Saturday
January 31, 2015

Posts by STEVE


Total # Posts: 28,515

algebra word problem
just solve the equation when y=0. Just a normal quadratic solution.
January 3, 2015

Geometry
since AC=BD, 8x-10 = 2x+20 Now solve for x and evaluate BD=2x+20
January 3, 2015

Geometry
No, because 2/3 (x-6) = 2/3 x - 4
January 3, 2015

Geometry
2y+3x=6 has slope -3/2 So, the line you want has slope 2/3 ow you have a point and a slope, so the new line is y-5 = 2/3 (x-6)
January 3, 2015

algebra
well, just plug in 7a for all the x's: f(7a) = 3(7a)^2 + 8(7a) + 6 Now just evaluate the coefficients of powers of a.
January 3, 2015

constitution
Hmmm. How about <PRE> in upper case? </PRE>
January 3, 2015

constitution
let's see what <pre> text can look like </pre>
January 3, 2015

math
so ...
January 3, 2015

math
32x^2+9y^2=324 3y^2-x^2=3 Since 3y^2 = x^2+3, we have 32x^2 + 3(x^2+3) = 324 I think you can solve that fairly easily, right? The intersections are at x=±3, y=±2. See the graphs at http://www.wolframalpha.com/input/?i=plot+32x^2%2B9y^2%3D324%2C+3y^2-x^2%3D3
January 3, 2015

physics
A = (3.5,3.5) B = (6.1,-3.5) C = (-2.0,-3.5) Now just add up the (x,y) components and convert back to magnitude and direction form.
January 3, 2015

Calculus
∫csc x cot^2 x dx = ∫csc x (csc^2 x -1) dx = ∫csc^3 x dx - ∫csc x dx You probably have handy the form for ∫csc x dx, and you can use the power reduction formulas for ∫csc^3 x dx, or note that d/dx (cscx cotx) = -csc^3 x - csc x cot^2 x
January 3, 2015

CALC AB
profit is revenue minus cost, or x*p(x) - c(x) = x(18-x/400)-(820+5x+0.01x^2) = -0.0125x^2 + 13x - 820 That's just a parabola, with its vertex at x = -b/2a = 520 work #2 the same way. Figure a quantity and a price in terms of x, the number of $10 rebates. Then, revenue is ...
January 3, 2015

Math Linear Equations
c'mon. The lines intersect where the functions are equal: -2 = 3x+1 Now find x, and you know darn well that y = -2, since one of the lines is y = -2 for any x. y = -2 is a function of x, like any other linear function. It just so happens that no matter what x is, y = -2! y...
January 2, 2015

AP CaLC. AB
Assuming you know that max/min problems involve finding when f'(x)=0, #1 If the base of the ladder is x feet from the fence, and the height up the wall is y, then the length z of the ladder is z^2 = (x+7)^2 + y^2 and using similar triangles, y/(x+8) = 8/x Now you can ...
January 2, 2015

equation and inequalities
In n games, he will chew 17n sticks of gum
January 2, 2015

math
well the price 2p for the 2 CDs produces 1.49 sales tax, so .05(2p) = 1.49 Now you can find p.
January 2, 2015

math-algebra HELP!!!!
do you not have a linear regression tool for finding a line of best fit? Use it, then the answers should be clearer. Just eyeballing the data, we can first sort it: 32 72 34 76 35 75 37 77 37 78 42 81 46 88 Looks to me like I'd expect about 44 chirps at 85°
January 2, 2015

Calculus
well, you know that critical points occur when h'(x)=0. So, we want 3x^2+b = 0 at x=2. So, b = -12 That means that h(x) = x^3-12x+d h(2) = 8-24+d = -4 So, d = 12, giving us h(x) = x^3-12x+12 The graph is at http://www.wolframalpha.com/input/?i=x^3-12x%2B12+for+x%3D0..3 ...
January 2, 2015

science
I think you can find the formula you want here http://www.livephysics.com/physical-constants/mechanics-pc/moment-inertia-uniform-objects/ so you can check your derivation.
January 2, 2015

algebra
general advice: study your text and google online for problems that trouble you. do you have a particular question? Any general explanation we could type here will look very much like your textbook.
January 2, 2015

Physics
As you know, the trajectory of a body kicked with velocity v at angle θ is y = x tanθ - g/(2 (v cosθ)^2) x^2 For your ball, that is y(x) = 1.11x - 9.81/(2(20*0.67)^2) x^2 = 1.11x - 0.0273x^2 So, now check to see whether y(33) >= 3.05
January 2, 2015

^Maths^
6/3(4-2) 2(4-2) 2(2) 4 6/(3(4-2)) 6/(3*2) 6/6 1 Most people are sloppy online with parentheses. You will have to decide what you really meant to say.
January 2, 2015

math
3000(1+.08/4)^(4*1) - 3000 = 247.30
January 2, 2015

Algebra
if the width is w, then w(3w-8) = 35 Hint: 35=5*7
January 2, 2015

Math
y-4 = -2(x-3) y-4 = -2x+6 Now just rearrange things into the standard form: Ax+By=C
January 2, 2015

mrr high school
well, 1W = 1J/s, so that'd be 1.5*72/60 W
January 2, 2015

math lit, accounting, business studies, cat
surely your school has advisors. Why not have a nice discussion with one of them, rather than look for a sound bite here?
January 2, 2015

math fractions
1/4 + 3/4x = (1+3x)/4
January 2, 2015

algebra
sum: 4x+3x
January 1, 2015

Maths
well, since T10 = ar^9 a(5/3)^9 = 5859375 = 3*5^9 So, a = 3^10 = 59049
January 1, 2015

calculus
I'd say that (X1,Y1) is the position of the base of the ladder, if the base of the wall is (0,0). Since it is moving at the rate of 2 ft/s, after t seconds it is 2t feet from the wall. Naturally, the Pythagorean theorem says that the height of the top of the ladder obeys h...
January 1, 2015

Math
since cos(kt) has a maximum at t=0, -3cos(kt) has a minimum of -3 at t=0. So, since the bottom of the tire touches the ground, the axle is 3 feet up, and if the point starts at the bottom of the circle, it is indeed given by 3-3cos(3pi/2 t). The height is from the ground, not ...
January 1, 2015

Math
Yes, if the seat starts at the top. Though you should write cos(6pi t). As it is, it looks like cos(6pi) is the function. The parentheses are used to enclose the argument of the function.
January 1, 2015

math
If x is at 2%, the rest (10000-x) is at 12%. So, add up the interest and you have .02x + .12(10000-x) = 600 Now just solve for x.
January 1, 2015

Geometry
Can't quite fathom your terminology. How do you take the measure of a triangle? I'll assume that WXZ is an angle, not a triangle. If XZ is a side of the triangle ZXY, how can it bisect ZXY? I'll assume your logic is sound, even if your exposition is not.
January 1, 2015

Math
Let's see what's what here... QR = √((-2+2)^2 + (1-5)^2) = √16 RS = √((-5+2)^2 + (1-1)^2) = √9 SQ = √((-2+5)^2 + (5-1)^2) = √25 DE = √((5-5)^2 + (-2+6)^2) = √16 EF = √((2-5)^2 + (-2+2)^2) = √9 FD = √((5-...
January 1, 2015

physics
avg speed = total distance ----------------- total time = (1+1)km/(1/60 + 1/40)hr = 48 km/hr
January 1, 2015

earth science
but you would be wrong. Try looking it up, and I'm sure any explanation you find will explain why this is so.
January 1, 2015

earth science
and you would be wrong. Think about it. To study the universe you need to use a telescope to view distant objects. On earth, the atmosphere makes such sightings faintly blurry. On the moon, with virtually no atmosphere, the images will be a lot clearer. That is why we have ...
January 1, 2015

chemistry
2CS2 + 6O2 -> 2CO2 + 4SO2 So, now you know that you will need 6 moles of O2. What is the volume of 6 moles of any gas at STP?
December 31, 2014

chemistry
You know that PV=kT Since P is held constant, that means that V/T = k/P, which is constant. The temperature is reduced by a factor of (273+3)/(273+27), so the volume must also decrease by the same factor for V/T to remain constant.
December 31, 2014

Algebra
Or, you can think of it as looking for the intersections of a circle and a line. The circle: (x-2)^2 + (y-1)^2 = 45 The line: y=7 They intersect where (x-2)^2 + (7-1)^2 = 45 now the math proceeds as above
December 31, 2014

Calculus
f(x)=(10-3x) / 2√(5-x) quotient rule: f'(x) = [(-3)(2√(5-x))-(10-3x)/-√(5-x)] / 4(5-x) = [-6(5-x)+(10-3x)] / 4(5-x)^(3/2) = (3x-20) / 4(5-x)^(3/2) Using product rule: f(x) = 1/2 (10-3x)(5-x)^(-1/2) f'(x) = 1/2[(-3)(5-x)^(-1/2) + (10-3x)(-1/2)(5-x)^(-3...
December 31, 2014

Calculus
you know that h = 2d = 4r. So, the volume v is v = 1/3 pi r^2 h = 4/3 pi r^3 to find the height after 5 minutes, just recall that the volume will be 5min * 20m^3/min = 100 m^3 So, just solve for h (4r) when v = 100 To find how fast the pile is increasing, recall that dv/dt = ...
December 31, 2014

Math- Max and Minimum
better review your max/min topic. f has a max/min where f'=0 and f"≠0. f' = x^3-3x^2-6x+6 This does not factor over the rationals, so a graphical solution is probably the best bet. The graph of f' is at http://www.wolframalpha.com/input/?i=x^3-3x^2-6x%...
December 31, 2014

Calculus
You went to too much work on f" f' = (1-x)/(1+x)^3 f" = [(-1)(x+1)^3 - 3(1-x)(x+1)^2]/(x+1)^6 = [-(x+1)+3(x-1)]/(x+1)^4 = (-x-1+3x-3)/(x+1)^4 = (2x-4)/(x+1)^4 Just because the quotient rule says you wind up with v^2 in the bottom, you don't have to leave it ...
December 31, 2014

Calculus
(a) and (b) are correct (c) what's the problem? f"(x) = 2(x-2)/(x+1)^4 the denominator is positive always. So, f" < 0 for x < 2 f" > 0 for x > 2 Now you can say where f is concave up or down, and where the inflection point is.
December 31, 2014

MATHS
volume changes as the cube of the scale. So, each piece as 1/6^3 the volume of the container.
December 31, 2014

Math
use the distance formula many times to find the lengths of the sides. The two triangles with all congruent sides are congruent (SSS).
December 30, 2014

equation and inequalities
b-15 = -12 b = 3 So, on the number line, put a dot at 3.
December 30, 2014

math
Solve for x in x(1.15)^5 = 1400
December 30, 2014

Pre-Calc/Trigonometry
As I recall, our model is T(t) = 205 + (72-205)e^-kt So, solve for k in T(10) = 195 Then use that k to solve for t in T(t) = 180 What do you get?
December 30, 2014

Pre-Calc/Trig
T(t) = 350 + (350-50)e^-kt So, just solve for k in T(2) = 60 Then use that k to solve for t in T(t) = 150
December 30, 2014

Pre-Calc/Trig
T(t) = To + (50-To)e^-.1947t I think we can assume that To = 98.6, so T(t) = 98.6 - 48.6 e^-.1947t So, just solve for t in T(t) = 66. That will give the number of hours since death (t=0).
December 30, 2014

Algebra 1
Both equations are for straight lines. Two lines can intersect in only one point, so I can't imagine how you got two solutions. Did you work the problem two different ways, and the answers disagreed? It would be really nice if you showed your work. Now for the bad news: ...
December 30, 2014

Algebra 1
my answer is 5/17 or 16/17
December 30, 2014

Algebra 1
What is the solution to the system y=10x-3 y=-7x+3 answers from 5/17, 16/17 4/17, 16/19 -5/17, 16/17 3/17, 5/17
December 30, 2014

math
or, you can divide first: -5(4x+1) =15 4x+1 = -3 4x = -4 x = -1 Damon's way is nice if you expect to run into awkward fractions by doing the division first.
December 30, 2014

algebra
clearly the baby has gained 22/16 oz/day. So, starting with the birth weight of 50 oz, add that much for each day. And what does the no. of days in a month have to do with anything?
December 30, 2014

maths
subtract the inside volume from the outside volume: (29)(21)(13) - (28)(20)(12) = ?
December 30, 2014

Math
such a reflection takes (x,y) -> (x,-y), so it is neither set of vertices. You want (–1,2), (–4,4), (–3,5)
December 29, 2014

Algebra 1
They are the same line.
December 29, 2014

Algebra 1
How many solutions does the system of equations have? 3x+12y=20 y=-1/4x+5/3
December 29, 2014

Algebra 1
I think the Answer is 3x+5y=-10
December 29, 2014

Algebra 1
Write y=-3/5x-2 in standard form using Integers.
December 29, 2014

Algebra 1
thank you
December 29, 2014

Algebra 1
Tell whether the lines for then pair of equations are parallel, perpendicular, or neither? y=-2/3x +1 2x-3y=-3
December 29, 2014

Pre-Trig/Calc
e^-kt -> 0 as x->∞ 1-e^-kt -> 1 So, T(t) -> a+b at t=0, T(t) = b So, b is the initial temperature of the potato, 50°F a is the initial temperature difference between the potato and the oven: 300 in this case. You know this because it is clear that as time...
December 29, 2014

Algebra 1
Write the equation of a line that is perpendicular to the given line and that passes through the given points. y-2 = - 1/4(x+3), (-3,5)
December 29, 2014

Algebra 1
Write an equation in point slope form for them line through the given point with the given slope. (-4,6) m= 3/4
December 29, 2014

Algebra 1
actually, the slope of the V would be 2, not 1. |x| has slope 1. Extra credit: what if you had meant y=|2x+1|?
December 29, 2014

Algebra 1
Assuming you meant |2x| + 1, just like |x|, but squeezed half as wide, and shifted up 1.
December 29, 2014

Algebra 1
What would the graph look like for y= the absolute value of 2x plus 1
December 29, 2014

Pre-Calculus
Wow - a lesson in precision, as well as catching my typo! Still, if you just typed in 800 tan 33 /(tan 35-tan 33) I feel sure that the internal 32-bit precision would avoid any serious rounding error in this case.
December 29, 2014

Pre-Calculus
(800+x)tan33=xtan35 800 tan33 + x tan33 = x tan35 x tan35 - x tan33 = 800 x(tan35 - tan33) = 800 x = 800/(tan35-tan33) aside from the trig values (which are just constants), that's just good old algebra I, right?
December 29, 2014

Algebra 1
good question
December 29, 2014

Algebra 1
sorry I meant c(n) =.50n-.80
December 29, 2014

Algebra 1
Suppose soda is on sale for .50 a can and you have a coupon for .80 off the total price. Write a function rule for the cost of n cans of soda. My answer is c(n() = .80n -.50
December 29, 2014

geometry
the locus is the perpendicular bisector of the line from (0,0) to (-2,5). It's easy to find the midpoint, and the slope of the line. Now just find the line with perpendicular slope, through the midpoint.
December 29, 2014

Algebra 1
thank you
December 29, 2014

Algebra 1
What is the simplified form of the expression? 7(63/(5 sq-2 sq)-1)
December 29, 2014

algebra
x/50 = 0.8
December 29, 2014

calculus
you want dv/dt, where v = x^2 h The good old product rule says that dv/dt = 2xh dx/dt + x^2 dh/dt You have all the stuff you need, so just plug it in and watch the fun!
December 29, 2014

Math and Finance
5000(1+.08)^8
December 28, 2014

Math
d = √((5-1)^2 + (3-0)^2)
December 28, 2014

Math
as you recall, the slope-intercept form y = mx+b describes a line with slope m and y-intercept b. Surely you see the connection with the question above...
December 28, 2014

math
the stopping distance for a vehicle moving with speed v and deceleration a is s(t) = vt - 1/2 at^2 Since that is a quadratic function, the QF gives a handy way to solve it. And that's "brakes." Give me a break!
December 28, 2014

geometry
just use the Pythagorean theorem to find the resultant speed (the hypotenuse of the right triangle) √(130^2+20^2)
December 27, 2014

Math
4 is half the max displacement period = 8/3 seconds, = 2π/k, so k = 3π/4
December 27, 2014

Math
No, it is negative because I assumed that at t=0 the point is at its lowest elevation. (As my first sentence stated.) If we had started when the point was level with the circle's center, we'd have sin(kt). If we started with the point at its maximum height, then we'...
December 27, 2014

Math
If the point in question is at the lowest height at t=0 minutes, then y = -cos(kt) diameter is 6, so the radius is 3 y = -3cos(kt) the lowest point is 6" = 0.5 ft, so the axis of the loop is 3.5 ft off the ground: y = 3.5 - 3cos(kt) Since cos(kt) has period 2π/k = 1/...
December 27, 2014

^Maths^
You could just do the subtraction in base 6 and then convert the answer to base 7: 451-301 = 150 1506 = 1237
December 27, 2014

math
or, 4 3/8 inches :-)
December 27, 2014

English
a bit less than average in height. If the average height for men is 5'8", then someone who is 5'4" could be said to be a little on the short side. Similarly, a man 6'0" might be called a little on the tall side. A guy 6'8" is a long tall ...
December 27, 2014

math
Damon is correct. Surely you can see that 48:80 is not correct. There are only 80 records in all. 48:80 is the correct ratio, but the wrong total. For every 3 new there are 5 hot. So, 3:5 requires 8 records. There are 80 records. 80/8 = 10, so there are 10 sets of 3:5, or 30:...
December 27, 2014

algebra (motion)
if B takes x minutes, then the two runners cover the entire track in 15 minutes. 1/40 + 1/x = 1/15
December 27, 2014

maths
-5+20-8 = ?
December 27, 2014

algebra
almost anything 3/5 4/6 123/125 932789238/932789240 In fact, anything except 1/3 2/4
December 27, 2014

Math
or, A :-)
December 26, 2014

Math
The initial position (at t=0) is not -1/2 Or is that initial - just a separator? Also, if you're going to use parentheses, it ought to be d = 1/2 sin(pi/2 t) - 1/2
December 26, 2014

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