Sunday
February 7, 2016

Posts by STEVE

Total # Posts: 37,440

Physics 30
see Coulomb's law.
February 6, 2016

Physics 30
since only one current is given, I'll assume the R are in series E = IR, so 22 = .012(27+R)
February 6, 2016

Physics 30
come on, that's ohm, not omega. Omega is just the symbol used for the unit. 1A = 1C/s P = I^2R = (10/5)^2 * 25 = 100 W energy = power * time
February 6, 2016

Physics 30
since the force is inversely proportional to d^2, it will be reduced by a factor of 25.
February 6, 2016

PHYSICS
Coulomb's law is discussed here: http://www.physicsclassroom.com/Class/estatics/U8L3b.cfm just plug in your numbers.
February 6, 2016

physics & math
well, recall that v = √(2as) so, plug in your a and s.
February 6, 2016

Calculus (polar coordinates)
recall that dA = r dr dθ so, since x = r cosθ you have ∫[0,π/2] r cosθ r dr dθ = ∫[0,π/2] r^2 cosθ dr dθ But, r changes at π/4, so that gives ∫[0,π/4]∫[0,2sinθ] r^2 cosθ dr dθ + ∫[&#...
February 6, 2016

Math
Hmm. I'm still unclear. What is an example where switching the hands is invalid?
February 6, 2016

Math
Do you mean the physical clock hands are switched? No problem. I mean, the hands still point to places on the dial, right? If you mean the digital time has hh:mm swapped to mm:hh, then any time from 01:01 to 01:12 is ok and so on for the other hours. As long as the minutes are...
February 6, 2016

Math
<head slap> dontcha hate it when that happens? Still, the aha! moment is worth the pain.
February 6, 2016

Math
recall that the y-intercept is where the line crosses the y-axis. The line y=16 clearly crosses the y-axis at y=16, because it is 16 for any value of x, in particular, x=0.
February 6, 2016

calculus
The curves intersect at (0,0) and (3,9) So, rotating around the x-axis, using discs: v = ∫[0,3] π(R^2-r^2) dx where R=3x and r=x^2 v = ∫[0,3] π((3x)^2-(x^2)^2) dx = 162π/5 shells (tubes): v = ∫[0,3] 2πrh dy where r=y and h=(√y)-(y/3...
February 6, 2016

Physics
A: since the initial v=0, only g is acting on the mass. B: ok C: D = bv^2 = b(√(mg/b)/2)^2 = mg/4 SO, net a = mg/4 - mg = -3/4 mg
February 6, 2016

Pre-Calculus
looks good to me. You can always check your answer by typing in the polynomial at wolframalpha.com
February 6, 2016

Pre-Calculus
enter your coefficients at http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php Looks like you goofed somewhere.
February 6, 2016

Do I have time
no, but google shows many hits, the first at (wow!) biography.com
February 6, 2016

Do I have time
Sure you have time. 3 days for 4 more paragraphs? No sweat, if you get to work. Of course, judging by your posting, you have some serious proofreading to do ...
February 6, 2016

algebra 2
the domain for all polynomials is (-∞,∞) Think about it -- pick any value of x and you can calculate f(x).
February 6, 2016

algebra
At first I thought your work was a hodgepodge, but further study shows that you are correct. except that 95/7 is not 13. Should have been 91, so you messed up somewhere.
February 6, 2016

Calculus
No, at 20 mi/hr, every mi/hr increase in speed decreases the fuel consumption by .05 gal/hr. Keep track of the units. Seems kind of odd though, that rate of fuel consumption decreases with increasing speed...
February 6, 2016

Calculus
#1 ok #2 f' = dc/dv = (gal/hr)/(mi/hr) = gal/mile #3 sort of - see units for #2.
February 6, 2016

Math Radicals
just expand like normal binomial multiplication: (a+b)^2 (2√5+3)(2√5+3) = (2√5)^2 + 2(2√5)(3) + 3^2 = 4*5 + 12√5 + 9 = 20 + 12√5 + 9
February 6, 2016

math
p(t) = 4i+8j + (4i+j)t q(t) = 4i+3j + (2i+5j)t the distance pq is d(t) = p(t)-q(t) = 5j + (2i-4j)t = (2t)i + (5-4t)j |d| = √((2t)^2 + (5-4t)^2) = √(20t^2-40t+25) Hmmm. I get √5 as the minimum distance. Better check my math.
February 6, 2016

Mathematics
8x^3 = 0
February 6, 2016

Math and Physic
Right off, I'd say the building has zero velocity. as for time to fall, h - 4.9t^2 = 0 plug in t= 7.57
February 6, 2016

Calculus
If the width is x and the rectangle's height is y, then x+2y + π/2 x = 24 so, y = (24-(1+π/2)x)/2 The area is a = xy + π/2 (x/2)^2 = x(24-(1+π/2)x)/2 + π/8 x^2 = 12x - (1/2 + π/8)x^2 Now just set da/dx=0 to find where the max occurs. Or, use ...
February 6, 2016

sinusoidal functions
The central axis is at y = 5 y = sin(x)+5 Two consecutive minima are found at (3, −1) and (13, −1) So, the period is 10, the amplitude is 5+1=6, and the shift is 3. cos has max at x=0, but we have a minimum, so y = -6cos(π/5 (x-3))+5 see the graph at http://...
February 6, 2016

math
rear legs get 2/3 and front get 1/3 now divide those amounts by 2, since there are two front and two rear legs.
February 6, 2016

calc
f'(p) is the rate of change of quantity as price changes Think of the units: f is yards p is dollars, so df/dp = yards/dollar no idea whether f'(16) is positive or negative. However, it is likely that as price goes up, demand goes down.
February 6, 2016

system of equations
a + 30b = 1300 a + 80b = 2200
February 5, 2016

Calculus
looks ok to me y = f^3(g(x)) dy/dx = 3f^2 df/dg * dg/dx for example, y = sin^3(x^2+1) dy/dx = 3sin^2(x^2+1) cos(x^2+1) (2x)
February 5, 2016

Linear Algebra
depends. what is b? As long as the matrix has a nonzero determinant, there will be a solution.
February 5, 2016

Math
Looks more like A to me.
February 5, 2016

Geometry
google online drawing tools. Or, hey! How about this idea? Go Buy Some Graph Paper! Actually, there are online sites which have graph paper you can print.
February 5, 2016

Maths
review the cotangent function. Draw a diagram and you will see that the distance the plane has flown is 880 cot24°30' - 880 cot67°40'
February 5, 2016

math
2a+3c = 44.40 3a+6c = 78.00 That's the same as 2a+3c = 44.40 a+2c = 26.00 subtract and you get a+c = 18.40 Note that we don't actually have to find the price of the individual tickets.
February 5, 2016

Geometry
#1 ok. #2 you figured the length of the hypotenuse. The perimeter is 9+12+15 = 36.
February 5, 2016

math college readiness
h(t) = 105 - 9t - 16t^2 When does it hit the ground? That would be when h(t) = 0, right? So, just solve the quadratic equation.
February 5, 2016

Math
If they are linear equations, it is A. Parallel lines (same slope) never intersect. But lines with different slopes must intersect somewhere.
February 5, 2016

Math
you are correct.
February 5, 2016

math
If the unknown force is x, then you just need to solve 550 - 300 + x = 0 because the sum of all the forces needs to be zero. I think that once you get your answer you will (a) see why the given formula works (b) notice the typo as written
February 5, 2016

math (sequence and series )
salary: 1st 8 years: 240 years >= 9: Tn = 9500+360(n-8) Total after 8 years: 8*240 = 1920 n years: (n > 8) Sn = (n-8)/2 (2*9500 + (n-9)*360) So, plug in your numbers for n
February 5, 2016

Physics
if the graph shows the actual error, just divide that by the correct value. For example if the correct value is 20, and the error is 3, then the percent error is 3/20 = 0.15 = 15%
February 5, 2016

precal
we can pick any direction for the 1st 3 blocks. Say, North. After the 1st 3 blocks N, E and W are interchangeable. Clearly, going N then S will not help, so she can do one of the following: E for 2, N for 1 E for 2, W for 1 E for 2, S for 1 I think you can tell which gives the...
February 5, 2016

Physics
well, uh, g, just read off the slope and equate it to 1/2 g: 5.00 = 1/2 g g = 10.00
February 5, 2016

Math
If each line represents 100 sales, then you are correct.
February 5, 2016

chemistry
wikipedia has a nice article on calcium, and lists several compounds which are essential for good health. Calcium always forms ionic bonds.
February 5, 2016

Math
Unless it's a large glass, I'd use ounces. Most glasses are 8-12 oz. Of course, those are fluid ounces. Plain ounces are a measure of weight, not volume. A fluid ounce is the volume occupied by one ounce of water.
February 5, 2016

MATH
google is your friend. I can tell you how, but you can find many illustrated instructions online. Place compass at one end of line segment. Mark an arc with radius more than half the line length. Do the same at the other end. Make sure the arcs are long enough to intersect in ...
February 5, 2016

Physics
The basic requirement for destructive interference is that the two waves be shifted by half a wavelength. Now, as you know, v = λν, so just plug in your numbers.
February 5, 2016

Math
just write that in symbols: nth denominator is 3^(n-1) nth numerator is 3^(n-1) - 2 So, the ntheterm is Tn = (3^(n-1) - 2)/3^(n-1) That can be massaged in various ways: Tn = 1 - 2/3^(n-1) Tn = 1 - 6/3^n Tn = (3^n - 6)/3^n
February 5, 2016

shuluka
Hora aderat briligi. Nunc et Slythia Tova Plurima gyrabant gymbolitare vabo; Et Borogovorum mimzebant undique formae, Momiferique omnes exgrabure Rathi.
February 5, 2016

Complex number
recall that (a+bi)(a-bi) = a^2+b^2 (1-i)/(1+i) * (1-i)/(1-i) = (1-i)^2 / (1+1) = (1-2i+i^2)/2 = (1-2i-1)/2 = -2i/2 = -i or, 0 - i
February 5, 2016

Pre-cal
use Heron's formula, or use law of sines/cosines to determine one of the angles. then the area is 1/2 ab*sinC
February 5, 2016

Maths
the new length is 4 times the old length.
February 5, 2016

Math
107.20 * 1.06
February 5, 2016

Math
if you mean eighteen and fourteen thousandths, that is 18.014
February 5, 2016

calc 1
The slope at any point is y': y' = 4-6x y'(2) = -8 Now you have a slope and a point: y+4 = -8(x-2)
February 4, 2016

Math
so, what are the constraints, and the value to maximize? In algebra, not words.
February 4, 2016

calculus
#1 and #2 look ok (except that x(3) = 18 units, not units/s) #3 flea moving right when x'(t) > 0 (s increasing) #4 evaluate x(t) at the extrema from part 2. Check with this graph: http://www.wolframalpha.com/input/?i=t^3+-+9t^2+%2B+24t #5 x(5)-x(0) #6 ∫[0,5] (1+(x...
February 4, 2016

math
eh?
February 4, 2016

calc
#1 as with any parabola, vertex is at t = -b/2a #2 use the t from #1 and evaluate h(t)+6 #3 dh/dt = 64-32t when is that 24 or -24? #4 h(t) = vt-g/2 t^2
February 4, 2016

Math
if truly linear, the slope is constant. If the slope is close to constant, then the growth is close to linear.
February 4, 2016

algebra - incomplete
sorry - no table
February 4, 2016

Physics (Electricity)
E = IR
February 4, 2016

Algebra
they are the same line, so infinitely many solutions.
February 4, 2016

Algebra
what, no calculator? Since 2015 is 5 years from 2010, you want to evaluate 32 * 2.1^5 = 1306.9 D should have been clearly wrong, since 2^5=32, so 32*32 = 1024 would be a good guess, though somewhat low.
February 4, 2016

Physics
recall that the max height is (v sinθ)^2 / (2g)
February 4, 2016

calc 1
For ε=0.1, you want to find δ such that |f(2+δ)-f(2)| < 0.1 |((2+δ)^3-5(2+δ)+3)-(2^3-5*2+3)| < 0.1 |δ^3+6δ^2+7δ| < 0.1 δ < 0.014
February 4, 2016

MAth
17 + x <= 26
February 4, 2016

Physics
would it not be opposite but equal in magnitude? If not so, there would be an acceleration.
February 4, 2016

Physics
the distance traveled is s = 12.4t - a/2 t^2 = 50.3 The velocity is v = 12.4 - at = 0 Solve that and you get a = 4.59 Now you can use F=ma
February 4, 2016

Physics
resolve the three forces into x- and y-components. Add them up, and take the magnitude.
February 4, 2016

Algebra 2
google equation of trend line for lots of help and examples.
February 4, 2016

algebra
better review your distance formula: d = √((∆x)^2 + (∆y)^2)
February 4, 2016

algebra
since the midpoint is halfway between the ends, its coordinates are the average of the x and y of the ends.
February 4, 2016

algebra
the perpendicular line has slope -4 Now you have a point and a slope, so use the point-slope form of the line. Then rearrange to slope-intercept form.
February 4, 2016

algebra
to find the x-intercept, set y=0 for the y-intercept, set x=0 Now you have two points on the axes -- connect them with a line.
February 4, 2016

algebra
why all those cluttery words? This is math, not English. x^2+y^2+8x-8y-49 = 0 x^2+8x + y^2-8y = 49 Now complete the squares: x^2+8x+16 + y^2-8y+16 = 49+16+16 (x+4)^2 + (y-4)^2 = 81 I think you can prolly take it from there, eh?
February 4, 2016

Algebra
it helps if you can find the roots of the function. In this case, you have y=(x+1)(x^2+16) So, you know the graph crosses the x-axis only at x = -1. Since the 2nd factor is always positive, y>0 where (x+1) > 0. Think you can take it from there?
February 4, 2016

anty alice
type you equation in at wolframalpha.com
February 4, 2016

math
Draw a diagram. The slant height is s = 42/cos30°
February 4, 2016

maths
check the intercepts. when x=0, y=b when y=0, x=a so, you have a right triangle with legs a and b, so its area is ab/2
February 4, 2016

Calculus
If the angle is x, then you have a trapezoid with lower base 4", and upper base 4+2*4cosx, and height 4sinx. So, the area of the cross-section is a = (4 + (4+8cosx))/2 * (4sinx) = 16 sinx (1+cosx) da/dx = 16(2cos^2(x)+cos(x)-1) = 16(2cosx-1)(cosx+1) da/dx=0 when cosx = 1/...
February 4, 2016

circumference...math
recall that the circumference of a circle of diameter d is C = πd
February 4, 2016

Math
vertical angles are equal, so 7x+7=112 x=15 you are correct.
February 4, 2016

math
solve for t with e^(.10*t) = 2
February 4, 2016

math
the small gear turns 4 times as fast as the large one.
February 3, 2016

Math
looks ok to me.
February 3, 2016

maths
well, here's the graph: http://www.wolframalpha.com/input/?i=%282^x%29%28cot+x%29%2Fx^1%2F2 did you have some question about it?
February 3, 2016

MATH
well, a = 8 r = 3/4 Tn = 8 * (3/4)^(n-1)
February 3, 2016

Calculus
what is the height of the tank? You need to know how far above the top of the oil is the spout, and how deep is the oil. Anyway, assuming the oil has a depth of d meters, and the spout is h meters above the top of the oil, then consider the oil as a stack of thin slices of ...
February 3, 2016

Calculus
a = dv/dt, so v(t) = 2t^3 = 2*6^3
February 3, 2016

Calculus
all look ok to me. good work.
February 3, 2016

calculus 1
clearly the limit is (8+1)/(6-4) = 9/2 Not sure what your definition 2 is, but if you need to find δ such that |f(x+δ)-9/2| < 0.5 then that means |(4(2+δ)+1)/(3(2+δ)-4)-9/2| < 0.5 Work your way through that and you will find that δ < 0.125 So...
February 3, 2016

Math
(a) stretch by 2 and shift up 3 (b) shift left 1 and down 3 (c) shrink by 2 and reflect in x-axis (d) shift left 1, reflect in y-axis, reflect in x-axis, shift up 3. Just plug in your numbers to find the image of the point.
February 3, 2016

Geometry
22+16-32 = 6 So, there are 6 juniors who do both. P(both) = 6/50 = 3/25
February 3, 2016

Math
assuming you have a hemisphere atop a cylinder, they both have the same radius. So, just plug your numbers into the usual volume formulas.
February 3, 2016

Math
clearly y is discontinuous at x=0, since lim(x->0-) = 3 lim(x->0+) = 1 y'=-2x for x<0 y'=2x for x>0 y" = -2 for x<0 y" = +2 for x>0 so, y is increasing everywhere, since y'>0 everywhere it is defined. y is concave down for x<0 y is...
February 3, 2016

Writing equations to represent situations
x = 17 xy = 680 2(x+y) = ?
February 3, 2016

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