# Posts by Scott

Total # Posts: 2,423

tan(90º - Θ) = cotan(Θ) cotan(Θ) = cos(Θ) / sin(Θ) [cos(Θ) / sin(Θ)] * sin(Θ) = cos(Θ)

Math
x (.20) + (300 - x)(.40) = 300 (.28) .2 x + 120 - .4 x = 84

physics
the rock reaches its peak after 12/g s it ascends at an average rate of ... (12 m/s + 0 m/s) / 2 it then free falls from h m g h = ½ m v² ... v = √(2 g h) t = 2 h / v

Physics
a * [1 - (p / density of Hg)]

algebra
(s + 7)² = s² + 189 s² + 14 s + 49 = s² + 189 14 s = 140

maths
h(x) = 2 - x g(x) = x²

maths
f(x) = g[h(x)] g(x) = x³ h(x) = 2x + 1

Physics
the energy stored in the spring is ... ½ k x² ... this energy is K.E. when the spring is in the neutral position (the middle of its travel) K.E. = ½ m v² ... so the velocity and the amplitude are directly related to each other (both squared) a) velocity...

Math
a) h / 300 = tan(16º) ... h = 300 * tan(16º) b) tan(Θ) = h / (300 - 75)

geometry
the 3rd side must be greater than the difference, and less than the sum, of the 1st two sides

Math
[(8 * 60) + 37] * 25 ft

physics
the average velocity is ... 36 m / 2 s = 18 m/s gravity has slowed decelerated) the arrow by ... 9.8 m/s² * 2 s = 19.6 m/s [v + (v - 19.6)] / 2 = 18 ... v = 27.8 m/s (launch velocity) time to peak is ... 27.8 m/s / 9.8 m/s² peak height is ... time to peak * 27.8 / 2 ...

Geometry
after translation ... [(-6 + 3),(-4 + 5)] = (-3,1) after rotation ... (1,3)

Maths
B = 3 J ... J = B/3 B = J + 450 ... B = B/3 + 450 ... 2B/3 = 450 ... B = 450 * 3/2

Statistics
15 is 1.5 above the mean ... this is 1.5/7.3 standard deviations ... .2055 use a z-score table to determine the fraction of the population this represents 15 yr or less ... 58%

engineering mechanics
normal ... m g cos(30º) parallel ... m g sin(30º)

math
1/A + 1/B = 1/8 ... 15/B = 15/8 - 15/A 6/A + 15/B = 1 ... 6/A - 15/A + 15/8 = 8/8 ... -9/A = -7/8 ... -72 = -7A

Math
x (25 - 2x) (32 - 2x) = 1575 expand the cubic equation find a solver online (use google)

physics
10 min = 600 s 600 s (20 m/s + 30 m/s) = 30 km ave spd = 30 km / 20 min = 1.5 km/min 10 km / 20 m/s = 500 s 10 km / 30 m/s = 1000/3 s 20 km / (1500/3 s + 1000/3 s) = ... 60 / 2500 km/s = 36/25 km/min = ... 1.44 km/min

CHECK MY ALGEBRA 2
?????

CHECK MY ALGEBRA 2
a hole is a disruption at a single point ... try [(x - 4) / (x - 4)] ... the division by zero causes the discontinuity, but the equal numerator means no other point is affected f(x) = (x - 4) / [(x - 4) (x + 2)]

Physics
assumptions ... the person does not ride the ice down ... the height of the break is even with the top of the slope the gravitational potential energy of the ice is converted to kinetic energy and then heat by friction the total energy dissipated is ... m g h = 100 kg * g * ...

College physics
this is the Doppler effect (google it) the pitch (frequency) is higher because you are moving toward the source f = [343 / (343 - 5)] * 4000

Physics
Vh = 3 m/s² * 30 s = 90 m/s ½ m Vv² = m g h ... Vv = √(2 g h) = √( 2 * 10 * 80) tan(Θ) = Vv / Vh

chemistry
pH = 14 - pOH pOH = - log[OH⁻] = - -8 = 8

Math
top area???

PHYSICS
acceleration ... d = 30 s * [(20 m/s + 0 m/s) / 2] cruise ... d = 15 s * 20 m/s deceleration ... d = 5 s * [(20 m/s + 0 m/s) / 2] add the three distances

math: permutations
couple in 1st row ... 2 ways for 1st row ... 4! ways for 2nd row couple in 2nd row ... 4*5 ways for 1st row ... 4! ways for 2nd row [(4 * 5) + 2] * 4!

math:age
2 s = u 3 (s - 9) = u 3 s - 27 = 2 s

Help me anyone - Pre-Calc
Θ is in radians 20º = (2 π / 18) rad 2340 = ½ (2 π / 18) r² 18 * 2340 / π = r²

math
e = p + 50 time = distance / rate ... 1.6 (1800 / e) = 1800 / p substituting ... 1.6 [1800 / (p + 50)] = 1800 / p solve for p, then substitute back to find e and the times

Calculus - Differentials
the error (in D) is ±.05 A = π D² dA = 2 π D dD = .6 π same difference...

Calculus
h = height up wall d = distance from wall by Pythagoras... h² + d² = 20² differentiating ... 2 h dh/dt + 2 d dd/dt = 0 substituting ... (2 * h * -3) + (2 * d * 4) = 0 ... 8 d = 6 h ... d = ¾ h h² + (¾ h)² = 400 solve for h substitute back...

physics
[16 * cos(20º)] / 4.9 the values in the problem are to 2 significant figures ... not sure about hundredths accuracy

Science
I can be traced back to 3000bc, often go unnoticed, can be overhead, under feet or somewhere in between, evolution has changed me, am lighter than I used to be, and can protect your investment.

Physics
distance = 70 * 5 = 350 km speed = distance / time = 350 / (5 + 2)

Math
3, 5, 9, 15

Physics
N is to the left google "right hand SOLENOID rule"

chemistry
(3 / 2) * 41.0

Math
if r = -2, then the denominator is zero...a big no-no factor the numerator and go with B

Chemistry
1.63 is [SO₂]² ... take the square root

Physics
heat capacity is proportional to mass mass is proportional to volume volume is proportional to the cube of the radius heat cap. ratio is ... 1³:2³

Physics
(a) 2400 + 1800 (b) 1800 / (2400 + 1800)

math
h = 4 mi * tan(5º) = 4 * 5280 ft * tan(5º)

Math
the area of the real world room is (36 / 2.5)² times the area of the plan

Physics
the velocity is half, so the remaining energy (kinetic) is a quarter of the original 3/4 of the energy to penetrate 15 cm it will penetrate another 5 cm

Science
m g h = ½ m v² h = v² / (2 g) h = ½ g t² ... v² / (2 g) = ½ g t² t = v / g .. this is ½ the flight time

Math
6000 = 2500 (1 + r/4)^(10 * 4) 2.4 = (1 + r/4)^40 log(2.4) = 40 log(1 + r/4) .0095053 = log(1 + r/4) 1.002213 = 1 + r/4

physics
the expansion coefficient is ... α = 1.20E-5 m /m·ºK ΔL = 1.20E-5 * 12.5 * (154 - 5) L = 12.500 + ΔL

Physics
energy (work) = 1/2 k x^2 w = 1/2 * 950 N/m * (.06 m)^2

Math
multiplying by 1/3 ... (1/x) / [x^(-2/3)] = 1 / [x^(1/3)] multiplying by x^(-2/3) ... 1/x = [x^(-2/3)] / [x^(1/3)] ... = 1 / [x^(3/3)] = 1/x

physics
units conversion a = v / t d = Vave / t = 30 mph / 3.2 s

Physics
average velocity is ... (.36 + 0) / 2 t = d / v = .8 m / .18 m/s acceleration ... a = .36 m/s / t f = 80 kg * a

Math
f - s = 28 2.5 (f + s) = 2320 f + s = 928 adding equations to eliminate s ... 2 f = 956

chemistry
He⁺ because the greater charge of the nucleus keeps a "tighter" hold on the electron

physic
you need the coefficient of friction to solve this

physic
g = 32.2 ft/s (a) 3.73 * 32.2 = w (lbs) (b) 3.73 * (32.2 + 5.5) = w (c) same as (a) (d) 3.73 * (32.2 - 5.5) = w

General Physics
integration is the correct approach work (energy) = F(x) dx the force goes to zero at √2.6, and then goes negative ... this is also the point of max energy

Algebra 2
they appear to be the same line (colinear)

math 101
145 is one s.d. above the mean 68% of scores are in this range 34% are above the mean 50% of scores are below the mean that leaves 16% of scores above 145

maths
good solution, Steve

maths
actually, slope-intercept is better

maths
find the equations (point-slope) of the diagonals and set them equal

math ratios
1 + 6 = 7 7 k = 21 ... k = 3 3 water and 18 fertiliser

Physics
m g h = .12 J .012 * 9.8 * h = .12

physics
the average speed is 40 m/s so it takes 25 s to cover the km the acceleration is 3.2 m/s² ... 80 m/s / 25 s speed halfway 500 = ½ * 3.2 * t² ... find t and multiply by the acceleration to find the speed half speed 40 m/s / 3.2 m/s² = 12.5 s ...average ...

Math
the Richter scale is logarithmic 10^(8.8 - 5.3)

physics
it takes the 1st stone 2 s to reach its peak and return to the top of the tower, now going downward with the same velocity as the 2nd stone that velocity is 9.8 m/s when it reaches the ground, its velocity is 39.2 m/s...4 s * 9.8 m/s its average velocity is 24.5 m/s ... (9.8...

science
.001 moles / .5 L = .002 M

science
λ =330 m/s / 1E4 cycles/s = 33 mm

physics
the average speed is 10.0 m/s ... 70.0 m / 7.00 s 1st point speed is 5.00 m/s ... 10 = (15 + 5) / 2 acceleration is (10.0 m/s / 7.00 s)

Science
mass * [heat of vaporization + (specific heat * temp change)]

Chemistry
a mole of ANY gas occupies 22.4 L at stp (5.2 / 22.4) * Avogadro's number

Algebra
(3 / 2s) + (1 / s) = 1 / 9 27/2 + 9 = s = 45/2 b = 2/3 s = 15

physics
combined force is 2 kN each pier acts as a fulcrum in a class 2 lever system 6 m * 2 kn = 10 m * f1 4 m * 2 kn = 10 m * f2

math
f + s = 205 5 f + 15 s = 2025 ... f + 3 s = 405 subtracting equations ... 2 s = 200

Physics
1 / R + 1 / 400 = 5 / R 1 / 400 = 4 / R

Chemistry
a liter of solution has a mass of 1.114 kg 20.0% of that is H₃PO₄ ... 222.8 g the molar mass of H₃PO₄ is ... 97.99 g so the moles/L is ... 222.8 / 97.99 the 20.0 means 3 sig fig

Math
g(x) = -2 (2x - 4)³ - 1

Math
f(x) = (x + a) (x + b)² (x + c)³

maths
2 sin(21º) = cos(69º) sin(29º) = cos(61º) so it's twice sin² + cos²

math,maths
x/x + 2/x ≥ .2 1 + 2/x ≥ .2 2/x ≥ -.8 2 ≥ -.8 x -5/2 ≤ x

Math
the distance is the same 10 (s - 21) = 7 s 10 s - 210 = 7s

math
r + b = 365 ... 10 r + 10 b = 3650 9.5 r + 10 b = 3645 subtracting equations ... .5 r = 5

Pre-Calculus 11
squaring ... 9 - 6x + x² = x² - 5 x = 7/3

math
L = w + 5 w * (w + 5) = 500 w² + 5 w - 500 = 0 factoring ... (w + 25) (w - 20) = 0 w = 20 ... L = 25

Physics
heat = mass * temperature change * specific heat for the water heat = 200 g * 7.2 ºC * 1 cal/gºC heat gained by the water is the heat lost by the metal for metal heat = 95 g * 70.8 ºC * s.h. s.h. = (water heat) / (95 * 70.8) be aware of significant figures in ...

Algebra
ln(y) + 5 ln(y+1)

physics
each of the four sides of the square is 5 Ω diagonally, there are two parallel paths of two 5 Ω resistances in series each path is 10 Ω (5 + 5), and the two paths in parallel results in a net resistance of 5 Ω

physics
a hanging spring with a freely hanging mass the force (from gravity) is ... m * g = .98 N k = F / d = .98 N / .01 m = 98 N/m

PHYSICS
multiplying or dividing ...add the percent uncertainties 16 ± 2.25% the cm are cancelled in the division process...it's just a ratio

Algebra
squaring both sides ... 36 = n^(2x) multiplying by n ... 36 n = n^(2x + 1)

Algebra
the drop time is ... t = 132 ft/s / 32 ft/s² it starts from rest, so the average velocity is ... (0 + 132) / 2 ft/s the distance is ... d = drop time * average velocity

Science
going directly from a solid to a gas is called sublimation

Physics
heat = mass * temp change * specific heat make sure the units are consistent

Calculus
the horizontal components of the two ropes' tensions balance each other the combined vertical components equal 400 N sin(60º) = T1v / 400 N T2v = 400 N - T1v cos(60º) = T1h = T2H T2 = √[(T2v)² + (T2h)²]

Chemistry
the iron is oxidized the hydrogen is reduced

Physics
80 C / .001 s = 80000 C/s = 80 kA