# 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)

**9th grade physical science**

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

**Science 6th grade**

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 ?