Friday
May 22, 2015

Posts by Jai


Total # Posts: 1,849

Algebra
4x + 5x = 180 9x = 180 x = 20 substituting, 4x = 4*20 = 80 degrees 5x = 5*20 = 100 degrees hope this helps~ :)
April 14, 2011

algebra
9*9*8*7*6*5*4 = 544320 ways
April 14, 2011

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...
April 14, 2011

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...
April 14, 2011

math
since it's factorable, 2u^2 + 5u - 18 (2u + 9)(u - 2) hope this helps~ :)
April 14, 2011

math
since it's factorable, 3u^2 - 11u - 14 (3u - 14)(u + 1) hope this helps~ :)
April 14, 2011

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 ...
April 14, 2011

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~ :)
April 14, 2011

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 ...
April 14, 2011

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 ...
April 14, 2011

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~ :)
April 14, 2011

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...
April 14, 2011

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 ...
April 14, 2011

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~ :)
April 14, 2011

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-...
April 14, 2011

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...
April 14, 2011

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~ :)
April 13, 2011

8th grade math
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...
April 13, 2011

MATH URGENT!!!!!!!!!
both can't be simplified further~
April 12, 2011

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 ...
April 12, 2011

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 = ...
April 12, 2011

grade nine math
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.
April 12, 2011

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~ :)
April 12, 2011

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 ...
April 11, 2011

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 ...
April 11, 2011

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~ :)
April 11, 2011

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~ :)
April 11, 2011

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 ...
April 10, 2011

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 - ...
April 10, 2011

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...
April 10, 2011

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 ...
April 10, 2011

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 ...
April 10, 2011

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...
April 10, 2011

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...
April 10, 2011

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 , ...
April 10, 2011

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...
April 10, 2011

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...
April 9, 2011

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 (...
April 9, 2011

maths(urgent....please...)
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 ...
April 9, 2011

Math
you mean (7x^2-18x-7)/[(x-4)(2x^2-6x+3)] ? if so, it cannot be further simplified.
April 9, 2011

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 ...
April 9, 2011

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 ...
April 9, 2011

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 ...
April 8, 2011

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~ :)
April 8, 2011

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...
April 8, 2011

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: ...
April 8, 2011

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, ...
April 8, 2011

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...
April 8, 2011

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. ...
April 8, 2011

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 ...
April 8, 2011

math
y = x^2 + 2x - 15 y = (x - 3)(x + 5)
April 8, 2011

chemistry
assuming the gas is ideal, we can use the formula, V1/T1 = V2/T2 where V1 = initial volume T1 = initial temperature (in K) V2 = final volume T2 = final temperature (in K) we first convert the given temp to Kelvin units: T1 = 7 + 273.15 = 280.15 K T2 = 15 + 273.15 = 288.15 K ...
April 8, 2011

Math!!!!!!HELP!!! :(
kilogram is a unit of mass while gallon is a unit of volume. you can relate them by using density of a particular substance (density is mass per unit volume or d = m/V) for example, if we consider water, which has a density of 1 g/mL or 1 kg/L, and recalling that 1 gallon is 3...
April 8, 2011

math
do you mean how many hours will it take for the feeder to give all of the food he/she is holding? if so, then we first convert 3 kg to grams: 1 kg = 1000 g ; thus 3 kg = 3000 g now we divide 3000 by 150 to get the time needed: 3000 / 150 = 20 hours hope this helps~ :)
April 8, 2011

math
recall that speed is distance travelled per unit time, or v = d/t since they are travelling towards each other, we add their speeds (since travelling towards each other consumes less time for them to meet than travelling in the same direction) substituting, v = d/t 610 + 618...
April 8, 2011

MATH VERY URGENT!!!!!!
first we observe that the motion of the ball is projectile and its trajectory (path followed by the ball) is shaped like a parabola. the horizontal distance travelled by the ball is thus given by: R = (vo)^2 * sin (2*theta) / g where R = range or the horizontal distance vo = ...
April 8, 2011

science
to get the heat released or absorbed, Q = mc(T2-T1) where m = mass of substance c = specific heat capacity T2 = final temperature T1 = initial temperature **note: if Q is (-), heat is released and if (+), heat is absorbed now we can only apply this to substances that did not ...
April 8, 2011

MATH URGENT!!!!
for (a), we substitute 17 to d in the equation for the height,h: h = -0.045d^2 + 2d h = -0.045*(17^2) + 2(17) h = 20.995 yards for (b), we are given the height and we need to find the horizontal distance. substituting, h = -0.045d^2 + 2d 8 = -0.045d^2 + 2d 0 = -0.045d^2 + 2d...
April 8, 2011

calculus
observe that we can further simplify (|x+h|-|x|)/h to (x + h - x)/h (h)/h 1 rewriting, lim 1 as h->0 at x = 4 is equal to 1, since the limit of a constant is also equal to that constant. hope this helps~ :)
April 8, 2011

Physical Science
to get the heat released or absorbed, Q = mc(T2-T1) where m = mass of substance c = specific heat capacity T2 = final temperature T1 = initial temperature **note: if Q is (-), heat is released and if (+), heat is absorbed now we can only apply this to substances that did not ...
April 8, 2011

chemistry
assuming that the gas is ideal, we use the formula for ideal gases: PV = nRT where P = pressure (in atm) V = volume (in L) n = number of moles R = gas constant (0.0821 L*atm/mol-K) T = temperature (in Kelvin) we first convert the 26 degrees Celsius to Kelvin: 26 + 273.15 = 299...
April 8, 2011

geometry
since the lengths of sides of the flag are equal, the shape of the flag is a square. recall that the area of square is A = s*s where s = length of a side of square. substituting, A = 60*60 A = 3600 square cm hope this helps~ :)
April 8, 2011

chemistry
assuming that the gas is ideal, we use the formula for ideal gases: PV = nRT where P = pressure (in atm) V = volume (in L) n = number of moles R = gas constant (0.0821 L*atm/mol-K) T = temperature (in Kelvin) we first convert the 26 degrees Celsius to Kelvin: 26 + 273.15 = 299...
April 8, 2011

MATH URGENT!
first we observe that the motion of the ball is uniformly accelerated motion (because of acceleration due to gravity while it's in the air), thus we use this formula to find time: h = ho + vo*t - (1/2)*g*t^2 where ho = initial height vo = initial velocity t = time g = ...
April 7, 2011

geometry
recall that area of trapezoid is A = (b1 + b2)*(h/2) where b1 and b2 are the bases of trapezoid h is the height substituting, 4 = (b1 + b2) * (1/2) 8 = b1 + b2 now we list two number whose sum is 8: 1 and 7 2 and 6 3 and 5 4 and 4 these are the possible lengths of bases. hope ...
April 7, 2011

Math
hmm,, recall that when we consider a parallelogram, we also consider square, rhombus, and rectangle (they are all parallelogram) now, let's analyze each choices: for (a), it's only true for a square. for (b), it's true for square and rectangle. for (c), it's ...
April 7, 2011

algebra
do you mean, 13/18 divided by 20/27 ? if so, then we first get the reciprocal of the divisor (the second term; that is, 20/27) ,, thus its reciprocal is 27/20 (note that reciprocal is just interchanging the numerator and denominator) now the process becomes multiplication. to ...
April 7, 2011

geometry
first represent unknowns using variables: let x = length of rectangle let x-6 = width of rectangle (according to first statement of problem) now we set up equation,, since in the problem we are given the perimeter, we can use this to set up the equation,, recall that perimeter...
April 7, 2011

math
triple 4 means 3 times 4: 3 x 4 = 12 since we subtract 2 from 12 each day , we need to divide 12 by 2 to get the number of days needed to reach zero: 12 / 2 = 6 days hope this helps~ :)
April 6, 2011

Math 8th Grade
there are many possible answers here. one answer could be the length of longer = 14 m and shorter = 9 m it can also be longer = 18 m and shorter = 7 m .. i think you forgot an information in the problem,..
April 6, 2011

Algebra
yes
April 5, 2011

Pre Algebra
x: 0 1 2 3 y: 5 4 3 2 to get the function, we choose two points. let's just choose the first two points,, that is, point1 (0,5) and point2 (1,4) now, we get first the slope. the slope is given by the equation, slope = m = (y2 - y1)/(x2 - x1) where y1 = y-coordinate of ...
April 5, 2011

Geometry
first, we represent the unknowns using variables: let x = number of 5-dollar bill since according to first statement, he has a total of 124 bills in 5 and 10, let 124 - x = number of 10-dollar bill now we set up the equation,, according to the second statement, the total value...
April 5, 2011

chem
first write the chemical equation: HCl + NaHCO3 -> NaCl + H2O + CO2 observe that it's already balanced. :) now we get the molar mass of NaHCO3 (sodium bicarbonate) and HCl (hydrochloric acid),, i expect you already know how to find molar masses. NaHCO3 : 23 + 1 + 12 + 3...
April 5, 2011

chemistry
recall that density is mass per unit volume, or d = m/V substituting, d = 100/200 d = 0.5 g/mL hope this helps~ :)
April 5, 2011

chemistry
recall that 1 mole = 6.022 x 10^23 atoms thus, 0.32 * (6.022 x 10^22) = 1.927 x 10^23 atoms hope this helps~ :)
April 5, 2011

math
always remember E.M.D.A.S. = Exponents, Multiplication, Division, Addition, Subtraction. this the order of which operation must be done first. here, of course we start with the operation inside the parenthesis: 5+(3x3-3)/2 5 + (9-3)/2 5 + 6/2 5 + 3 8 hope this helps~ :)
April 5, 2011

math
it means you will multiply 4/5 by 25,, thus 4/5 * 25 note that we can rewrite 25 as 25/1 (since any number divided by 1 is equal to itself),, rewriting, 4/5 * 25/1 to multiply fractions, we multiply numerator by numerator and denominator by denominator. note: numerator is the ...
April 5, 2011

Chemistry
Single Replacement Reaction~
April 4, 2011

math
note that a reflex angle is an angle greater than 180 degrees bu less than 360 degrees,, first, since the digits are factors of 8, we list all factors of 8: 1, 2, 4, 8 since the digits are even and are different, the digits of the reflex angle we're looking for are 2, 4 ...
April 4, 2011

Math
to do this, first we know that there are 18 ways for the first place (since there are 18 dogs), then 17 ways for the second place (18-1=17 since no dog can win two places), and 16 ways for the third. thus, we multiply these to get the number of ways: 18*17*16 = 4896 ways hope ...
April 4, 2011

Math
to do this, first we multiply the 1st terms or the number with no exponent (not the terms with 10 raised to an exponent). thus: 4.3*2 = 8.6 now we multiply the 2nd terms,, recall that if they have the same base (here, the base is 10) we can simply add the exponents: 10^3 * 10...
April 4, 2011

Math
to get the total weight, we multiply them: 2x10^(-5) * 1x10^15 to do this, first we multiply the first terms or the terms with no raised exponent,, thus that would be the 2 and 1: 2 * 1 = 2 next we multiply the second terms or the 10 raised to exponent,, to do this, recall ...
April 4, 2011

Geometry
to do this, we calculate both of the circles' circumference. the bigger circle has diameter of 26 in, while the smaller has diameter of 18 in. now recall that the circumference of a circle is given by C = 2*π*r or given the diameter, C = π*d where π = ...
April 4, 2011

math
when an object is dropped from a certain height, it is a freefall. when in freefall, the only external force acting on the body is gravitational force (neglecting air resistance). the motion of the object is unformly accelerated motion: (v2)^2 - (v1)^2 = 2*g*h where v2 = final...
April 4, 2011

math2
first, we list the factors of each number,, 15: 1, 3, 5, 15 34: 1, 2, 17, 34 55: 1, 5, 11, 55 since the only common factor among them is 1, the greatest common factor (GCF) of the numbers is 1. hope this helps~ :)
April 3, 2011

math
first, we convert 9 Liters to milliliter,, recall that 1 L = 1000 mL, thus 9 L = 9000 mL now we divide 9000 by 90 to determine how many 90 mL-bottle she needs: 9000 / 90 = 100 bottles hope this helps~ :)
April 3, 2011

chemistry
you need a periodic table of elements. in the periodic table, you can find certain properties of elements and and also atomic number and atomic mass. since in the problem, we are required to calculate for molar mass of H2O, you look for H and O in the periodic table and get ...
April 1, 2011

Chemistry
first write the balanced chemical equation: C3H8 + 5O2 -> 3CO2 + 4H2O **note: in combustion reaction of organic compounds, the usual products are carbon dioxide and water. then calculate for molecular weight of propane (the C3H8),, Carbon is 12 while H is 1: 3*12 + 8*1 = 44...
April 1, 2011

physics urgent please
an example of projectile motion would be the motion of the baseball when it is hit by the bat,, it the trajectory (the path followed by the object) has the shape like a parabola. projectile motion is possible because of gravity. about the velocity, since it followed a path ...
March 31, 2011

algebra
domain is the set of all possible values of x, while range is the set of all possible values of y. for example, y = x^2 since any values of x can be substituted here, we say that the domain is all real numbers (zero, positive and negative numbers -- any number actually ) while...
March 31, 2011

math
x squared is usually typed like this: x^2 (means x raised to two) :) anyways, the given in y = x^2 - 6x - 8 and we need to find x when y = 1. thus we substitute y into the equation: y = x^2 - 6x - 8 1 = x^2 - 6x - 8 now to solve for x,, first we make one side of the equation ...
March 31, 2011

Math
we can also rewrite this (a+b)squared=64 as (a+b)^2 = 64 first we expand (a+b)^2 (a+b)^2 = 64 (a+b)(a+b) = 64 a^2 + 2ab + b^2 = 64 since we are given the value of ab, which is ab = 3, we can substitute it here: a^2 + 2(3) + b^2 = 64 a^2 + 6 + b^2 = 64 a^2 + b^2 = 64 - 6 a^2 + ...
March 31, 2011

math
that 'n' is actually the Greek letter π which is equal to 3.1416... but since in the problem π = 22/7 , we use this value. recall that the area of a circle is given by A = π*r^2 where r = radius substituting, A = π*(7^2) A = (22/7)(49) A = 22*7 A = ...
March 31, 2011

Algebra
since it's 30 by 30, the shape is a square. recall that the diagonal of a square is given by: diagonal = sqrt(s) where s = length of a side thus, the diagonal is sqrt(30) hope this helps~ :)
March 31, 2011

math
if the given sequence is a geometric sequence, then it follows the formula A,n+1 = r*(A,n) where r = ratio between two consecutive terms A,n = the nth term A,n+1 = the term after A,n substituting the first and second term, 40 = r*16 r = 40/16 r = 2.5 to check, let's see if...
March 31, 2011

physics
recall that pressure is force per unit area or P = F/A first of all, we convert 10 cm^2 to m^2 for consistency of units (since the unit Newton is actually kg*m/s^2),, therefore 10 cm^2 (1 m / 100 cm)^2 = 0.001 m^2 substituting, P = 180/0.001 P = 180000 kg/(m*s^2) = 180000 Pa (...
March 31, 2011

math
(fog)(x) = f(g(x)) = [g(x)]^2 (fog)(x) = [sqrt(x-3)]^2 note that the sqrt and ^2 will just cancel each other out: (fog)(x) = x - 3 to find its domain,, recall that domain is the set of all possible values of x,, since we both considered f(x) and g(x) here, we find the ...
March 31, 2011

math
(gof)(x) means you substitute the whole expression of f(x) to g(x): (gof)(x) = g(f(x)) = f(x) + 1 (gof)(x) = x + 1 for #2, we do the same,, we substitute f(x) to f(x): (fof)(x) = f(x) (fof)(x) = x hope this helps~ :)
March 31, 2011

math
first we can actually substitute f(x) by y, thus f(x) = 3 - 5x y = 3 - 5x to get the inverse, interchange the x and y variables,, thus x = 3 - 5y now, we solve for y: x = 3 - 5y x - 3 = -5y y = -(x-3)/5 then we substitute back f(x) to y, but this time since we get its inverse...
March 31, 2011

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