Saturday
April 19, 2014

Posts by Jai


Total # Posts: 1,491

math
recall that the area of a circle is given by: Area = pi*r^2 since in the problem, diameter is given, we first get radius: diameter = 2*radius d/2 = r 15/2 = 7.5 ft = r thus A = pi*r^2 A = 3.14*7.5^2 A = ? now solve this using calculator,, to round off, first you need to know t...

geometry
..but we need to see the figure.

Math- Algebra II
8^(x-2) = (1/16) first, we can observe that both 8 and 16 are powers of 2, thus we express 8 and 1/16 as 2 raised to some power: 8 = 2*2*2 = 2^3 1/16 = 1/(2*2*2*2) = 1/(2^4) recall that when a certain number raised to an exponent is on the denominator, and we want it to be on ...

math?
to convert this to percent, first convert to decimal form,, you can use calculator to divide it: 9/54 = 0.1667 in percent, you just multiply it by 100: 0.1667*100 = 16.67% hope this helps~ :)

math
to get the greatest common factor, we first find the factors of each number (we call it a factor of a certain number if that certain number is divisible by the factor or it gives zero remainder when divided by the factor),, for example, 10 has factors 1, 2, 5 and 10, because 1...

no question
..what's the question?

alg 1
there are several ways to solve this, but any quadratic equations, factorable or non-factorable, we use quadratic formula: for a quadratic equation in the form ax^2 + bx + c = 0, we can solve the roots using the quadratic formula: x = [-b +/- sqrt[b^2 - 4ac]] / (2a) where the ...

prealgebra
let x = width of rectangle let x+7 = length o rectangle (since according to first statement, length is 7 greater than the width represented by x) recall that perimeter of rectangle is: P = 2*L + 2*W substituting,, 54 = 2(x+7) + 2x 54 = 2x + 14 + 2x 54 = 4x + 14 54 - 14 = 4x 40...

prealgebra
let x = width of rectangle let x+7 = length o rectangle (since according to first statement, length is 7 greater than the width represented by x) recall that perimeter of rectangle is: P = 2*L + 2*W substituting,, 54 = 2(x+7) + 2x 54 = 2x + 14 + 2x 54 = 4x + 14 54 - 14 = 4x 40...

physics
let x = support at left end let y = support at right end now, to get the reaction force at the left support, we sum moments at the right end, so that y will not be included in our calculation, and we can directly solve for x,, *recall that moment = (force)*(distance perpendicu...

Math
from the values, we can observe that the values of x are multiples of 8, and that if we multiply the values of y to 8, we get the values of x: 1*8 = 8 2*8 = 16 3*8 = 24 etc. now we can write an equation: y*8 = x or x - 8y = 0

Math
from the values, we can observe that the values of x are multiples of 8, and that if we multiply the values of y to 8, we get the values of x: 1*8 = 8 2*8 = 16 3*8 = 24 etc. now we can write an equation: y*8 = x or x - 8y = 0

Math
*i reposted this from the values, we can observe that the values of x are multiples of 8, and that if we multiply the values of y to 8, we get the values of x: 1*8 = 8 2*8 = 16 3*8 = 24 etc. now we can write an equation: y*8 = x or x - 8y = 0

Geometry-8th grade
it's correct~ :)

math
for the 1st question: it would be difficult to present here the solution for long division... but the answer should be 149.375 for the 2nd question: weight which can be carried by truck: 225 kg / truck thus, 4 trucks can carry all in all: 4*225 = 900 kg but the weight of all d...

math
but we don't see the figure...

physics -- projectile motion
oops, sorry the formula for range must be R = (vo)^2 * sin (2*theta) / g i just remembered that the 2g is for the max height: h,max = (vo)^2 * [sin (theta)]^2 / 2g but explanation and proving is still the same~ :)

physics -- projectile motion
recall that the formula for range is: R = (vo)^2 * sin (2*theta) / (2g) where vo = initial velocity theta = angle of release g = acceleration due to gravity (9.8 m/s^2) now, if we're given the initial velocity, the value of range will depend on theta,, observing this, if w...

Pre-Algebra
useful conversion: 1 meter = 100 centimeters first, we convert the given with units of centimeters into meters: 480 centimeters = ? meters to do this, we just divide 480 by 100 or: 480/100 = 4.80 meters 98/100 = 0.98 meters then we add these two to get the total length that he...

Math
let x = length of the first let 64 - x = length of the second since they are in ration 2:3, we can write this as: 2/3 = x/(64-x) cross-multiplying, we have: 2(64-x) = 3x 128 - 2x = 3x 128 = 5x x = 25.6 inches 64-x = 38.4 inches hope this helps~ :)

Math: Logarithms
recall that when the expression inside the log is raised to a certain power, we can write the exponent outside of the log, for instance: log (x^2) = 2 log x log [(2y)^0.5] = 0.5 log 2y thus for the problem, we can rewrite it as: (log(x^6) + 2log(y^3)) / log(xy) (6 log x + 6 lo...

math
(1) x + 5y = -3 (2) 3x - 2y = 8 substitution method: we first choose one of the equation, and express one of the variables in terms of the other variable,, here let's choose equation (1), and express x in terms of y: x + 5y = -3 x = -3 - 5y now, we substitute this to equat...

math
recall that the area of a triangle is A = bh/2 b = base and h = height substituting the values: 90 = b*12/2 90 = b*6 b = 15 meters hope this helps~ :)

Geometry
recall some formulas: Volume of Sphere = (4/3)*pi*(r^3) Surface Area of Sphere = 4*pi*(r^2) since we do not know the value of radius, we get it from the surface area: 804 = 4*pi*r^2 now solve for r with your calculator~ after solving r, plug in this value to the formula for vo...

math
first, we convert the given in same units,, let's use ft as units,, since 12 inches = 1 foot, we convert the given dimensions for the tiles into ft: 12 inches = 1 ft 12 inches = 1 ft then we get the areas of both tiles and floor area to be installed by tiles: A,tile = 1*1 ...

maths
i think you mean, x^2 + 5x - 36 = 0 to factor this, first we get the factors of the constant (which is 36),, the factors of 36 are: +- 1, 2, 3, 4, 6, 9, 12, 18, 36 now, we see from the given equation that 36 is negative,, thus we choose two factors from this set which are in o...

Alegbra 1
the 500 pounds represent the Ao in the equation (Ao is the initial amount),, since there is time given (x = 140 years), we can substitute the values directly: A = Ao*e^(-0.01386x) A = (500)*e^(-0.01386*140) A = ? now plug in these values in calculator and you'll get A~ hop...

Trigonometry
values in x column will change, as well as the values in y column, but you will see a pattern --- you would observe that the pattern repeats every pi interval,, remember that you'll graph this in rectangular (Cartesian) coordinate plane, not in polar coordinates,, to get t...

Math
it has 5 sides, so it's a pentagon~ :)

Algebra/geometry
let x = length of the original rectangle let x-4 = width of the original rectangle using the conditions given by the 2nd statement, new width: (x-4) + 5 new length: x - 3 using the next condition given in the problem, and recalling that the area of a rectangle is just length*w...

mathh
let n = number half the number, so n/2 three less than, so - 3 putting them together, three less than half a number is: n/2 - 3 hope this helps~ :)

mathh
let n = number half the number, so n/2 three less than, so - 3 putting them together, three less than half a number is: n/2 - 3 *i just reposted my reply :)

math
let x = number of candy bars of Neil 3 less than 4 times as many candy bars as Neil means: 4x - 3 hope this helps~ :)

Algebra
3x^2 - 15x + 18 do you need to factor this??? if so, first since the numerical coefficients (the number before the variable x) are all multiples of 3, we can factor out 3: 3(x^2 - 5x +6) then we factor the term inside the parenthesis: 3(x-2)(x-3) hope this helps~ :)

Algebra
let x = area to be painted (in sq ft) let y = gallons of paint needed therefore, using the second statement of the problem, we can find the ration of sq ft area painted per gallon: 10000 sq ft / 20 gallon = 500 sq ft / gallon thus, to get the number of gallons needed, we divid...

geometry
first we get the ratio of the arclength to circumference: 60 cm / 240 cm = 1/4 since the arc covers 1/4 of the circumference, it also means that it forms 1/4 of the total angle of a circle. angle of a circle is 360 degrees, thus central angle associated by XW is: (1/4)*360 = 9...

Algebra
let x = number of bracelets you will make since you ill use 30 beads per bracelet, the total number of beads you will use is 30x, and this total number of beads must be no more than 145 beads (or it will not exceed 145),, therefore: 30x < 145 to see if you can make 4 bracel...

precalculus
to solve for the vertex, there are actually many ways, but i think the fastest is to get the derivative (since the derivative is either a maximum or a minimum --- like the vertex, which can be a maximum if parabola is concave downward, or a minimum if it is concave upward) get...

Calculus 12th grade.
recall that velocity is the change in position over change in time, or: v = dx/dt where x=distance, and t=time thus equating this to the given function, dx/dt = 9t^2 + 2t dx = (9t^2 + 2t)dt integrating, x - xo = 3t^3 + t^2 + C if we assume that the initial displacement is zero...

Calculus 12th grade.
first, we find where the curve touches the x-axis, or simply get the roots,, to get the roots, equate y = 0: 0 = 4x - x^2 0 = x(4-x) x = 0 and x = 4 this will be our boundary conditions for integration,, we'll use integration since area under the curve: integral (4x - x^2)...

advanced math
what method would be the best if i want to solve more than one ordinary differentials equations? or how would i attack this kind of problem? for example: dy/dt = (1-y)/(1+x+y) dx/dt = (y-x)/[2(1+x+y)] i just need a starting point cause i couldn't think of a way~ :P any hel...

math
first represent unknowns using variables: let x = rate of Mill let x+6 = rate of Julie recall that rate (or speed) is the distance travelled over time, or: v = d/t therefore, since 714 miles is their distance after 6 hours, and noting that they travel in opposite directions: v...

algebra
the first term.. is that (-6^v2 + 2v + 4)?? if it is, then, you almost got the correct answer---you just forgot to put a negative sign before 12v^2 :)

algebra
for similar triangles, the ratio of the sides of the first triangle is equal to the ration of the corresponding sides of the second triangle,, like: let h1 = height of 1st triangle let h2 = height of 2nd triangle let b1 = base of 1st triangle let b2 = base of 2nd triangle ther...

algebra
recall the formula for midpoint: let Xm = x-coordinate of the midpoint let Ym = y-coordinate of the midpoint Xm = (X1 + X2)/2 Ym = (Y1 + Y2)/2 therefore: Xm = (2+4)/2 = 6/2 = 3 Ym = (-3+9)/2 = 6/2 = 3 thus midpoint is at (3,3) hope this helps~ :)

algebra
the max distance in a rectangular solid is its diagonal,, like in a rectangle, the max distance is the diagonal,, recall: the square of the diagonal of a rectangular solid the sum of the squares of its sides, or: L^2 + W^2 + H^2 = D^2 where L=length, W=width, H=height, D=diago...

Math
but we do not see the figure.

Grade 10 Math
sorry for the first post by the way~ ^^; i just accidentally hit the enter button~ ^^;

Grade 10 Math
(a) no solution recall that two linear equations have no solution if they are parallel (solution means they meet at a certain point),, thus the two equations, in order to be parallel must have the SAME SLOPE. to determine the slope of the given equation, we rewrite it in this ...

Grade 10 Math
(a) no solution

Alg 2
first get the roots,, (x-7)(x+3)=0 thus equating each term inside the parenthesis to zero, x-7=0 and x+3=0 therefore, x=7 and x=-3 the roots are 7 and -3 sum: 7 + (-3) = 4 product: 7(-3) = -21 the questions asks for the difference between the sum and product, therefore: 4 - (-...

algebra
3x / (x^(-1)) recall some laws of exponents: a number raised to a negative exponent is equal to its reciprocal raised to the positive exponent for example, 3^(-1) = (1/3)^1 = 1/3 5^(-2) = (1/5)^2 = 1/25 therefore, here, the x^(-1) becomes (1/x)^1 or simply 1/x 3x / (x^(-1)) 3x...

math
6x + 2y = -2 4x + y = 1

Algebra
recall: speed (v) is distance (d) travelled over a certain period of time (t), or v = d/t since Suzi is faster that Jim given their speeds, we can get the difference of their speeds: 69 - 41 = 28 mph *this 28 mph only means that after 1 hour, the gap or distance between them i...

Math
first recall law of exponents,, if terms have the same base (or the number which is raised to a certain exponent), we can add the exponents,, thus: 8^(8) * 8^(-8) we can rewrite this as: 8^(8-8) 8^(0) since any number (expect zero) raised to zero is one, 8^(0) = 1 hope this he...

Algebra
wait, it should be t > -2 *i forgot to tell that if you divide both sides by a negative number, the inequality sign becomes the opposite,, that's why (<) becomes (>) and so please don't mind the "thus t is any number less than 2, so it can be 1.7, 1, 0, -...

Algebra
so it's an inequality~ i think for the first equation you've written, you mean: r > -0.075t + 3.85 because you've written -0.075t + 3.85 < 3.7 (it's the same as r > -0.075t + 3.85 ; the left side just became the right side of the inequality and vice-ve...

9th grade
you multiply the term to each term inside the parenthesis and then combine them,, for example, 3(x+2y+2) multiply 3 to each term: 3*x + 3*(2y) + 3*2 3x + 6y + 6 hope this helps. :)

math
discount: amount of money you can save (amount that is deducted from the original price),, discount = %discount * original price first convert 5% to decimal,, just move 2 places to the left of decimal point: 5% = 0.05 therefore, discount = 0.05 * 8.49 = ?

6th grade
first represent unknowns using variables: let x = first decimal let y = second decimal then set up equations using conditions given: (1) x + y = 3.9 (according to first statement) (2) x - y = 0.9 (according to second statement) (3) xy = 3.9 i think there's something wrong ...

Math
Volume of a cylinder = area of the base * height, or: V = pi*(r^2)*h therefore, V = pi*(5^2)*4 V = pi*25*4 simplify this. units is in cubic units. Volume of cube is s^3,, solving for the length of one side: V = 27 = s^3 cuberoot(27) = s s = 3 inches Surface area of cube = 6*ar...

math
first represent the unknowns using variables: let x = age of the Emma let 9x+7 = age of Karen (according to first statement) then set-up equation using the given conditions: x + (9x+7) = 57 combine similar terms,, for terms with the same variable, add the numerical coefficient...

4th grade
let n be the number for instance, five less than the number means 5 is subtracted to the number: n - 5

physics
since given angle is 30 deg to the horizontal, the horizontal force is just, Fx = F*cos(theta) Fx = 70*cos(30) now simplify this.

5th grade
if 5/17 is shaded, then the rest is not, therefore, 1 - 5/17 in order to subtract this, we first convert 1 into a fraction such that its denominator (*denominator is the number below the line of a fraction) is the same as the second term (which is 17),, thus we can rewrite 1 a...

algebra
(7/3)x + (1/3)x = 4x + 48/3 + (8/3)x combine similar terms,, for terms with same variables, add the numerical coefficient (number before the variable) and copy the variable: (7/3 + 1/3)x = 4x + 48/3 + (8/3)x *since 7/3 and 1/3 have the same denominator, just add the numerator ...

calculus
y1 = x^2 + 3x - 1 y2 = x - 5 for y1 - y2, combine similar terms,, for terms with same variables, add their numerical coefficients (number before the variable) and copy the variable: x^2 + 3x - 1 -(x - 5) x^2 + 3x - 1 - x + 5 x^2 + 3x - x - 1 + 5 *i just rearrange the terms* x^...

geometry
recall the properties of parallelogram,, one of the properties of a parallelogram is that the opposite angles are congruent/equal,, since you are given angles A and C, and they are opposite, equate them to get x: 4x - 57 = x + 3 combining similar terms, 4x - x = 57 + 3 *when t...

Precalculus
x-intercept occurs when y = 0, thus substitute zero value to y: 0 = -0.01x^2 + 0.7x + 6.1 since this is not factorable, use the quadratic formula: x = [-b +- sqrt(b^2 - 4*a*c)]/(2*a) note: +- is plus or minus where a = -0.01, b = 0.7 and c = 6.1 substitute these values and sol...

algebra
shift to the left: y = x + 1 then shift to one space up,thus: y - 1 = x + 1 or y = x + 2

math
speed is distance traveled over unit time: v = d/t rearranging, d = vt let v = speed going there (forth) since in the problem, you traveled the same distance, d,forth = d,back 3v = 5(16) 3v = 80 v = 80/3 or 26.67 k/h

algebra
#1 , #2 and #4 are correct. :) for #3, you have two cases, first: 7-x > 2 (positive case). thus, -x > 2-7 -x > -5 x < 5 second: -(7-x) > 2 (negative case). thus, -7+x > 2 x > 2+7 x > 9 thus, it should be x < 5and x > 9 or (-infinity, 5) U (9, +inf...

Math
-11x-24 < 27-10x combine similar terms: -11x + 10x < 27 + 24 *when transposing terms to other side of equation, the sign must become the opposite* then, -x < 51 multiply by -1 to get positive x: x > -51 *note that when all terms are multiplied or divided by a NEGAT...

math
*when in percent and you want to convert into decimals, just move the decimal point 2 place to the right: 3.5% = 0.035 rewriting this using equation: 0.035*d = 0.105 note that "of" means multiply and "is" is equals. to get d alone, divide all terms by the n...

algebra
first represent the unknowns with variables: let x = first number let x+2 = second number let x+4 = third number *since they are consecutive, and all of them are odd, they have a difference of 2, that's why it's x, x+2, x+4* now, setup equation using the given conditio...

math
using long division, first, since 34 is the one that is divided, 34/123.08 must be written like this: 123.08 ) 34 since the divisor (the 123.08) has five digits, and the dividend has only 2 digits, we write zeros to the right of decimal point of 34: 34 becomes 34.000 (now it h...

algebra
-3/7x = 6/35 to get x alone, you must divide all terms by the numerical coefficient (the number before the variable) of x, thus: (-3/7)x/(-3/7) = (6/35)/(-3/7) = -(6/35)/(3/7) *i just rewrite the negative sign outside* on the left side, -3/7 will be cancelled, and on the right...

integrals!!
first graph y = 2x + 8,, now, using the boundaries given, find the value of y at x = -4, and find the value of y at x = 1: at x=-4, y = 2(-4) + 8 = 0 at x=1, y = 2(1) + 8 = 10 now, look for these points on your graph and draw a vertical line (this is only a guide) from this po...

calculus
first, you have to get the value of x where |x^2 - 1| becomes zero, thus x = -1 and 1 since the boundaries given are only from 0 to 4, we consider only what happens to the graph at x = 1 (because 1 is within the boundaries) first, draw or imagine the graph. the graph of x^2-1 ...

math
right. :) but since it's amount per pound, the units must be in dollars/pound.

math
right. :) now, subtract them to get amount per pound that can be saved.

math
right. :) how about 15.5/25 = ?

math
you have to solve for amount per pound of each: 23.5/50 = ? 15.5/25 = ? then subtract the answers you got to get the amount per pound that can be saved by buying the lower unit price. hope this helps. :)

chem
are 7.60 and 3.00 in moles? if it is, recall the formula relating moles (n) and volume (V), at a constant P and T: n1 / V1 = n2 / V2 plug in the given values to the equation: 7.60 mol/ 31.0 = (7.60 + 3) mol / V2 then solve for V2. hope this helps. :)

math
is a and b restricted only to positive numbers (or can they be negative)?

math
useful conversion: 1 km = 1000 m 1 hr = 60 min = 60*60 s *note: you can rewrite 846 km/hr into: (846 km)*(1/hr) thus, using dimensional analysis to cancel units, (846 km)*(1000 m / 1 km) = 846*1000 m (1/hr)*(1 hr / 60*60 s) = 1 / 60*60 s now multiply both: 846*1000 * 1/(60*60)...

Chemistry
molarity is moles of solute per liter of solution: M = moles/L plug in the given values in the equation, therefore: M = 1.77 / 30.6 = 0.0578 M is it required to write the answer in correct number of significant figures? if not, i think 0.06 M is acceptable ; but if yes, it mus...

Physics
nope. it's not D,, power is work per unit time, or P = w/t where w = work in Joules (J) and t = time in seconds (s) thus the unit of power is Joules/second or J/s (A) hp = horsepower --> a unit of power,, (B) J = Joules --> unit of work (C) W = watts --> a unit of...

math
oh, i see you already have an answer,, right. the difference is 3/8 m/s. :)

math
nope,, 15 3/8 is greater than 15,, it's like you have 15 whole pizza plus 3 slices, while the other has only 15 whole pizzas, that's why, 15 3/8 > 15 then, "by how much" means you will get the difference: 15 3/8 - 15 = ?

math
yes, that's right~! :) now comparing the speed: Anna: 15 Julia: 15 3/8 which of the two is slower (or has smaller speed)? then, "by how much" means you will get the difference: 15 3/8 - 15 = ?

math
right~! :) now, we simplify 246/16,, since the numerator and denominator have a common factor 2, we can cancel it out: (2*123)/(2*8) = 123/8 123/8 is in simplest form,, now change this to mixed number.

math
you're on the right track,, now, what is 60/4 ?

math
nope, it's not 12,, remember that a whole number can be written to: 20 = 20/1 now, 20/1 * 3/4 = ? ..and we will not divide the answer by 246/16,, we will just compare them. first, let me see your answer.

math
when dividing a number by a fraction, first get the reciprocal of the fraction,, *to get reciprocal: you just interchange the numerator and denominator, thus: reciprocal of 4/3 = 3/4 now the operation becomes multiplication instead of division: 20 * (3/4) i think you know how ...

math
it's 20/(4/3),, first simplify this,,

math
recall that speed or rate is distance traveled over time, or: speed, v = d/t thus, you compare Anna's speed and Julia's speed: Anna: v = 20/(1 1/3) Julia: v = 246/(16) *note: first convert mixed number to improper fraction before dividing. hope this helps. :)

College Algebra URGENT
(fog)(x) is also f(g(x)) which means you substitute g(x) to the function of f(x),, (the x variables in f(x) will be g(x)), thus: (fog)(x) = 1/([g(x)]+4) (fog)(x) = 1/[(1/(6x+4) + 4] then simplify it.

math correct or not correct
Right. :)

math correct or not correct
right~! :)

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