 1/√2 Now draw the right triangles for arctan(x...
July 27, 2016

pre cal
f(x) = a(x+5)(x-2)(x-4) f(-10) = a(-5)(-12)(-14) = -840a = -4 a = 1/210 f(x) = 1/210 (x+5)(x-2)(x-4)
July 27, 2016

Algebra
Well, you found the midpoint wrong. It is (-7.5,2.5) unless there's a typo in the coordinates. clearly x+y = -12 is wrong, since -8+4 = -4 That should have been your first clue. Using correct midpoint, the slope is -3. So, the answer is y-4 = -3(x+8) y-4 = -3x-24 3x+y = -20
July 27, 2016

Maths
I'll get you started. These problems are all about the same. The percent change is the amount pf the change divided by the starting amount. In this case, the two changes are (100-120)/120 = -20/120 = -1/6 = -16.67% (80-100)/100 = -20/100 = -20%
July 27, 2016

Geometry
it's a dilation, not a translation. for a dilation, each coordinate is multiplied by the scale factor.
July 27, 2016

Algebra
sina = cos(π/2-a) cosa = sin(π/2-a) 1+sina+icosa = 1+cos(π/2-a) + i sin(π/2-a) = 1 + cis(π/2-a) There is no simple cis(x) form because of that pesky 1.
July 27, 2016

Math
6n - 2(n-1) = 4n+2
July 27, 2016

math
(x)+(2x-32)+(x+18) = 534 Solve for x, and then the 3 parts.
July 27, 2016

F/maths
let the time spent on XY and YZ be a and b, respectively. Then on XY: s = 5a + a^2; v@Y=5+2a on YZ: s = (5+2a)b - 7/4 b^2; v@Z=0 Then we have 5a + a^2 + (5+2a)b - 7/4 b^2 = 475 5 + 2a - 7/2 b = 0 Just solve for a and b, and then you can answer the questions.
July 27, 2016

maths - eh?
eh? √16 = √4 ?
July 27, 2016

Math
This can also be seen by noting that a^2-b^2 = (a+b)(a-b) In this case, since the numbers are consecutive, that is just S*1 = S
July 27, 2016

chemistry
counting the moles, if there are x L of 6M HCl, then 6x + 2(2-x) = 3*2
July 27, 2016

maths
Assuming you meant 6 liters of paint, then he needs 5m*3m * 6L/10m^2 = 9L That's for one wall. No idea how many walls there are.
July 27, 2016

Science
google is your friend.
July 27, 2016

Maths
well, the volume is 2.5*20*1.5 = 75m^3 Your mission, should you choose to accept it, is to convert that to liters.
July 27, 2016

Math
2/3 x = -28
July 27, 2016

SPANISH
¿Y qué?
July 27, 2016

maths
a(1+2r) = 8320 a(1+3.5r) = 9685 a = 6500
July 26, 2016

Math
g(x) = f(x)+5, so it is shifted up 5 units. or, f(x) = 2x-3 g(x) = 2x+2 = 2(x+5/2)-3 So, g(x) is f(x) shifted left 5/2
July 26, 2016

Geometry - incomplete
Can you not see how incomplete is your description?
July 26, 2016

Math
8cis30° + 8cis120° = 8√2 cis75° or, 8<√3/2,1/2>+8<-1/2,√3/2> = 4<√3-1,√3+1> either way, the y-component is 4(1+√3) ≈ 10.928
July 26, 2016

math
what do you mean by "their age" ?
July 26, 2016

Algebra
When you do the synthetic division, there will be an "a" in the remainder. The remainder is -52+a So, you set -52+a = -4 and get a=48 The bottom row of the division is 2 -15 26 -52+a
July 26, 2016

Algebra
As it is written, f(-2) = 80+a So, 80+a = -4 means a = -84 But, there is apparently a typo in f(x). If we set f(x) = 2x^3−11x^2−4x+a f(-2) = -52+a = -4 so, a = 48 So, how did you come by your results? I showed you mine. Show me yours.
July 26, 2016

Algebra
By the Remainder Theorem, f(-2) = -4. So, evaluate f(x) at x = -2 and solve for a. Or, do a synthetic division and see what the remainder is. Set that equal to -4 and solve for a.
July 26, 2016

maths
If w games were won, then 15-w were lost, so the points add up as 5w - 2(15-w) = 54 So, solve for w.
July 26, 2016

math
5C3 = 10
July 26, 2016

Math
If Alger is x, then Abigail is x+7. So, just solve for x in x(x+7) = 144 Note that 144 = 9*16
July 26, 2016

Maths
clearly, 0.25L which is the increase in volume.
July 26, 2016

physics
(a) You want 1/2 meve^2 = 1/2 mpvp^2 so that means that ve^2/vp^2 = mp/me = 1836 ve = √1836 vp (b) that would of course be 1836K
July 26, 2016

Trigo
Draw a diagram. Review your basic trig functions Now it is clear that the distance x between the ships is x = 30cot23° - 30cot28°
July 26, 2016

math
or, equivalently, 1/A + 1/B = 1/8 6/8 + 9/B = 1
July 26, 2016

math
well, it's 333 to the nearest integer. whether that's the nearest meter is something else entirely.
July 26, 2016

Physics
looks good, but I'd have gone from 180 = 36a/2 to 180 = 18a
July 26, 2016

Maths
posted the same gibberish twice and still no question. what the heck do you mean by whose he=5cm each=6cm
July 26, 2016

Maths
ok now what?
July 26, 2016

maths
28*40 = x(40+16)
July 26, 2016

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