# Posts by Jai

Total # Posts: 1,999

Math
(2/3)y = (-1/5)x to get the slope, we first transform this equation into slope-intercept form, y = mx + b where m = slope and b = y-intercept. note that the numerical coefficient of y (number before the variable y) in slope-intercept form is 1, thus to change the given ...

math
note that in elimination method, we first simplify/modify one (or both) the given equation until if we add the two given equation, one of the variables will cancel out. in the problem, we can obviously see that the 2y in the first equation will be cancelled out by the -2y of ...

math
..it's difficult to show long division here,, but the answer is 4 - 4x.

math
(3x + 3)(-4x^2 + 4x - 2) -12x^3 + 12x^2 - 6x - 12x^2 + 12x - 6 note that the 12x^2 and -12x^2 will cancel out, and we combine -6x and 12x: -12x^3 + 6x - 6 hope this helps~ :)

math
f(x) = x^2 – 18x + 81 f(x) = 16 substituting the value of f(x) to the quadratic equation, 16 = x^2 - 18x + 81 0 = x^2 - 18x + 81 - 16 0 = x^2 - 18x + 65 0 = (x-13)(x-5) thus, x = 13 and x = 5 hope this helps~ :)

math
*reposted* ..it's difficult to show long division here,, but the answer must be 4 - 4x.

Physical Science
i'll try my best to explain them as simple as possible. (i) distance - how far an object has moved. it is in units of length (meters, kilometers, etc) (ii) speed - distance traveled over certain time, or in formula, v = d/t where v = speed d = distance t = time it has ...

Calculus
x^2 / ln 3x getting the derivative, [(2x)(ln 3x) + (x^2)(1/(3x))(3)] / [(ln 3x)^2] simplifying, [ (2x)ln 3x + x ]/[(ln 3x)^2] hope this helps~ :)

Algebra
note that you cannot simplify the right side equation log3 (4) + log3 (y+8) , by 4 + y + 8 ... they should be multiplied. recall some laws of exponents; if we are add terms of the same base, for example log 3 + log 5 this simplifies to log(3*5) or log 15 going back to the ...

Algebra Unit Analysis
for #1, 1 mi = 1609.344 m since we need units in cubic meters, we raise both sides by 3: (1 mi)^3 = (1609.344 m)^3 1 mi^3 = 4168181825.44 m^3 for #2, we first convert the 58 ft into miles. we use ration and proportion (let n = unknown): 1 mi : 5280 ft = n mi : 58 ft thus 1/...

Mathematics
consecutive numbers are numbers which are next to each other. for example, 2 and 3 are consecutive. also, 5, 6, 7 and 8 are consecutive. for the first question, first, we represent the unknowns using variables. let x = first number let x+1 = second number note that the second ...

Math
from the first statement, it implies that Dominic is 8 years older than his sister. first we represent unknowns using variables: let x = sister's age let x+8 = Dominic's age since the sum of their ages is 56, x + (x + 8) = 56 then we solve for x: 2x + 8 = 56 2x = 48 x...

statistics
3.5 % increase means additional 0.035*10.85 to the his original salary. thus, 10.85 + 0.035*10.85 10.85 + 0.37975 11.23 dollars (rounded off) hope this helps~ :)

calculus
to do this, we get the derivative of (ax^2 - a^2)^4 + c assuming a is constant, the derivative is 4[(ax^2 - a^2)^3](2ax) hope this helps~ :)

calculus
to do this, we get the derivative of (ax^2 - a^2)^4 + c assuming a is constant, the derivative is 4[(ax^2 - a^2)^3](2ax) hope this helps~ :)

math
we use ratio and proportion: 1 : 2 1/2 = x : 1 thus, x = 1/(5/2) x = 2/5 of the lawn hope this helps~ :)

algebra
(1) 2x - 3y = 2 (2) x + 2y = -20 to solve this by substitution, we choose one of the equations. from there, we choose a variable and represent it in terms of the other variable. here, let's choose equation (2), and make variable x in terms of y: x + 2y = -20 x = -20 - 2y ...

math
to get unit price (the price per liter), we just divide it: 1.40/4 = ?

Algebra 2 review
when you place the ladder on the house, it forms a right triangle, where the length of ladder is the hypotenuse. recall Pythagorean theorem: c^2 = a^2 + b^2 where c = hypotenuse, and a and b are the legs substituting (letting a = 36), 39^2 = 36^2 + b^2 1521 = 1296 + b^2 1521...

Chemistry HELP!!
yes, we'll use the ideal gas law formula. PV = nRT rearranging and noting that n = mass/molar mass, n = PV/RT = m/MM m/MM = PV/RT we first convert the given pressure to atm, and temperature to Kelvin, and volume to L: P = 74.3 mm Hg * (1 atm / 760 mm Hg) = 0.0978 T = 20 + ...

Math
recall that the derivative of f(x)*g(x) is just f'(x)*g(x) + f(x)*g'(x) which means, we first take the derivative of the first function of x (the f(x)) then multiply this by the second function of x (the g(x)) and add this to the product of f(x) and derivative of g(x...

math
recall that speed is distance travelled per unit of time, or v = d/t substituting, 80 = 84.2 / t 80t = 84.2 t = 84.2/80 t = 1.0525 h hope this helps~ :)

Math
x^2 - x = -2 can be rewritten as x^2 - x + 2 = 0 observing, the given equation is not factorable, thus we use the quadratic equation: x = [-b +- sqrt(b^2 - 4ac)]/(2a) where a = numerical coefficient of x^2 b = numerical coefficient of x c = constant substituting, x = [ -(-1...

algebra 1
recall that the equation of a circle is given by (x-h)^2 + (y-k)^2 = r^2 where h = x-coordinate of center of circle k = y-coordinate of center of circle r = radius thus from the given equation, (x-2)^2 + (y+4)^2 = 9 the radius is sqrt(9) = 3 also, recall that area of circle is...

Math
36x^3 + 53x^2 + 38x + 35

geometry
recall that surface area of rectangular prism is given by SA = 2*(LW + LH + WH) where L = length W = width H = height substituting, SA = 2*[(8)(5) + (8)(2) + (5)(2)] SA = 2*(40 + 16 + 10) SA = 2*(66) SA = 132 in^2 hope this helps~ :)

Geometry
recall that the diagonal of a cube is given by d = sqrt(3*s^2) where s = length of side of cube substituting, d = sqrt(3*6^2) d = sqrt(108) d = 10.39 = 10.4 in hope this helps~ :)

Science
(1) True (2) False

Science
liquids and gases

chemistry
to get the number of He atoms, we dive the given mass to the mass of each He: 1.0 / (6.65 x 10^(-24)) = 1.50376 x 10^23 He atoms hope this helps~ :)

chemistry
first we write the chemical reaction: Al + HCl -> AlCl3 + H2 then we balance it: 2Al + 6HCl -> 2AlCl3 + 3H2 also we need to look for the masses of Al. from the periodic table, Al = 27 g/mol therefore, 54 g Al * (1 mol Al / 27 g Al) * (3 mol H2 / 2 mol Al) = 3 mol H2 or ...

chemistry
recall that molarity is just moles of solute per liter of solution, or M = n / V first we convert the 400 mL to L: 400 mL = 0.4 L substituting, M = 0.4 / 0.4 M = 1 M hope this helps~ :)

More Solutions Chem
first we balance the given chemical equation, thus: 2NaOH + H2SO4 -> Na2SO4 + 2H2O note that we need to balance a chemical equation because we need their stoichiometric coefficients (number before the chemical formula of a compound or element) to make ratios. since we are ...

Chemistry
first let's see if the chemical equation is balanced. Zn + HCl --> ZnCl2 + H2 since not yet balanced, then we balance it :P Zn + 2HCl --> ZnCl2 + H2 since we are given grams of Zinc, we need to find the mass of Zn from periodic table to convert it to moles. thus Zn...

algebra
*reposted* first note that we can't combine radicals if the radicands (term inside a radical sign) are not equal. notice that we can further simplify squareroot of 45 as sqrt(45) = sqrt(3*3*5) = sqrt(3^2 * 5) = 3*sqrt(5) now, we can combine them: 3*sqrt(5) + 4*sqrt(5) 7*...

algebra
first note that we can't combine radicals if the radicands (term inside a radical sign) are not equal. notice that we can further simplify squareroot of 45 as sqrt(45) = sqrt(3*3*5) = sqrt(3^2 * 5) = 3*sqrt(5) now, we can combine them: 3*sqrt(5) + 4*sqrt(5) 7*sqrt(5) hope ...

Chemistry
2C2H6 +7O2 --> 4CO2 + 6H2O since this is already a balanced equation, we can now use their stoich coefficients for the ratios. first, since we need grams of CO2, we find it's molecular mass. from the periodic table, the masses of C and O are C = 12 and O = 16 , thus 1*...

algebra
*reposted* first note that we can't combine radicals if the radicands (term inside a radical sign) are not equal. notice that we can further simplify squareroot of 45 as sqrt(45) = sqrt(3*3*5) = sqrt(3^2 * 5) = 3*sqrt(5) now, we can combine them: 3*sqrt(5) + 4*sqrt(5) 7*...

Algerbra
(x+2)(x+4) = 30 + x first we expand the left side of the equation,, multiplying them, x^2 + 2x + 4x + 8 = 30 + x then we combine similar terms and make the right side of equation equal to zero (since it's quadratic equation) : x^2 + 6x + 8 - 30 - x = 0 x^2 + 5x - 22 = 0 ...

yes. if you're using MS Word, first highlight the text you want to double space, then right click and choose 'Paragraph' . you will see at the bottom right, 'Line Spacing' , and from there choose 'Double'. hope this helps~ :)

math
yes, it's linear equation in 3D. notice that e^2 + ln(2) looks complicated, but it's actually just a constant.

calculus
you're welcome~ :) by the way, i just want to make a correction. fro the value of V and SA, it's not 100, it should be 100*pi = 314.16 . sorry i forgot the pi, because i cancelled it right away, but the answers for r and h is still the same. i'll just retype the ...

calculus
sorry i haven't replied to your reply earlier. anyway, here's an example: there are many possible examples for this. but since we need to calculate volume (V) and surface area (SA), we choose a figure where its V and SA can easily/readily be calculated. for instance we...

calculus
yes :) do you want me to cite an example?

or you can also make it 1 by dividing it by itself : 9-4.2) / (-4.2) = 1

what do you mean "make -4.2 a one" ? is it something like you express -4.2 as sum of two number where one of them is 1 ?

math
distributive property~

algebra
first we represent the unknown using variable, let x = pounds of nuts needed then we set up equation. since we are given the number of pounds of raisins and its price per pound, we'll multiply it to get the total amount of the 12-lb raisins. we do the same for the the nuts...

Math
first we represent unknowns using variables, let x = the number of students asked then we set up the equation,, since the given were the fractional parts of the total number, we represent each part as (1/6)x : the number of students who like math (2/3)x : the number of ...

Math
first we represent unknowns using variables, let x = the number of students asked then we set up the equation,, since the given were the fractional parts of the total number, we represent each part as (1/6)x : the number of students who like math (2/3)x : the number of ...

Algebra
4x + 5x = 180 9x = 180 x = 20 substituting, 4x = 4*20 = 80 degrees 5x = 5*20 = 100 degrees hope this helps~ :)

algebra
9*9*8*7*6*5*4 = 544320 ways

Chemistry: Stoichiometry
first we write the combustion reaction: C6H12O6 + O2 -> H2O + CO2 then we balance it: C6H12O6 + 6O2 -> 6H2O + 6CO2 since mass of glucose is given, we get its molecular weight,, from the periodic table mass of each element in glucose is H = 1 , C = 12 , O = 16 6*12 + 12*1...

Chemistry: Stoichiometry
*i'll just repost my answer~ :) first we write the combustion reaction: C6H12O6 + O2 -> H2O + CO2 then we balance it: C6H12O6 + 6O2 -> 6H2O + 6CO2 since mass of glucose is given, we get its molecular weight,, from the periodic table mass of each element in glucose is...

math
since it's factorable, 2u^2 + 5u - 18 (2u + 9)(u - 2) hope this helps~ :)

math
since it's factorable, 3u^2 - 11u - 14 (3u - 14)(u + 1) hope this helps~ :)

chemistry
to get the heat released or absorbed, Q = mc(T2-T1) where m = mass of substance (units in g) c = specific heat capacity (units in J/g-K) T2 = final temperature T1 = initial temperature *note: units of temp doesn't matter if it's in degree Celsius or Kelvin, as long as ...

physics
oops, scrap my first answer,, i forgot to convert 35 km to meters: 35 km = 35000 m substituting, 51.6 * 10^(-3) = -3.31*( 11.7 - T1 )/(35000) 0.0516*35000/(-3.31) = 11.7 - T1 -545.62 = 11.7 - T1 -557.32 = -T1 T1 = 557.32 deg C sorry~ ^^; hope this helps~ :)

physics
recall that for an energy transfer, q = -kA * dT / dx where q = rate of heat tranfer (in Watts) k = thermal conductivity (in W/m-K) dT = differential change in Temperature (in Celsius or in Kelvin) dx = differential change in position (x-direction) *note: this is negative ...

Geometry
recall that when lengths of diagonals are given instead of base and height of a rhombus, we can still calculate it's area using the formula A = (1/2)*(d1 * d2) where d1 and d2 are lengths of the diagonals. substituting, 1326 = (1/2)*(39 * d2) 2652 = 39 * d2 d2 = 2652 / 39 ...

Geometry
recall that area of triangle is just A = (1/2)(bh) where b = base h = height since we need to find the height, thus the given AC is the base. substituting, 494 = (1/2)(19)*h 988 = 19*h h = 988/19 h = 52 inches hope this helps~ :)

Math
first, we get the volume of each solid. for the cube, recall that volume is just V = s^3 where s = length of a side substituting, V,cube = 2^3 = 8 in^3 for the rect. prism, recall that volume is just V = l*w*h where l = length, w = width, h = height substituitng, V,prism = 8*6...

chemistry
to get the heat released or absorbed, Q = mc(T2-T1) where m = mass of substance (units in g) c = specific heat capacity (units in J/g-K) T2 = final temperature T1 = initial temperature *note: units of temp doesn't matter if it's in degree Celsius or Kelvin, as long as ...

math/115
let n = any real integer. the absolute value of n, or | n | , means you always get its positive value. for example, | 2 | = 2 |-5 | = 5 | 0 | = 0 thus for -|-618| , we first get its absolute value, then multiply by -1 : -|-618| = -(618) = -618 hope this helps~ :)

algebra
let's write the old and new equations: (i) 6x+3y=12 (ii) 6x+3y=36 notice that they have the same slope, thus the new line (ii) is parallel to the original line (i). also , transforming this into slope-intercept form, they become (i) y = -2x + 4 (ii) y = -2x + 12 the y-...

Math
work backwards. first we start with -34. from the second statement, it was said that she doubled it, but since we're working backwards, we divide -34 by 2: -34 / 2 = -17 then subtracted by 12,, thus we add 12 by -17 : -17 + 12 = -5 multiplied by -5,, thus we divide by -5...

chemistry
at STP (standard temperature and pressure: T = 0 deg C , P = 1 atm), one mole of gas occupies a volume 22.4 L . or to you can derive this one using ideal gas law: PV = nRT where P = 1 atm (STP) T = 273.15 K (STP) R = gas constant = 0.0821 L*atm/mol-K n = 1 mol hope this helps~ :)

observe that we can factor xy from (x^2)y + x(y^2): (x^2)y + x(y^2) + x + y = 100: xy [ x + y ] + x + y = 100 then we can factor (x + y): (x + y)(xy + 1) = 100 since xy = 9, (x + y)(9 + 1) = 100 (x + y)(10) = 100 x + y = 10 getting its square, (x + y)^2 = 100 x^2 + 2xy + y^2...

MATH URGENT!!!!!!!!!
both can't be simplified further~

calculus
x-intercept is a point on the curve where it crosses the x-axis, thus y = 0. substituting, y = 2x^3 + 2 0 = 2x^3 + 2 0 = x^3 + 1 0 = (x + 1)(x^2 - x + 1) thus the only real solution is x = -1 ; and the x-intercept is at (-1, 0) for the second question, when the numerical ...

physics
recall pressure is force per unit area, or P = F/A where the force is in Newton (N) , pressure is in Pascal (Pa) and area is in square meters (m^2) thus, we first convert the dimensions to meters: 19 cm = 0.19 m 27 cm = 0.27 m A = 0.19*0.27 = 0.0513 m^2 substituting, 100000 = ...

from the 2nd line, when -35 is transposed to other side, 15r - 35 + r = 3r - 9 15r + r - 3r = 35 - 9 ...it must be positive 35. you forgot to change its sign.

Math
since we don't see the figure, but know that two consecutive angles of a parallelogram is supplementary (sum is equal to 180 degrees), 180 - 70 = 110 degrees (measure of angle F) hope this helps~ :)

chemistry
Fe2O3(s)+3CO(g)--->2Fe(s)+3CO2(g) we see that this chemical equation is already balanced. to get the number of moles of CO, we multiply the given moles of Fe2O3 by the stoichiometric ration from the balanced equation,, thu 1.75 mol Fe2O3 * ( 3 mol CO / 1 mol Fe2O3 ) = 5.25 ...

math
1/4 of 48 means you multiply 1/4 by 48. 1/4 * 48 note that we can rewrite 48 as 48/1 since any number divided by 1 is equal to itself. thus rewriting, 1/4 * 48/1 to multiply fractions, we multiply numerator by numerator and denominator by denominator. (note: numerator-the ...

maths
h t t p : / / w w w . w o l f r a m a l p h a . c o m / i n p u t / ? i = y % 3 D x + a n d + y % 3 D x ^ 2 - 6 x - 1 0 ..without the spaces~ :)

algebra 1
you forgot to multiply 20 by 8: n+8(n+20)=110 must be n+8n+160=110 but you're on the right track~ :)

math
first we represent unknowns using variables,, let x = first number let x+2 = second number note that since they are consecutive but both even numbers, the difference between them is 2, that's why the second number is x+2 now we set-up the equation,, since the sum of the ...

math
first represent unknowns using variables,, let x = first number let x+1 = second number note that the second number is x+1 because they are consecutive numbers. now we set up the equation,, according to problem, their product is 240, thus: x(x+1) = 240 x^2 + x = 240 x^2 + x - ...

math
first we represent the unknowns using variables,, let x = width let 3x-3 = length (according to the first statement) now we set up the equation,, since we are given the area, recall that the area of a rectangle is A = L*W where L=length and W=width. substituting, 90 = (3x - 3...

elementry algebra
since this equation is already in the slope-intercept form, we can readily determine the slope and y-intercept. note that in slope-intercept form , y = mx + b, m is the slope ; and b = y-intercept thus in the given equation, y = 2x + 2 m = 2 ; and b = 2 since y-intercept is a ...

math
for (1), a^2 * b^(-3) note that when a term is raised to a negative exponent, we get its reciprocal and raise it by the positive exponent,, for example, 2^(-4) = 1/(2^4) ; thus we can rewrite b^(-3) = 1/(b^3) therefore, a^2 * (1/(b^3)) a^2 / b^3 for (2), (5/3)^-3 we do the ...

chemistry
assuming the gas is ideal, we can use the formula, P1*V1/T1 = P2*V2/T2 where P1 = initial pressure V1 = initial volume T1 = initial temperature (in K) P2 = final pressure V2 = final volume T2 = final temperature (in K) we first convert the given temp to Kelvin units: T2 = 12...

Calculus
ahh i think i know why y = (a+b)/2 is wrong,, it's actually the MINIMUM, not the maximum~ ^^; i tried assigning some values to the variables,, and from the graph, rate -> infinity at y -> inifinity , or at a finite value of a and b, when the reaction is at completion...

Calculus
for (a) since a < b , for a certain value of y , the value of (a - y) will become negative first, and thus the Rate becomes negative,, then after some time (b - y) will become negative too, and the Rate becomes positive. let's look at some points: at 0 <= y < a , ...

jordan high
umm i think in the problem, you mean "the volume DECREASES",, assuming the gas ideal, we can use the formula P1*V1 = P2*V2 where P1 = initial pressure V1 = initial volume P2 = final pressure V2 = final volume *this equation is Boyle's Law substituting, 0.63 * 324...

calculus
antiderivative = integral to get the integral of this, note that we can rewrite (cos x)^3 as (cos x)(cos x)^2 . then recall that (cos x)^2 = 1 - (sin x)^2 ,, rewriting: integral of [ (cos x)(1 - (sin x)^2) ] dx then we let u = sin x ; and thus du = cos x dx substituting these...

Algebra
x + (1/6)y = 1/2 to transform this into y = mx + b, first we isolate the y term into the left side of equation,, thus the x on the left side must be transposed to the right side. to do this we change the sign of x to its opposite (positive becomes negative): x + (1/6)y = 1/2 (...

hello arun~! i think i also answered this yesterday,, i'll just re-post my solution here. if there's something you didn't understand, feel free to ask. :) first we observe that the motion of the ball is projectile and its trajectory (path followed by the ball) is ...

Math
you mean (7x^2-18x-7)/[(x-4)(2x^2-6x+3)] ? if so, it cannot be further simplified.

algebra
note that you cannot combine radical terms if their radicands (the terms inside the radical sign) are not equal. for example, sqrt(8) + sqrt(18) you cannot add them right away since 8 is not equal to 18,, thus we first simplify each term. for sqrt(8), note that we can rewrite ...

Physics
note that voltage is constant across each resistor. also in parallel circuit, the sum of the currents across each resistor is equal to the total current,, since there are only two resistors in the circuit in the problem, I1 + I2 = I,total substituting, 1 + I2 = 3 I2 = 3-1 = 2 ...

math
recall that speed is distance travelled per unit time, or v = d/t since the given speed is in miles per hour, we first convert the given time (the 12 minutes) to hours: 60 minutes = 1 hour ; thus 12 minutes = 0.2 hour substituting, v = d/t 35 = d/0.2 d = 7 miles hope this ...

physics
recall that I = V/R where I = current (in Amperes) V = voltage (in Volts) R = resistance (in Ohms) substituting, I = 6.7/70 I = 0.0957 A hope this helps~ :)

algebra
let's put parenthesis so that it's not so confusing: (x-1)/(x-9) - (x+1)/(x+9) + (x-153)/(x^2-81) first we get the least common denominator (LCD) of these,, observe that (x-9)*(x+9) = x^2 - 81 . thus the LCD is equal to x^2 - 81 . multiplying all terms by (x^2-81)/(x^2...

Physics
recall that speed is distance traveled per unit time, or v = d/t also recall that work is force exerted times distance, or W = Fd since in the problem we are only given the force, we calculate for the distance first. substituting the given speed and time to formula for speed: ...

Chemistry 1001
note that gases are more soluble in higher pressures, thus CO2 gas will be most soluble in 900 torr. i think the most common example (observation) for this is when you open a carbonated drink,, before it is opened, CO2 gas is dissolved in the liquid. when you open the bottle, ...

Maths
first we represent unknowns using variables,, let x = number of boys let y = number of girls according to first statement, ratio of boys to girls is 3:2 or 3/2 . thus we can write, x/y = 3/2 or x = (3/2)*y according to second statement, there are 11 more boys than girls, thus...

math
first we represent the unknowns using variables: let x = length according to first statement, the width is 1 more than half the length,, thus let (1/2)x + 1 = width now we set up the equation,, since we are only given the area, we can use this to solve for length and width. ...

algebra2
y = 8*(3^x) recall that domain is the set of all possible values of x,, here there is no restriction for x thus the domain is all real numbers. recall that range is the set of all possible values of y,, here note that y cannot be negative since the term 3^x is always positive ...