# Posts by Scott

Total # Posts: 2,430

math
sin(0) = 0 ... sin(90) = 1 so ... sin(50) > sin(40) cos(0) = 1 ... cos(90) = 0

Chemistry
there are 1000 L in a cubic metre so the density is 3000 g/L the molar mass is 44.956 g so one L contains ... 3000 / 44.956 moles the number of unit cells is half the number of atoms the volume is ... 1 L / [(3000 / 44.956) * 6.02E23 / 2]

math
d = 3 q 10 d + 25 q = 385 solve the system using substitution or elimination

Further Mathematics
11th term is 10 cr from 1st term 7 * 3^10

Math
-5 = -a + b - c y' = 3a x^2 + 2b x + c ... 4 = 3a - 2b + c y" = 6a x + 2b ... 0 = -6a + 2b 3 equations, 3 unknowns ... solve the system

mATH
520 X [1 + (0.04/12)]^60 IS THIS RIGHT WAY TO DO THIS just clarifying

Physics
150 kN to pull 12 cars to pull one car ... 150/12 kN

physics
momentum is conserved (75 * 2) + (50 * v) = 0

Math
x * x * (x - 3) * (x + 1)

Chem
reacts with water to form sulfuric acid this is the "acid rain" reaction

Math
it's an even power regardless of the sign of x, f(x) will always be positive

Math
h + c = 160 ... 200 h + 200 c = 200 * 160 500 h + 200 c = 369 * 160 subtract equations to eliminate c solve for h, then substitute back to find c

Mathematics
the area of the bottom of the box is ... 3456 / 6 = 576 (x + 12) [(576 / x) + 12] = 1500 x is one dimension, 576/x is the other

Physics
800 N * 20 m = 16000 J per second means 16 kilowatts

Math
h(g(x)) = 9 - (x + 3)^2 ... = -x^2 - 6x the max is on the axis of symmetry ... x = -b / 2a = 6 / -2 = -3 plug in -3 to find the maximum

science
v = mass/density = 2.4 kg / 2.70 g/cm^3 2.4 is only 2 sig fig

Math
let x be the edge length of the corner squares the volume of the box is ... v = x (12 - 2x)^2 ... v = 144 x - 48 x^2 + 4 x^3 the 1st derivative will show the maxima/minima plug in the values to find the volume

Physics
the difference in densities gives you the "lift mass" per m^3 v = 800 kg / (1.25 kg/m^3 - 0.18 kg/m^3)

Physics
the metric unit of pressure is the Pascal (Pa) ... one Newton of force over one square meter a cubic meter of water has a mass of a thousand kg (a metric ton) ... it exerts a force of 9.81 kN stacked 100 high, the pressure at the bottom is ... 981 kPa

Algebra
the vertex is on the axis of symmetry x = -b / (2 a) = -6 / (2 * -1) = 3 plug 3 into the function to find the y-coordinate

physics
a straw works because when you lower the pressure on one end (by sucking), atmospheric pressure pushes the liquid from the other end the airtight cork prevents the atmospheric pressure from pushing on the liquid, so it won't go up the straw

physics
a cubic meter of water is a metric ton ... 1000 kg .4 m^3 / 24 m^2

Intermediate Algebra
c + h = 150 ... 325 c + 325 h = 325 * 150 325 c + 525 h = 445 * 150 subtract equations to eliminate c ... then substitute back to find h

Math
0 = x^2 - 2x + 15 x = [2 ± ?(4 - 60)] / 2 x = 1 ± i?14

physics
v is squared, doubling the uncertainty the value is then divided by y, which adds its uncertainty (2 * 3.34%) + 5.00%

physics
v is sq

physics
gas is correct

physics
the ke at the bottom equals the pe at the top both measured in Joules

physics
e = m g h = 7.2 * 9.8 * 1.2 (Joules)

math
worst case ... he takes out 5 ya and 7 gp the 13th fruit will fill the requirement

maths
find the average area of the top and bottom multiply by the height ... this is the volume in cm^3 divide by 1000 to find litres

Algebra
savings is dependent on weeks (98 - 65) / (6 - 3) = \$11 / wk

Alg/Trig
0 = -16 t^2 + 112 t factoring ... 0 = -16 t (t - 7) 0 = -16 t ... t = 0 (launch) 0 = t - 7 ... t = 7 (return)

the density

Science
as the stone travels upward, its kinetic energy becomes potential energy the potential at the top is equal to the kinetic at the bottom ... e = 1/2 m v^2 = m g h ... h = ?[v^2 / (2 g)]

Pre-Calculus
?[389^2 + (389 + 50)^2]

science
h = -1/2 g t^2 + 7 t + 55 h is zero when the bottle hits the ground 0 = -4.9 t^2 + 7 t + 55 you want the positive solution

Algebra2
30 * (54/42)^2 * (26/85)

physics
do they start timing at a crest? there are 19 wavelengths between 20 crests

Chemistry
K.E. = 1/2 m v^2 look up the mass of the electron (in kg), and solve for v

Math
f = t - 20 j = 2f = 2t - 40 p = 3j = 6t - 120 9t - 180 = 340 solve for t, then substitute back

Science
Elodea uses photosynthesis to convert carbon dioxide and water into oxygen and carbohydrate the most bubbles should be in the carbon dioxide enhanced sample the degassed sample should have no bubbles the oxygen enhanced sample should be somewhere in between

math
b = 20000 (1 + .07)^6

math
this seems to be two questions 1st b + g = 30 b = g + 4 substitute to find solution 2nd 4 + 1 = 5 30 / 5 = 6 30 - 6 = 24 there are 24 of one and 6 of the other

Math
f + s = 45 s - f = 37 adding equations ... 2 s = 82

Science
velocity = distance / time

they are more massive (heavier) than the inner planets; and their greater gravities allow them to hold the lighter gasses

Maths
[(1.025 x) - 1000] * 1.025 = 23517.6

Math
(6 x)^2 + [5 (x - 4)]^2 = (7.5 x)^2

Math
f + s = 11000 ... 8 f + 8 s = 88000 5 f + 8 s = 75250 subtract equations to eliminate s 3 s = 12750

Trigonometry
theta is a Quad IV angle with a sine of -3/5 find cos, tan, sec, csc and cot

algebra
[.30(8080 - x)] + [1.0(x)] = .80(8080)

MATH
yes ... not to confused everything gets raised to the power

algebra
x + y = 48 x / 3 = (y / 6) + 5 ... 2x = y + 30 ... 2x - y = 30 add equations to eliminate y substitute back to find x

math
40000 L takes 30 pump-hr so 60000 L takes 45 pump-hr ... one and a half times as much 45 pump-hr / 9 pump = ?

trig
use the "Law of Cosines"

math
you have one equation and two unknowns there is no "unique" solution the solution is a line

Chemistry
find the energy (heat) for each step ... the mass of H2O is constant warm ice to 0ºC melt ice warm water to 100ºC boil water warm steam to 112ºC

physics
v initial = 100000 m / 3600 s v final = 0 v ave = (vi + vf) / 2 time = .85 m / (v ave) accel = vi / time

math
p = e + 10 15 p + 22 e = 446 15 (e + 10) + 22 e = 446 37 e = 296

Math
the normal line is perpendicular to the tangent the slope of the tangent is the 1st derivative normal slope ... -2 tangent slope ... 1/2 1/2 = 4 x^3 ... 1/8 = x^3 ... 1/2 = x point ... (1/2 , 1/16) equation ... y - 1/16 = -2 (x - 1/2)

Probability, Stats
d = defective , n = not defective this is a binomial distribution ... a battery is or isn't 100C2 * .985^98 * .015^2

physics
assuming flat ground distance = v^2 * sin(2?) / g

physics
235 - 92

Pre Cal 12
1400 = 900 [1 + (i / 4)]^(12 * 4) log(14 / 9) = 48 log[1 + (i / 4)]

Math -
multiplying 2nd equation by 2 ... 12x + 14y = 20 subtracting equations (to eliminate y) ... 4x = -4 solve for x, then substitute back to find y

Pre Cal
the sides are in the same ratios as the sines of their opposite angles a = c * [sin(A) / sin(C)]

Geometry
find the distance between two points on the original figure, and the same points on the dilated figure the ratio of the distances is the scale factor

Math
d = r * t twice the speed means half the time

science
the molar mass of CaO is ... 40 + 16 so 44 g contains ... [44 / (40 + 16)] moles

Chemistry
warm the ice from -15ºC to 0ºC melt the ice warm the water from 0ºC to 100ºC boil the water heat the steam to 114ºC each step has its own heat input

math
the system of equations has no solution ... the lines are parallel

Chemistry
a mL is a cm^3 a foot is ... 2.54 * 12 cm 1 ft^3 Hg ... mass = (2.54 * 12)^3 * 13.6 g multiply by g to find the weight

Maths
a1, a1 + 36, a3, a3 + 900 (a1 + 36) / a1 = (a3 + 900) / a3 1 + (36 / a1) = 1 + (900 / a3) a3 = r^2 * a1 36 = 900 / r^2 ... 6 r = 30

Math
50000 = 30000 (1 + i)^18 log(5/3) = 18 log(1 + i) .012325 = log(1 + i)

math
A = 100 * (1 + .03)^30

maths
a = 40 m/s / 2 ms = 20000 m/s^2 f = m a = .05 kg * 20000 m/s^2 answer is in Newtons

Math
divide the expression by the factor that will leave a quadratic that you can use the formula on

Physics
1) no horizontal acceleration ... v = 17 m/s * cos(34º) 2) same vertical velocity as at launch, except in opposite direction ... v = 17 m/s * sin(34º) ... downward 3) the flight time is twice the initial vertical velocity, divided by gravitational acceleration 4) the...

physics
mass * temp change * specific heat make sure the specific heat value is in Joules

Geometry
5 b + 5 b + b = 121

Physics
you're not accelerates to 12 m/s, then travels for 20 s ... that's 240 m, plus the acceleration distance d = 1/2 a t^2

Geometric Progression.
(x + 9) / x = (x + 22.5) / (x + 9) x^2 + 18 x + 81 = x^2 + 22.5 x 81 = 4.5 x a1, a2, 18, 27, 40.5

Physics/Energy
work = m g h the time is only a factor for power calculation

Math
60x + y = 87.15 subtracting equations ... 30x = 33.60 substituting ... 33.60 + y = 53.55 ... y = 19.95

Matha
compounding period?

Physics
KE = 1/2 m v^2 m = .02 kg v = (200000 / 3600) m/s answer is in Joules

physics
1/2 m v^2 = m g h h = v^2 / (2 g)

Physics
the same depth means the same pressure at the bottom the forces are equal

science
K.E. is proportional to the square of the velocity this means that the energy change from 80 kph to 70 kph is greater than the change from 10 kph to zero use (1/2 m v^2) to find the energies the lost energy (from braking) is usually frictional (heat)

Maths
each cut results in a cake that is 3/4 of the size before the cut starting with a whole cake (1) after 3 cuts ... 1 * (3/4) * (3/4) * (3/4)

physics
his energy at the bottom is the change in potential energy, minus the work of friction ... m * g * h - 520 * h ... E = (88 kg * 9.8 m/s^2 - 520 N) * 5.9 m his velocity is (from K.E. equation) ... v = ?(2 * E / m) while he is slowing down, his average velocity is ... (v + 0) / ...

math
2 x^2 + 13 x - 84 = 0 use the quadratic formula

science
the molar mass of sulfur is 32.1 g there are 6.02E23 atoms in a mole of sulfur (10.0 / 32.1) * 6.02E23

Chemistry
1. -3 means 3 "extra" electrons ... this element is atomic number 7 2. +2 means 2 "lost" electrons ... this element is atomic number 20 3. column 2, row 3

math
30 m / x = tan(78º)

math
[1 - (5/8)] * [1 - (1/6)]

Geometry
the x-distance from p1 to p2 is ... 6 - -4 the y-distance from p1 to p2 is ... 9 - -7 divide the distances by 4 to find the "length" of each step start at p1 and add consecutive steps to find the 3 division points

algebra
biologists use a Punnett square to show the geneotypes if both parents are RL, the following outcomes are equally probable ... RR, RL, LR, LL

math
2.1 = a [1/2^(1000/24360)] log(2.1) = log(a) + (1000/24360)log(1/2) 2.1606 ?

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