Posts by Jai

Total # Posts: 2,000

MATHS
By trial and error: Perry's age = 73 Laura's age = 37 Difference of their ages = 36 years Checking: 73-1 = 2(37-1) 72 = 2(36) 72 = 72

Pre-Calc
f(x) = (x^5+3x^3+5x) / (4x^4+2x^2) The only common factor of numerator and denominator is x, but it isn't really necessary to cancel it. i. Vertical Asymptote To get this, we get the limit of x, as f(x) approaches infinity. lim x as f(x)->infinity Or easier way is to ...

Math
1. Yep 2. Yep 3. Yep

math
a. As the problem hinted, Let x = number of weeks Let y = dollars saved For the first equation: you have initially \$50, and \$10 is added each week. Therefore, at the end of x weeks, the total amount of money you'll have is, y = 50 + 10x For the second equation: same ...

Math
Yes, x can be -13 or 13.

maths
What is the operation? Are we to divide them? And, please clarify the 13^1/2x^2, if it's 13^(1/2 x^2) or 13^(1/(2x^2)).

math
Let x = Mary's age The condition given, in symbols, is x + 10 = 2x - 5 Solving for x, x - 2x = -10 - 5 -x = -15 x = 15 years old hope this helps ;)

chem 211
Write the balanced chemical reaction: C2H4 + H2 -> C2H6 , ΔH = -144 kJ/mol C2H4 Then we get the number of moles of C2H4 using the given mass, 14.6 kg of C2H6. Molar mass, C2H6 = 2*12 + 6*1 = 30 g/mol n,C2H6 = 14.6 * 1000 g / 30 g/mol = 486.67 mol Since the mole ratio ...

chem
Recall that the heat absorbed (+) or released (-) by a substance is given by Q = mc(T2 - T1) where m = mass (g) c = specific heat capacity (J/g-K) T2 = final temperature T1 = initial temperature Note that in the problem, the source of energy or heat came from the alloy. Thus ...

math
Let x = capacity of carton Let y = capacity of cup According to the first statement of the problem, x = 2y According to the second statement, 1.8 = 3y + 2x Now, we have the equations. What we'll do is substitute the first equation to the second: 1.8 = 3y + 2(2y) 1.8 = 3y...

math
Yes.

math
y = 3x - 2(4^x) Yep, the derivative of 3x is 3. Yep, it's true that derivative of 2 is 0, but this is not necessary. Note that 2 is multiplied by 4^x, and does not act as a separate term. Yep, the derivative of 4^x is 4^x(ln(4)). Therefore, y' = 3 - 2*(4^x (ln(4))) or ...

1. Yes it's false, because velocity is a vector quantity (which depends on magnitude & direction). 2. Yes, it's acceleration and velocity because both are vector quantities.

Geometry
Note that the sum of interior angles of a triangle is equal to 180 degrees. Therefore, we get the sum of angles R, S and T, then equate to 180: (2x + 10) + (2x + 25) + (x - 5) = 180 Solving, 5x + 30 = 180 5x = 180 - 30 5x = 150 x = 30 degrees Hope this helps~ :)

math
For #s 1 and 2: go to wolframalpha . com and type the equation. For #3: To get the slope, we convert the given equation into the form, y = mx + b where m is the slope and b is the y-intercept. Therefore, -2x - 3y = 5 -3y = 5 + 2x y = 5/(-3) + 2x/(-3) y = (-2/3)x - 5/3 Thus the...

school of engineering
i. Acceleration is the change in velocity over time. a = (v,f - v,o) / t where v,f and v,o are the final and initial velocities respectively, and t is the time. Substituting, a = (100 - 50 km/h)*(1000 m / 1 km)*(1 h / 3600 s) / 10 s a = 1.39 m/s^2 ii. Since the motion is ...

Math
Subtract the final temperature to the initial temperature: 8 - (-3) = 8 + 3 = 11

geomrtry
Recall that the sum of exterior angles of any polygon is equal to 360 degrees. Therefore, we just divide 360 by 40 degrees to get the number of sides: 360/40 = 9 sides hope this helps :)

Math, Factoring
(11x + 5)(11x + 5)

Thank you Mr. Steve! :3

1. Yep 2. Yep 3. Yep

calculus
Integral (2x^2-4x-6)dx from 0 to 1 = (2/3)x^3 - 2x^2 - 6x from 0 to 1 = (2/3)(1)^3 - 2(1)^2 - 6(1) - ((2/3)(0)^3 - 2(0)^2 - 6(0)) = 2/3 - 2 - 6 - (0 - 0 - 0) = 2/3 - 8 = 2/3 - 24/3 = -22/3 Hope this helps :3

1. You have to just multiply them, because it says 20% of those 50 students got milk, so 50 * 0.2 = 10 students 2. Yep 3. Yep 4. Yep 5. [Unit ratio] What we'll do here is to get the cost per oz. Thus we divide \$1 by 3.6 oz and \$2.50 by 11.5 oz, then compare. \$1/3.6 = \$0....

math
Let x = son's age Let 38-x = Mr. Bellini's age (since the sum of their ages must be equal to 38) Set up the equation using the the second statement: (38 - x) - 4 = 5(x - 4) Solving, 34 - x = 5x - 20 34 + 20 = 6x 54 = 6x x = 9 years old (son's age) 38-x = 29 years ...

Calculus
y = log(8x^2-3x+9) Note that derivative of log(x) = 1/(x*ln(10)) Thus, dy/dx = ( 1/(8x^2-3x+9)*ln(10) ) * (16x - 3) = (16x - 3) / ((8x^2 - 3x + 9)*ln(10)) Hope this helps~ :3

Calculus
f(x) = ax^n f'(x) = a*n*x^(n-1) Substitute the given conditions. f'(3) = a*n*(3)^(n-1) 14 = a*n*(3)^(n-1) f'(6) = a*n*(6)^(n-1) 28 = a*n*(6)^(n-1) We can solve this since there are two equations, two unknowns. From the first equation, we can say that a = 14 / n*(3...

Calculus
y = cos^4(pi*t-20) Note that the derivative of cos(x) = -sin(x) and the derivative of x^n = n*x^(n-1). We'll apply them here, and we'll also use chain rule. dy/dt = 4 * pi * cos^3 (pi*t - 20) * (-sin (pi*t - 20)) Hope this helps~ :3

Calculus
y = log(8x^2-3x+9) Note that derivative of log(x) = 1/(x*ln(10)) Thus, dy/dx = ( 1/(8x^2-3x+9)*ln(10) ) * (16x - 3) = (16x - 3) / ((8x^2 - 3x + 9)*ln(10)) Hope this helps~ :3

algebra
Hi. I answered you previous post and it was almost similar, except that here, the roots must be complex/imaginary so D must be less than zero. Anyway, Recall the formula for discriminant. For a quadratic equation in the general form, ax^2 + bx + c = 0, D = b^2 - 4ac if D = 0...

algebra
Recall the formula for discriminant. For a quadratic equation in the general form, ax^2 + bx + c = 0, D = b^2 - 4ac if D = 0 : real, equal/double root D > 0 : two real, unequal roots D < 0 : two imaginary roots Since we're required to have one real root, we equate D ...

pre-Algebra
17x - 22x = 1/2 -5x = 1/2 x = (1/2)/(-5) x = -1/10

calcus
integral (sec u) du This is pretty tricky, but what we'll do here is multiply both numerator and denominator by (sec u + tan u): = integral (sec u * (sec u + tan u)/(sec u + tan u)) du = integral (sec^2 (u) + sec(u)*tan(u))/(sec u + tan u)) du Then we use substitution. Let...

calcus
integral (tan^3 (x) sec^3 (x)) dx Recall the identity, tan^2 (x) = sec^2 (x) - 1 We substitute it here: = integral (tan(x) * (sec^2 (x) - 1)(sec^3 (x))) dx Let u = sec (x) Thus du = sec(x) tan(x) dx Substituting, = integral (u^2 (u^2 - 1)) du = integral (u^4 - u^2) du = (1/5)*...

calcus
integral cos(x) sin(x) dx We simply use substitution. Let u = sin(x) Thus du = cos(x) dx Rewriting, = integral (u du) = (1/2)*u^2 + C = (1/2)*sin^2 (x) + C Or you may also use substitute the formula sin(2x) = 2sin(x)cos(x) to the original, and then directly integrate. Hope ...

Calculus
Hi. I think Mr. Steve had already answered this before (on your previous post), you may want to check it out. I also answered this on that previous post too, but I'll just copy-paste my answer. s = t^6 * tan(t) - sqrt(t) ds/dt = t^6 (sec^2 (t)) + 6t^5 (tan(t)) - (1/2)(1/...

Algebra
7m + mn + 35 + 5n = m(7 + n) + 5(7 + n) = (m + 5)(7 + n)

Algebra
26(5-x)^2 - 5(5-x)^3 = (5-x)^2 (26 - 5(5-x)) = (5-x)^2 (26 - 25 + 5x) = (5-x)^2 (5x+1)

Algebra
by + ay + bx + ax y(b + a) + x (b + a) Note that you can still factor out the (b + a): (b + a)(y + x) Hope this helps~ :3

Math
What do mean? @_@ Anyway, both sides of equation must be equal. I'll just show the step by step. Note that you should always follow the order of which operation comes first: PEMDAS or Parenthesis - Exponents - Multiplication - Division - Addition - Subtraction But there ...

Math
14 = 50 - 42/(3+4) * 6

Algebra
If only two numbers are involved, Let A and B be real, non-zero numbers. 1) (+)A + (+)B = (+) ? This is always true. 2) (-)A + (-)B = (-) ? This is always true. 3) (+)A - (-)B = (+) ? This is always true. 4) (-)A - (+)B = (-) ? This is always true. 5) (-)A - (-)B = (+) ? This ...

Calculus
s = t^6 * tan(t) - sqrt(t) ds/dt = t^6 (sec^2 (t)) + 6t^5 (tan(t)) - (1/2)(1/sqrt(t))

Chemistry
Assuming the gas is ideal, we can use Boyle's law: P1 * V1 = P2 * V2 where P1 = initial pressure P2 = final pressure V1 = initial volume V2 = final volume Substituting, (1.75 atm)(10.7 L) = P2 * 20 L P2 = 1.75 * 10.7 / 20 P2 = 0.936 atm Hope this helps~ :3

Chemistry
Assuming the gas is ideal, we can use Boyle's law: P1 * V1 = P2 * V2 where P1 = initial pressure P2 = final pressure V1 = initial volume V2 = final volume Substituting, (1.75 atm)(10.7 L) = P2 * 20 L P2 = 1.75 * 10.7 / 20 P2 = 0.936 atm Hope this helps~ :3

Chemistry 12
First we get the molar mass of K2CrO4. To get the molar mass, just get a periodic table, find the individual masses of the elements and add them all based on the chemical formula. Thus, K2CrO4: 2*39.1 + 1*52 + 4*16 = 194.2 g/mol Then recall that molarity is equal to moles of ...

Algebra 1
Let x = time in hours Since their costs must be the same, 100 + 15x = 75 + 17x Solving, 100 - 75 = 17x - 15x 25 = 2x x = 25/2 or 12.5 hours Hope this helps~ :3

Algebra 1 (Reiny)
To solve for a, combine all terms with variables on the left side of the equation, and all constants on the right side of equation. Note that when we transpose a term to the other side, its sign becomes the opposite: 12a - 11 = 9a - 1 12a - 9a = 11 - 1 3a = 10 To get a, divide...

Chemistry
First, you must have the specific substance to know its chemical formula (whether it's H2O, NH3, NaOH, etc.) And then you'll get its molar mass. To get its molar mass, just add the individual masses of the elements in the chemical formula. For instance, MM of H2O: 2*1...

Math
I suppose that "XER" means the domain (all possible values of x) is all real numbers. And the answers there are both...wrong. Anyway, range is the set of all possible values of y (or f(x)). Let's analyze each problem. :) a) f(x) = (x^2+3)^2 Note that x^2 can ...

Algebra1 Math
Let x = time in hours Since their costs must be equal, 800 + 16x = 720 + 21x Solving, 800 - 720 = 21x - 16x 80 = 5x x = 16 hours Hope this helps~ :3

maths2
Formula for discriminant: d = b^2 - 4ac note that if d = 0 : real, equal/double root d < 1 : imaginary roots d > 1 : real, unequal roots 7x2 + 3x + 1 = 0 d = 3^2 - 4(7)(1) d = 9 - 28 d = -19 Thus, it's D. imaginary roots. Hope this helps~ :3

math
There are many ways to do this. Graphing is one. Another way is to convert it to the vertex form: y = a(x-h)^2 + k where (h,k) is the vertex and the axis of symmetry is x=h. Thus, y = -4x^2 - 24x - 36 y = -4(x^2 + 6x) - 9 y = -4(x^2 + 6x + 9) - 9 + 9 y = -4(x+3)^2 Thus, V(-3,0...

Taking Time to Thank
OMG I'm not really a homework helper, it's just like my pastime answering some questions that I think I know. :3 But you're welcome and I'm very happy I could be of help! (◕‿◕✿)

Chemistry
First we get the mass of NH3 (ammonia) in the concentrated NH3 solution, by using the relationship between density, mass and volume: d = m/V 0.88 = m/28.2 m = 24.816 g Since ammonia is only 28% of this mass, m,NH3 = 24.816 * 0.28 m,NH3 = 6.9485 g NH3 Then we change this to ...

chemistry
Total mass of solution = 5 + 95 = 100 grams Recall that the formula for calculating the heat absorbed or released is given by Q = mc(T2 - T1) where m = mass c = specific heat capacity (T2 - T1) = change in Temperature Substituting, Q = 100 * 1.1 * 10 Q = 1100 cal Hope this ...

1. Yep, the limit approaches infinity 2. Nope, the limit is zero. lim (2^x+x^3)/(x^2+3^x) as x-> infinity We'll use L'Hopital's rule here (I hope it was already taught in your class). It is used when you get the form 0/0 or infinity/infinity when the x value is ...

Algebra
a. Let x = amount of 10% salt solution in gallons Since the total volume must be equal to 5, Let 5-x = amount of 25% salt solution in gallons We'll do a salt balance here. Thus, the equation would be, 0.1x + 0.25(5-x) = 0.2(5) b. Solving, 0.1x + 0.25(5-x) = 0.2(5) 0.1x + 1...

maths2
D. No solution

maths
What's the question? If the question says, which of the following points satisfies the equation, then there is no answer. Probably there is a typo...

chemistry
Recall the formula M1 * V1 = M2 * V2 where M1 = initial concentration M2 = final concentration V1 = initial volume V2 = final volume Substituting, 4.7 * 4 = M2 * 45 M2 = 4.7 * 4 / 45 M2 = 0.418 M Hope this helps :3

math
It's hard to show here the actual graph so I'll just tell you what to do. There are plenty of ways to graph them, but this is, for me, the simplest: 1. First, find the x- and y-intercepts. To the x-intercept, let y = 0 and solve for x. To find the y-intercept, let x = ...

math
Recall that the circumference of a circle is equal to C = pi*d where d is the diameter. First we get the circumference, then we multiply it by the number of revolutions, which is 20: C = 3.14 * 65 C = 204.1 cm (this is only equal to 1 revolution) Therefore, total distance ...

Calculus
Req'd: area bounded by y = x and y = 2*sqrt(x) First thing to do here is to find their points of intersection, so we'll know the bounds. We can do it algebraically or graphically. To find algebraically the points of intersection, we just use substitution. Since y = x, ...

letter D is false. For instance, 90 is divisible by 6 and 10, but not divisible by 60.

MATH
Let x = amount of John's or Matt's money Set up the equation. According to the first statement, x - 130 = 3(x - 480) Solve for x: x - 130 = 3x - 1440 x - 3x = -1440 + 130 -2x = - 1310 x = \$ 655 Hope this helps~ :3

calculus
d/du ( 1/(2u^2 - 1)^2 ) d/du ( (2u^2 - 1)^-2 ) = -2(4u)(2u^2 - 1)^-3 = -8u / (2u^2 - 1)^3 Hope this helps~ :3

chemistry
Standard Temperature = 273 K or 0 deg Celsius Standard Pressure = 1 atm STP is needed to have a reference value in order to make comparisons with different sets of data values.

geometry
Note that point B is in segment AC, therefore we can say that the sum of lengths of AB and BC is equal to AC, or AB + BC = AC Substituting, (2x - 1) + (3x + 5) = 24 5x + 4 = 24 5x = 20 x = 4 Thus, AB: 2(4) - 1 = 7 units Hope this helps~ :3

Intermediate Algebra
sqrt(5x^2 - 3x) = 2x First thing to do is to square both sides of the equation, then solve for x: [sqrt(5x^2 - 3x)]^2 = (2x)^2 5x^2 - 3x = 4x^2 x^2 - 3x = 0 x(x - 3) = 0 x = 0 x = 3 Then to check if it really satisfies the original equation, substitute the x values back to the...

Intermediate Algebra
sqrt(y + 10) = y - 2 First thing to do is to square both sides of the equation, then solve for x: y + 10 = (y - 2)^2 y + 10 = y^2 - 4y + 4 0 = y^2 - 5y - 6 0 = (y - 6)(y + 1) y = 6 y = -1 Now to check, substitute the x values back to original equation. y = -1: sqrt(-1 + 10...

math
15y^7 / 5y^4 = (15/5) * (y^7 / y^4) = 3y^3

Intermediate Algebra
sqrt(5x - 4) = 6 First thing to do is to square both sides of the equation, then solve for x: [sqrt(5x - 4)]^2 = 6^2 5x - 4 = 36 5x = 36 + 4 5x = 40 x = 8 Hope this helps~ :3

math
10^1 - 10^0 = 10 - 1 = 9

math
(a+b)^9 / (a+b)^9 = 1

math
(ab^8)*(a^5)*(b^6) To multiply, just add the exponents of those terms with the same base: = a^(1+5) * b^(8+6) = (a^6)(b^14) Hope this helps~ :3

Intermediate Algebra
3 squareroot(13) + 7 squareroot(13) Note that you can only add or subtract terms with radicals if they have the same radicand (expression inside the radical sign) and same root (square root, cube root, fourth root, etc.) Therefore, it becomes = 10 squareroot(13) Hope this ...

Recall that the formula for density is d = m/V where m is the mass and V is the volume. Substituting, d = 30/7500 d = 0.004 g/cm^3 Hope this helps~ :3

math
Note that 0.7 is also 7/10. The given are 1/4, 7/10, 3/5 What you can do here is first find the LCD (Least Common Denominator) or the smallest number where it is divisible by 4, 10 and 5. By looking, we can say that the LCD = 20. Then we convert each fraction at which their ...

Math
134n + 55

Math
We let the unknowns using variables: Let n = number of quarters Let k = number of dimes Note that the sum or total of quarters and dimes is 47. Therefore, we can say that n + k = 47 Since we need to find the number of dimes (which is k) in terms of umber of quarters (that is n...

Math
q + 49

Math
Let w = width Let 2w - 5 = length (according to first statement) Then we set up the equation. Recall that the perimeter of a rectangle is equal to P = 2L + 2W where L is length and W is width. Thus, 26 = 2(2w - 5) + 2w We solve for x: 26 = 4w - 10 + 2w 26 = 6w - 10 36 = 6w w...

Math
Note that the difference between two consecutive integers is equal to 1. Thus, Let x = first number Let x+1 = the second number Then we set up the equation. It says in the problem that their sum is 59, so x + x + 1 = 59 Finally we solve for x: 2x + 1 = 59 2x = 59 - 1 2x = 58 (...

Math
Recall the formula to convert degree Fahrenheit to degree Celsius: C = (5/9)*(F - 32) Substituting, C = (5/9)*(-4 - 32) C = (5/9)*(-36) C = -20 deg Celsius Hope this helps~ :3

algebra 1
First represent the unknowns with variables. Note that the difference between two consecutive integers is one, so: Let x = first integer Let x+1 = second integer Let x+2 = third integer Let x+3 = fourth integer Then we set up the equation by following the given condition. x + ...

maths
Substitute (a,a) to x and y: a = -2a + 27 3a = 27 a = 9 Hope this helps~ :3

chemistry
Molarity is a measure of concentration of a solution. It is equal to moles of solute per one liter of solution, or M = n/V units is in mol/L. hope this helps :3

Math
I'll just write some definitions first: * Mixed numbers are composed a whole number and a fraction, for example, 4 4/5 * Improper fractions are fractions whose numerator is greater than the denominator, for instance, 8/3. * Numerator is the number above the bar line of a ...

You're welcome! :)
You're welcome! (◕‿◕✿)

Chem
Let M1 be the concentration of the stock solution. Recall the formula relating molarity and volume: M1 * V1 = M2 * V2 where V1 = initial volume V2 = final volume M2 = final concentration Substituting, M1 * (15.0 mL) = (700 mL) * M2 We solve for M2: M2 = M1 * 15/700 M2 = 0.0214...

math
Because those students who have a sister probably have a brother also or vice versa. So it's like they are counted twice. So naturally the count would be greater than the actual number of students. I'll give you an example. For instance, Marshall has 14 classmates. 5/7...

math
Because those students who have a sister probably have a brother also or vice versa. So it's like they are counted twice. So naturally the count would be greater than the actual number of students. I'll give you an example. For instance, Marshall has 14 classmates. 5/7...

math
First convert feet to inches: 2 1/2 = 5/2 feet 5/2 feet * 12 inches / 1 foot = 30 inches Then we divide this by 9/16 inch: 30 / (9/16) = 30 * 16 / 9 = 160 / 3 = 53 1/3 We only need the whole number (because the number of DVDs cannot be a fraction or decimal). Therefore, 53 ...

math
T = 1/f We solve for f. What we can do here is to get the reciprocal of both sides to get f: reciprocal of T: 1/T reciprocal of 1/f: f Therefore 1/T = f, or f = 1/T

math
I interpreted the inequality as 0.3(0.3x + 0.8) < -0.3 What we'll do here is to solve for x, like what we do in equations: 0.3(0.3x + 0.8) < -0.3 0.09x + 0.24 < -0.3 0.09x < -0.3 - 0.24 0.09x < -0.54 x < -0.54/0.09 x < -6 Hope this helps~ :3

math
Yes, that's right, because notice that the numbers are in harmonic sequence.

math
Yes, that's correct. :)

math
Note that 3x / x = 3, thus 3 * (2x / 6) = 6x / 6 = x

Dma 040
Since we're given the values of V and h, we'll solve for a: V = (1/3)ah 3V = ah 3V/h = a a = 3V/h a = 3*21 / 3 a = 21 hope this helps :3

Dma 040
Since we're given the values of V and h, we'll solve for a: V = (1/3)ah 3V = ah 3V/h = a a = 3V/h a = 3*21 / 3 a = 21 hope this helps :3