# Posts by Jai

Total # Posts: 1,998

Geometry -need help
recall that the surface area of cylinder is given by SA = 2πr^2 + 2πrh where r = radius h = height π = "pi" equal to 3.14 (constant) substituting, SA = 2*(3.14)*3^2 + 2*(3.14)*3*9 SA = 226.08 in^2 then we divide this by his speed, 40 in^2/5 min: 226.08...

math
we need to divide both sides of the equation by 0.8 to get T alone: 0.8T = 24 0.8T / 0.8 = 24 / 0.8 T = 30

algebra
note that this equation is already in the slope-intercept from: y = mx + b , where m is the slope and b is the y-intercept. thus in the given, y = 2x + 6 the slope is 2. hope this helps~ :)

algebra
6y -6 < 5y - 3 6y - 5y < -3 + 6 y < 3 hope this helps~ :)

algebra
7+3x < 19 we just solve it like a normal equation (not an equality). 7 + 3x < 19 3x < 19 - 7 3x < 12 x < 4 hope this helps~ :)

algebra
5 - 9y - 2y < 27 we just solve it like a normal equation. 5 - 11y < 27 -11y < 27 - 5 -11y < 22 y > -2 note that when dividing both sides by a negative number, the inequality sign becomes its opposite. like here, both sides are divided by -11, and thus the sign ...

maths
first convert the time given in hours. 2 hours & 30 min = 2.5 hours then recall that speed is just distance traveled over time, or v = d/t substituting, v = 220/2.5 v = 88 km/hr hope this helps~ :)

math
x-intercept occurs at y=0. thus we substitute it to the given equation, y = x^2 + 4x - 12 0 = x^2 + 4x - 12 0 = (x-2)(x+6) x = 2 and x = -6 at these values of x, y is zero. thus the x-intercepts are (2,0) and (-6,0) hope this helps~ :)

Pre-algebra
8(4s-7) < 6(2s+4) 32s - 56 < 12s + 24 20s < 80 s < 4 hope this helps~ :)

Pre-algebra
-5(3e-2)<-2(6e+7) -15e + 10 < -12e - 14 -3e < -24 e > 8 *note that when dividing both sides of the equation by negative number, the sign changes to its opposite. like here, both sides were divided by -3 and the sign changes from < to >. hope this helps~ :)

Pre-algebra
-3(2b+4)>4(b+7) -6b - 12 > 4b + 28 -10b > 40 b < -4 *note that when dividing both sides of the equation by negative number, the sign changes to its opposite. like here, both sides were divided by -10 and the sign changes from > to <. hope this helps~ :)

Pre-algebra
48>3(w+7) 48 > 3w + 21 27 > 3w 9 > w or w < 9 hope this helps~ :)

Pre-algebra
-12(c-6)<120 -12c + 72 < 120 -12c < 48 c > -4 *note that when dividing both sides of the equation by negative number, the sign changes to its opposite. like here, both sides were divided by -12 and the sign changes from < to >. hope this helps~ :)

Pre-algebra
7(v+5)>56 7v + 35 > 56 7v > 21 v > 3 hope this helps~ :)

Math
but we need the figure to solve for this.

Math
you can answer this in two ways~ systematic way (lol): let x = units digit let y = tens digit from the second statement, (1) xy = 14 from the first statement, (2) 10x + y = 3(10y + x) - 9 from equation (1), we can express y in terms of x, yielding y = 14/x substituting this to...

Math
2x^2 + 7x -15 =0 (2x - 3)(x + 5) = 0 therefore, x = 3/2 and x = -5 hope this helps~ :)

physics
just imagine when you dribble. you use force (directed downward) from your hand to "throw" it downwards.

algebra
numerical coefficients : 2, 4, 8

algebra
(-8x^2-2x+4)+(x^2-9x+7) to add, we just combine the numerical coefficients (or the numbers before the variable) of the same variables (meaning same letters and same exponents). thus, (-8x^2 - 2x + 4 ) + ( x^2 - 9x + 7 ) -7x^2 - 11x + 11 hope this helps~ :)

chemistry
(1) assuming the gas is ideal, the volume becomes 1/3 of the original. (2) recall that STP, pressure is at 1 atm. assuming the gas is ideal, P1*V1 = P2*V2 where P1 = initial pressure V1 = initial volume P2 = final pressure V2 = final volume substituting, 1*2000 = (P2)*15 P2 = ...

math
i think you mean 3k^2 + 6k = 6 thus, we can re write this as 3k^2 + 6k - 6 = 0 note that we can factor out 3 from each term and cancel it. thus we can re write this as k^2 + 2k - 2 = 0 using quadratic formula, k = [-b +- sqrt(b^2 - 4ac)]/(2a) substituting, k = [-2 +- sqrt(2^2...

algebra2
to do this, we just multiply the exponents. [x^9]^11/7 x^(9*11/7) x^(99/7) hope this helps~ :)

Maths
|| means they are parallel. since AB and CD are parallel, they will never meet.. thus i think the first statement is wrong that they meet at point E.

Algebra
(q-2)/4 * -2q/(q+5) to multiply, we just multiply numerator by numerator and denominator by denominator. thus, this becomes: (q-2)(-2q) / (4)(q+5) observe that we can factor 2 from numerator and denominator and cancel it, and this becomes: -q(q-2) / (2)(q+5) hope this helps~ :)

science
recall that current is voltage per resistance, or I = V/R *units of current in Amperes (A) *units of voltage in Volts (V) *units of resistance in ohms (Ω) substituting, 8 = 1.1/R R = 1.1/8 = 0.1375 Ω hope this helps~ :)

chemistry
first thing to do here is to balance the chemical equation. 2Na + Cl2 --> 2NaCl then we get the masses of Sodium and Chlorine from periodic table of elements in order to calculate the molar mass of NaCl. from periodic table, Na = 23 Cl = 35.5 thus, NaCl = 23+35.5 = 58.5 g/...

*reposted -- because i think you haven't read my previous post in this problem* first, we solve for the initial velocity from the formula of the maximum height: h,max = [(vo)^2]/(2g) where vo = initial velocity g = acceleration due to gravity = 9.8 m/s^2 substituting, 30...

geometry
note that complement means the other angle in which their sum should be 90. thus to get the complement of each angle, we just subtract them from 90: 90 - 44 = 46 90 - 15 = 75 90 - 72 = 18 90 - 89 = 1 90 - 10 = 80 90 - 30 = 60 hope this helps~ :)

math
we'll solve this in two cases: Case I: absolute value is positive. |n+1| < 4 n+1 < 4 n < 3 Case II: absolute value is negative. |n+1| < 4 -(n+1) < 4 n+1 > -4 n > -5 getting the intersection (common between them) of the two answers, thus n must be ...

Algebra
the formula is wrong. it should be y = a(x-h)^2 + k where (h,k) is the center then to solve for a, you choose one of the points to substitute for the value of x and y. for instance you choose (-4,-1): y = a(x-h)^2 + k -1 = a(-4+3)^2 - 2 then solve for a. if you want to make ...

Algebra
yes~ :)

Algebra
yes, you're right. :)

Algebra-right question for Jai
the volume of a triangular prism is given by V = (1/2)*(B*H*L) where B = base H = height L = length thus the new volume becomes, V' = (1/2)*(2*B)(2*H)*L V' = 2*(1/2)*(B*H*L) or V' = 2*V thus the new volume is twice the original. note that first statement is tricky...

Algebra- word problem
sure~ :)

Algebra- word problem
original area: A = L*W A = 6*3 = 18 in^2 new area: A' = L'*W' A' = 8*5 = 40 in^2 the difference between these areas is the amount of wall space needed: 40-18 = 22 in^2 thus it's A. hope this helps~ :)

algebra
recall that the volume of a rectangular prism is given by V = L*W*H where L = lenght W = width H = height. if 4 is multiplied to both length and width, the new volume, V', is V' = (4L)*(4W)*(H) V' = 16*(L*W*H) or V' = 16*V thus the new volume is 16 times ...

algebra
oh, i see.. the choices are wrong. i guess you typed it wrong because "volume" is in the choices.. it must be "area" since it is the required. (and rectangles don't have volume)

algebra
original area: A = L*W new area: A' = (3L)*(3W) A' = 9*(L*W) or A' = 9*A thus there is no correct answer in the choices, since the new area is 9 times greater than the original. hope this helps~ :)

algebra
yes~ :) original area: A = L*W new area: A' = (3L)*(3W) A' = 9*(L*W) or A' = 9*A thus there is no correct answer in the choices, since the new area is 9 times greater than the original. hope this helps~ :)

Math
(a) to get this, we just use ratio and proportion: let x = weight of 150 books. 108 books : 30 kg = 150 books : x kg we can thus rewrite this as 108/30 = 150/x 3.6 = 150/x x = 150/3.6 x = 41.67 kg (b) we also use ratio and proportion here: let y = number of books that has ...

physics
recall that the volume of a sphere (geometry of the ball) is given by V = (4/3)πr^3 where r = radius π = 3.14 (constant) thus to get radius, we need to first get the volume from the given mass and density. recall that density is just mass per volume, or d = m/V ...

Math
#1 to get this, we just use ratio and proportion. let x = weight of 1000 cm^3 liquid. 250 cm^3 : 125 g = 1000 cm^3 : x g thus we can rewrite this as, 250/125 = 1000/x solving for x, 2 = 1000/x 2x = 1000 x = 500 grams #2 here, we also use ratio and proportion. first we convert ...

algebra
to get this, you just substitute t=6 to the given equation: v = (-1/2)t + 3 v = (-1/2)*6 + 3 v = -3 + 3 v = 0 plot: h t t p : / / w w w 4 c . w o l f r a m a l p h a . c o m / Calculate/MSP/MSP412219fd25cdf0efbh880000587daeb9i9ea74bg?MSPStoreType=image/gif&s=11&w=424&h=166&cdf...

math
first, we solve for the initial velocity from the formula of the maximum height: h,max = [(vo)^2]/(2g) where vo = initial velocity g = acceleration due to gravity = 9.8 m/s^2 substituting, 30 = [(vo)^2]/(2*9.8) vo = sqrt(588) vo = 24.25 m/s (a) note that the motion of the ...

algebra
*reposted* 9t^4 + 7t - 45 t^3 + 10t note that when combining terms with variables, we just add the numerical coefficient of the same variable (and exponent). here, we can only combine 7t and 10t. thus 9t^4 + 7t - 45 t^3 + 10t 9t^4 + 17t - 45 t^3 rearranging, 9t^4 - 45 t^3 + ...

algebra
*reposted* 9t^4 + 7t - 45 t^3 + 10t note that when combining terms with variables, we just add the numerical coefficient of the same variable (and exponent). here, we can only combine 7t and 10t. thus 9t^4 + 7t - 45 t^3 + 10t 9t^4 + 17t - 45 t^3 rearranging, 9t^4 - 45 t^3 + ...

math
sin 90 = 1 hope this helps~ :)

math
sin 90 = 1 hope this helps~ :)

algebra
9t^4 + 7t - 45 t^3 + 10t note that when combining terms with variables, we just add the numerical coefficient of the same variable (and exponent). here, we can only combine 7t and 10t. thus 9t^4 + 7t - 45 t^3 + 10t 9t^4 + 17t - 45 t^3 rearranging, 9t^4 - 45 t^3 + 17t hope this...

Math
first observe that you are 24 years older than your son. also, since we are required of the ages, we represent these unknown ages using variables: let x = your son's age let x+24 = your age note that when your son's age is x years, you are three times as old. therefore...

Applied Physics
equilibrium means that all forces acting on the object are balanced / cancel each other out. it can also mean that the object is not accelerating. thus, an object can be in equilibrium whether it is motion or not, as long as forces are balanced. since it's said that it ...

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: if Q is (-), heat is released and if (+), heat is absorbed now we can only apply ...

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: if Q is (-), heat is released and if (+), heat is absorbed for water c = 4.184 J/g-K...

Math
X(bar) = 10,000 M = 1,000 D = 500 C = 100 L = 50 X = 10 I = 1 thus XMMDCLXII is equal to 12,662 hope this helps~ :)

mensuration
recall that the area of rectangle is given by A = L*W where L is length and W is width. substituting, A = 20*12 = 240 m^2 (we'll use this later) since there is 2 m wide path, (and thus there is total of 4 m on both sides), 20 - 4 = 16 m 12 - 4 = 8 m getting the area of ...

physics
hello~ you can find answers on google. just type "why candle flame up" , there are links discussing this topic. i can't post links here that's why~ ^^;

Math- college
to get this, we just use ratio and proportion: let x = miles travelled with 24 gallons 22 miles : 1 gallon = x miles : 24 gallons therefore, 22/1 = x/24 x = 22*24 x = 528 miles hope this helps~ :)

Math- college
(a) to get this, we just divide 1148 by 13. type this in you calculator: 1148 / 13 the answer must be 88.308. since the number of bags can not be decimal, we only take the whole number, which 88 sand bags. (b) to get this, we multiply the number of bags used (which is 88) by ...

Math
first let's represent their weights using variables: let C = weight of one piece of cake let A = weight of one apple let H = weight of one cherry from the first statement, (1) 2C = A + H for the second statement, (2) A = 5H + C now we need to find how mach does cherries ...

Algebra 8th
do you mean "square root" for the "radical"? if so, 2[sqrt(8) + sqrt(5)] note that we cannot combine the radical terms since their radicands (term inside the radical sign) are not equal. but we can rewrite this as 2[2*sqrt(2) + sqrt(5)] 4*sqrt(2) + 2*sqrt(5...

Calculus
recall that the derivative of cos^-1 (x) or arccos (x) is -1/[sqrt(1-x^2)] * dx thus the derivative of cos^-1 (x^2) -(2x)/[sqrt(1 - x^4)] note that the 2x is the dx that came from the derivatice of the term inside the cos^-1, which is x^2. hope this helps~ :)

Math
to convert PERCENT to DECIMAL, we move 2 decimal places to the LEFT. thus for 0.06%, we move 2 decimal places, and it becomes: 0.0006 now we know the decimal, we can convert this to fraction. first we count the places to the right of decimal point. there are 4 decimal places (...

Geometry
recall that length of arc is given by s = r*theta where r = radius theta = angle in radians first we convert the given angle to radians: 20 * pi/180 = pi/9 = 0.349 rad substituting, s = 1*0.349 s = 0.349 s = 0.35 (nearest hundredth) hope this helps~ :)

physics
(a) the motion of the book is projectile, and uniformly accelerated motion. thus we use the formula, h = ho + vo*t - (1/2)*g*t^2 where h = final height ho = initial height vo,y = initial vertical velocity = vo*sin(theta) t = time g = acceleration due to gravity (9.8 m/s^2) ...

physics
..what do you want to solve?

math
note that 36/9 is also equal to 4. thus we look for fractions that is also equal to 4. the denominator of 4 is 1 (any number divided by 1 is itself). thus we only multiply the numerator and denominator by the same number to get an equivalent fraction. for instance, let's ...

math
do you mean x^(2-n) ? if so at x = 8, 8^(2-n) = 0 , we can rewrite this as (8^2)/(8^n) = 0 64/8^n = 0 note that this equation has no solution and only at n-> infinity, it will approach zero. also at x=-8, it has no solution. hope this helps~ :)

science
in physics, note that mass is different from weight. mass has units in kilograms, grams, etc., while weight has units of Newton. (Newton = kg*m/s^2) to determine weight, we use the formula W = m*g where m = mass (in kg) g = acceleration due to gravity = 9.8 m/s^2 substituting...

* means multiply or times / means divided by to solve, input this on your calculator: 77.18 x 9.81 x 5.83 / 4.37

geometry: volume of cone
recall that volume of cone is given by V = pi*(r^2)*h/3 where pi = 3.14 (constant) r = radius h = height if r becomes (1/2)r, V,new = pi*[(1/2)r]^2*h/3 V,new = 1/4[pi*(r^2)*h/3] V,new = (1/4)V thus multiplied by 1/4. hope this helps~ :)

math!!!!
you use the distance formula: d = sqrt[ (x2 - x1)^2 + (y2 - y1)^2 ] where (x1,y1) = first point (x2,y2) = second point hope this helps~ :)

math
for the first question, we just use ratio and proportion. let x = time it takes to travel 3 miles. 0.75 mi : 0.25 min = 3 mi : x min therefore, writing in fraction, 0.75/0.25 = 3/x cross-multiplying, 0.75x = 0.25*3 0.75x = 0.75 x = 1 minute for the second, we also use ratio ...

math
it's positive~ example for (+) answer: 7 - 3 = 4 **3 (the lesser integer) is being subtracted from 7 (greater integer) other examples, -3 - (-8) = 5 0 - (-2) = 2 2 - (-1) = 3 hope this helps~ :)

math
note that the next term has a numerator 3 greater than the previous and has denominator 4 greater than the previous. thus, if 4/3 is the first term, (4 + 3(n-1))/(3 + 4(n-1)) where n = nth term (if 1st, n=1, if 2nd, n=2, etc.) or simplifying, (3n + 1)/(4n - 1) hope this helps~ :)

Math
x = -1/4 - 5/8 first, we convert 1/4 to a fraction whose denominator is 8, so that we can combine the fractions. we can do this by multiplying both numerator and denominator by 2: 1*2 / 4*2 = 2/8 therefore, x = -(2/8) - 5/8 then we simply add the numerator and copy the ...

trig
(1/m)= (m-34)/(2m^2) we cross-multiply: 2m^2 = m(m-34) 2m^2 = m^2 - 34m m^2 + 34m = 0 m(m+34) = 0 m = 0 and m = -34 but note that m = 0 is extraneous since when substituted back to original, 1/0 = (0-34)/(2*0^2) and any number divided by zero is undefined. thus x = -34 only. ...

math
(1) -4 + 7log(x) = 10 7log(x) = 14 log(x) = 2 x = 10^2 = 100 (2) log(x+3) + log(x-2) = log 14 recall some laws of exponents. when we add two log terms with same base, we can combine them by multiplying the terms inside the log. thus, we can rewrite this as, log[(x+3)(x-2)] = ...

Algebra
yes, you got the right answer for simplifying it. 2/(x^2-16) + 3/(x^2 -2x-8) = 5x+16/(x-4)(x+4)(x+2) but the question says that if numerator is equal to 6, what is x? thus we equate the numerator to 6: 5x + 16 = 6 5x = 6-16 5x = -10 x = -2 hope this helps~ :)

math
yes~ :)

Quick Question
25s + 25 = -15s first, we transpose all terms containing the variable s to one side of the equation (in this problem, let's transpose them to the left side), and all other terms to the other side. thus, we transpose -15s to the left side. to transpose, we change its sign ...

Math
it's (x^11)*sqrt(x), because sqrt(x^23) sqrt(x*x^22) sqrt( x * (x^11)^2 ) then sqrt of (x^11)^2 is x^11, so we can take it out: x^11 * sqrt(x) hope this helps~ :)

precalc
domain = set of all possible values of x range = set of all possible values of y therefore, (1) y = sqrt(x-3) note that the term inside the sqrt can be zero but cannot be negative, for it will become imaginary. thus, Domain: x must be greater than or equal to 3. also, y can be...

physics
the energy needed to increase or decrease the temperature of a given substance is given by Q = mc(T2-T1) where Q = heat (in J or cal) m = mass (in g) c = specific heat capacity (in J/g*K or cal/g*K) T = temperature (in Kelvin) **change in temperature can have unit degree ...

Math
first, we factor the radicand (the term inside the radical sign or the squreroot): sqrt(27*b^11) sqrt[ (3*3*3) (b*b^10) ] then we separate the perfect squares: sqrt[ 3*(3^2) b*((b^5)^2) ] and we take the squarerrot of the perfect squres. the squareroot of 3^2 is 3, while (b^5...

MAth
they are the reciprocal of each other. *reciprocal = when you interchange the value of numerator and denominator hope this helps~ :)

algebra
substituting, A = (1/2)bh A = (1/2)(30)(30) A = 450 m^2 hope this helps~ :)

IPC
there was a typo. from the first paragraph, ...this only means that when two objects are in thermal equilibrium (or their temperature is the same/equal), NO heat is being transferred... and the rest is ok. :)

IPC
Zeroth Law of Thermodynamics = two objects in thermal equilibruim will have no net heat flow between them. **this only means that when two objects are in thermal equilibrium (or their temperature is the same/equal), heat is being transferred. this is a consequence of the ...

geometry
recall that the general equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2 where the point (h,k) is the center of the circle, and r is the radius. thus in the given equation, (x + 4)^2 + (y – 9)^2 = 18 18 = r^2 therefore, r = sqrt(18) = 3*sqrt(2) and so the ...

IPC
the energy needed to increase or decrease the temperature of a given substance is given by Q = mc(T2-T1) where Q = heat (in J or cal) m = mass (in g) c = specific heat capacity (in J/g*K or cal/g*K) T = temperature (in Kelvin) **change in temperature can have unit degree ...

math
thousands

math
to round off, first you need to know the place of the digit you want to round off,, in the problem it's "to the nearest ten". then we look at the number to the right of tens digit if the number to the right of tens digit is: *greater than or equal to 5, you add 1...

algebra1
..then?

Chem5
recall that density is mass over volume, or d = m/V substituting, 1 = m / 4200 m = 4200 g H2O to get the mass of dioxin, we just multiply its percent mass: 4200 * 0.00052 = 2.184 g dioxin hope this helps~ :)

physical science
assuming the gas is ideal, we can use Charles' Law: V1/T1 = V2/T2 where V1 = initial volume V2 = final volume T1 = initial temperature (in Kelvin) T2 = final temperature (in Kelvin) we first convert the given temp to Kelvin: T1 = 30 + 273.15 = 303.15 K substituting, V1/T1...

calculus
yes. the substitution is correct: let u = x^(1/2) thus du = 1/[2(x^(1/2))] dx, or dx = 2(x^(1/2)) du, or dx = 2u du substituting these to original integral, integral of [e^x^(1/2) / x^(1/2)] dx integral of [(e^u) / u] * (2u) du the u's will cancel out: integral of [2*e^u] ...

algebra 1
3(2x-5) > x+15 6x - 15 > x + 15 combining similar terms, 6x - x > 15 + 15 5x > 30 x > 6 hope this helps~ :)

physics
assuming the air is ideal, we can use the formula, P1/T1 = P2/T2 where P1 = initial pressure P2 = final pressure T1 = initial temperature (in Kelvin) T2 = final temperature (in Kelvin) we first convert the given temp to Kelvin: T1 = 20 + 273.15 = 293.15 K T2 = 250 + 273.15 = ...

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 ...