Tuesday
July 29, 2014

Posts by Jai


Total # Posts: 1,493

Calculus
f(x)=sqrt(x^3+2) We can also rewrite this as, f(x) = (x^3 + 2)^(1/2) Then we can use chain rule, f'(x) = (1/2)*(3x^2)*(x^3 + 2)^(-1/2) Finally, the second derivative is f''(x) = (3/2)(2x)(x^3 + 2)^(-1/2) + (3/2)(x^2)(3x^2)(-1/2)(x^3 + 2)^(-3/2) And simplify. Hope t...

geometry
Recall the Pythagorean theorem: c^2 = a^2 + b^2 where c is the hypotenuse (which is also the longest side of a right triangle) and a & b are the legs. Substitute each side lengths to the equation. Of course the longest side is c, and the remaining sides are a and b. If the set...

phys
A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6 mph (with respect to the boat). The speed of the man with respect to the ground is:

Math - Check my answer?
Yes that's correct.

Math check
1. Actually it's B. Expanding, 2(x - 3) = 2x 2x - 6 = 2x -6 = 0 Note that if you get an answer like this (constant = zero), there is no solution. 2. It's D. (btw I don't know why you put question mark beside 3) Expanding, 3(y - 3) = 2y - 9 + y 3y - 9 = 3y - 9 or 0 ...

algebra
Let A = number of sweets of Alvin Let C = number of sweets of Calvin Let M = number of sweets of Melvin According to the statements, A < C A + C = 31 M = A + 24 Note that to maximize M, A should also be maximized. Maximum value of A is 31 (that is, if C = 0), but according ...

geometry
Recall that surface area of cone is SA = pi*r^2 + pi*r*s where r = radius s = slant height Substituting, SA = 3.14 * 15^2 + 3.14 * 15 * 11 SA = 706.5 + 518.1 SA = 1224.6 sq units Hope this helps :3

MATHS
Area of disc (circle): A = pi*r^2 A = 3.14 * 7^2 A = 153.86 cm^2 Area of cardboard (rectangle): A = L * W A = 70 * 50 A = 3500 cm^2 Divide area of rectangle by area of circle: 3500 / 153.86 = 22.75 Take only the whole number: 22 discs Hope this helps :3

Genius Math
Hmm, the triangle seems impossible, because if you draw it, given the condition that AC = BC (thus it's an isosceles triangle), then angle ACB = 96, therefore BAC = 96 degrees also (since the sides opposite to the angles are equal). So if there are two angles which are 96,...

Chemistry
When naming alkanes, alkenes, alkynes, yes, it's the longest chain that is first counted. And then identify the groups attached to to. (For instance methyl, ethyl, etc). Then number the carbon in the longest chain, starting from the nearest attached group (if it's alka...

Mechanics
Recall that Pressure is just Force over a unit Area, or P = F/A We are given the force (which is 220 N), therefore, we only need to find area. A = L*W A = 4*3 = 12 m Therefore, P = 220 / 12 P = 18.33 N/m^2 P = 18.33 Pa Hope this helps :3

math
Find the value of df^-1/dx at x=f(a). f(x)=5x+8, a=-1 i got 5?

science
That's correct. :)

Algebra 1
Let x = weight of chicken in pounds Let y = total cost of x pounds of chicken Therefore, y = 2.99x To see the graph of this, go to wolframalpha . com and type in the equation. Hope this helps :3wol

math
f(x) = 7x - 2

algebra
Substitute T = 141 to the equation: 141 = –0.005x^2 + 0.45x + 125 Simplify: –0.005x^2 + 0.45x + 125 - 141 = 0 –0.005x^2 + 0.45x - 16 = 0 Recall that discriminant is just D = b^2 - 4ac if D < 0 : imaginary root D = 0 : real, equal root D > 0 : two real, une...

Pre-Calculus
*I mean you get all the factors of x = +/- p/q. In the problem, x = +/- 20, and its factors are written there above. The factors are the ones you have to check by substituting them to the expression. :)

Pre-Calculus
You use rational root theorem. Let p = constant term Let q = numerical coefficient of highest degree of x x = +/- p/q In here, p = -20 and q = 1. Thus, x = (+/-) 1 , 2 , 4 , 5 , 10, 20 You have to substitute each factor (for instance x = -1) to the expression, and if you get a...

Math Quick Question
You spoke to that person for 45 minutes only.

Chemistry(DrBob222)
Yes, that's right. :)

math
1/13 = 0.0769230769230... The repeating numbers are 076923 (six numbers), thus, 43 / 6 = 7 remainder 1. Therefore counting from zero, the 43rd digit after the decimal point is 0. hope this helps. :3

Math
1. No 2. Parallel

Math
x + 7 ≥ 3x x - 3x ≥ -7 -2x ≥ -7 x ≤ 7/2 x ≤ 3.5 3x + 4 ≤ 5x 3x - 5x ≤ -4 -2x ≤ -4 x ≥ 2 Therefore, the common solution is from 2 to 3.5, or 2 ≤ x ≤ 3.5 Hope this helps :3

algebra
d = 0.05r^2 + r Substitute r = 45: d = 0.05(45)^2 + 45 d = 101.25 + 45 d = 146.25 ft To the nearest foot, d = 146 ft Hope this helps :3

math
h(n) = 100 / 9 n Substitute n = 27: h(27) = (100 / 9) * 27 h(27) = 100 * 3 h(27) = 300 dollars hope this helps :3

math
12 - q ≥ -13 Just solve it like a true equation: 12 + 13 ≥ q 25 ≥ q or q ≤ 25 Hope this helps :3

Chemistry
Formula to be used: Molality = moles of solute / kg solvent Steps: #1. To do this, get the molar mass of Tin, using a periodic table. Fomula for Tin in Sn (look it up in the periodic table, and you'll see its mass). #2. After you get the mass of Tin, divide it by 5 g, and ...

Chemistry
*repost* Formula for osmotic pressure: Π = MRT * i where m = molarity (mol solute / L solution) R = universal gas constant = 0.0821 L-atm/mol-K T = temperature (K) i = van't Hoff factor (approximately equal to ionizable ions) Note that sucrose is soluble in water, but...

Chemistry
Formula for osmotic pressure: Π = MRT * i where m = molarity (mol solute / L solution) R = universal gas constant = 0.0821 L-atm/mol-K T = temperature (K) i = van't Hoff factor (approximately equal to ionizable ions) Note that sucrose is soluble in water, but does not...

Algebra 1
Yes, your answer is correct. :) (I thought at first the radius is 2 and 1/2, not 21/2, but I guess that's too small) :3

Geometry
Use Heron's formula. Let a, b and c be the sides of a triangle. Let s = a + b + c Therefore the area of triangle can be calculated using this formula: A = sqrt[ (s)(s-a)(s-b)(s-c) ] It should be a little easy using this formula, so I guess you can do it on your own. :) Hop...

Calculus
limit (sin(4x+12))/(5x+15) as x -> -3 If we try substituting, = (sin(4(-3)+12))/(5(-3)+15) = sin(-12+12) / -15+15 = sin(0) / 0 = 0 /0 Note that 0/0 is indeterminate, and if you arrive at this answer, you use the L'hopital's rule. To use the L'hopital's rule,...

Physics
You can use the formula for Uniformly Accelerated Motion (UAM): h = (v,o)t - (1/2)gt^2 Or you can use another formula, which does not use time: v,f^2 - v,o^2 = 2gd where v,f = final velocity v,o = initial velocity g = acceleration due to gravity = 9.8 m/s^2 d = distance (in th...

math
1. Yep 2. The remaining distance is is 120 - 60 = 60 miles (because the first 60 miles was already covered in 1.2 hours according to #1) Speed is distance over time, or v = d/t Substituting, 40 = 60/t t = 60/40 t = 1.5 hours 3. Yep

math
Let x = multiplier. Thus, Men = 7x Women = 5x The ratio of men to women is still 7 to 5. Since there are 440 more men than women, we can say that 7x = 5x + 440 Solving for x, 7x - 5x = 440 2x = 440 x = 220 The total men and women is 7x + 5x = 12x. Thus the total is, total = 12...

Physics
Steps: 1. Get the volume of the sphere (baseball). You re given the diameter, and you can get the radius by dividing this by 2. You are also given the formula: V,sphere = 4/3 * π * r^3 Just substitute the value of radius to get V. 2. Divide the given mass by volume to get...

Physics
If you use the equation for heat released/absorbed to support your explanation, Q = m*c*(T2 - T1) where m is the mass, c is the specific heat capacity and T is the temperature. Since the only substance involved is water, c is the same for both systems. We can also say that the...

Physics
Because ice can absorb more heat from the soft drink to change its state from ice to water (latent heat), than water only. If you use the equation for heat released/absorbed, Let T2 = final temperature of ice (assume it's above 0°C, so it became water at some temp >...

Math
y = (1/2)x^2 - (3/2) -> this is a parabola differentiate: dy/dx = (1/2)*2*x - 0 dy/dx = x The line 4x - 8y = 5 has a slope of, -8y = -4x + 5 y = (1/2)x - 5/8 slope = 1/2 If this line and the tangent line of the parabola are parallel, they have the same slope: dy/dx = x 1/2 ...

Physics
Because it absorbs heat change its state from liquid to gas. This is called the latent heat, and it is a constant-temperature process. If the temperature changes without changing the state of a substance, it is called sensible heat. Hope this helps :3

Math
2a^2 b^3 (4a^2 + 3ab -ab) Distribute to each: 2a^2 b^3 * 4a^2 = 8a^4 b^3 2a^2 b^3 * 3ab = 6a^3 b^4 2a^2 b^3 * (-ab) = -2a^3 b^4 Adding them, 8a^4 b^3 + 6a^3 b^4 -2a^3 b^4 = 8a^4 b^3 + 4a^3 b^4 Actually either there's no answer in the choices, or there is a typo. :3

algebra 1
Um, I think I answered the same question before.. but probably I didn't explain it clearly. :3 First thing we know is that the boiling temperature of water is dependent on the altitude. We can let x as the altitude (independent variable) and y as the boiling temp (dependen...

Math
Yes. :) The equation containing (2,4) with slope equal to -2 is y = -2x + 8.

Math
Is this the continuation of your question? :) In the previous question, we know the slope is -2, and therefore we use the point-slope formula to get the equation: y - y1 = m(x - x1) We only need the slope and one point to get the equation. Let's use the point(2,4). Substit...

PreCal
^No, I'm sorry don't mind my post ^^;

PreCal
2yi = 5x - 2i + 4 Divide everything by 2i to get y alone: 2yi / 21 = (5x - 2i + 4) / 2i y = (5/2i)x - 1 + 2/i Hm, I think there's a typo..

Math
There are actually infinite number of possible point B here, because if point A and point B lie on a line with a slope of -2, then two different points on that line have can be connected with a line of slope equal to -2. (I hope that's clear ^^;) But just to show how to ge...

Math
1. Yep 2. Yep 3. Yep 4. Yep 5. Yep 6. Yep 7. Yep 8. Yep

MATH
Gemma: the first and second ordered pairs Tessa: the third and fourth ordered pairs I think you can observe them easily. hope this helps :3

MATH :)
They are all correct, except #5. 1.30 x 10^4 has three significant figures (1,3 and 0). hope this helps :3

Chemistry
Get first the number of moles (n) of each species. To get the moles, divide the mass by the molar mass. To get the molar mass, get a periodic table and add the individual mass of the elements in the chemical formula. H2O (water): 2*1 + 1*16 = 18 g/mol C3H8O3 (glycerine): 3*12 ...

Chemistry
Get first the number of moles (n) of each species. To get the moles, divide the mass by the molar mass. To get the molar mass, get a periodic table and add the individual mass of the elements in the chemical formula. H2O (water): 2*1 + 1*16 = 18 g/mol C3H8O3 (glycerine): 3*12 ...

Math
64 x 6^4 = 2^6 * 2^4 * 3^4 = 2^10 * 3^4 = 82944

math
Let n = number of laptops sold 5 / 9 = 20 / n 5n = 9 * 20 5n = 180 n = 36 laptops

algebra 1
You can observe that the difference between two consecutive numbers in the pattern is 9.

Chemistry
I think you lack data, and thus, this question cannot be answered.

Chemistry
Molar mass of SO2 = 64 g/mol Divide the given mass by molar mass to get the moles: n = 0.7 / 64 n = ? Now solve for n.

Calculus
Integral of x / sqrt(x-1) dx We can use substitution method. Let u = x - 1 Thus, x = u + 1 and dx = du Substituting, Integral of (u+1)/sqrt(u) du Integral of (u+1)(u^(-1/2)) du Integral of u^(1/2) + u^(-1/2) du = (2/3)*u^(3/2) + (2)*u^(1/2) + C = (2/3)*(x-1)^(3/2) + 2(x-1)^(1/...

Algebra
Just substitute x = -3 to the function: f(x) = 3x - 10 f(-3) = 3(-3) - 10 f(-3) = -9 - 10 f(-3) = -19 Hope this helps :3

math
x = (2/y^2) + 2 Place the 2 from the right side to the left side. x - 2 = 2 / y^2 Multiply both sides by y^2. (x - 2) * y^2 = (2 / y^2) * y^2 (x - 2) * y^2 = 2 Divide 2 from the right side by x - 2 to isolate all terms with y. y^2 = 2 / (x - 2) Finally, get the squareroot. y =...

math
Let n = total number of students. It was said that 60% of n are girls, which is according to the problem, equal to 30. Thus, 60% * n = 30 Note that 60% is also equal to 0.6 in decimal form: 0.6 * n = 30 n = 30/0.6 n = 50 students Hope this helps :3

Chemistry
To do this, you need the the latent heat of vaporization (Lv) for water. In references, the Lv for water is 2256 J/g. The formula for the heat released of absorbed is Q = m * Lv where m = mass Lv = heat of vaporization In this case, heat is released (negative Q) because the st...

Chemistry
To do this, you need the the latent heat of vaporization (Lv) for water. In references, the Lv for water is 2256 J/g. The formula for the heat released of absorbed is Q = m * Lv where m = mass Lv = heat of vaporization In this case, heat is released (negative Q) because the st...

Pre-Calc (Prove the identity)
Recall that formula for sum in tangent: tan (a +/- b) = [tan(a) +/- tan(b)] / [1 -/+ tan(a)tan(b)] Applying this, tan^2(x/2 + π/4) = { [tan(x/2) + tan(π/4)] / [1 - tan(x/2)tan(π/4)] }^2 Note that tan(π/4) = 1, so = [(tan(x/2) + 1) / (1 - tan(x/2))]^2 = (tan...

Math grade 9 and up
x/s + y/w = 1 s/x + w/y = 4 You can use substitution. From the first equation, wx + sy = sw x = (sw - sy)/w Substitute to the second equation: s/x + w/y = 4 sy + wx = 4xy sy + (w)((sw - sy)/w) = 4((sw - sy)/w)y sy + sw - sy = 4y(sw - sy)/w sw^2 = 4swy - 4sy^2 4sy^2 - 4swy + sw...

chemistry
When NH4NO3 is dissolved in water, it dissociates into its ions, followed by a temperature drop: NH4NO3 -> NH4+ + NO3- (though it's not really that relevant though ^^;) Anyway, the heat gained or lost can be calculated using the formula Q = mc(T2 - T1) where m = mass (g...

pre-algebra
Are you sure the first term is w^2 or w^3? Anyway, if it's w^3, w^3 + 4w^2 - 4w = 16 w^3 + 4w^2 - 4w - 16 = 0 w^2(w + 4) - 4(w + 4) = 0 (w^2 - 4)(w + 4) = 0 (w + 2)(w - 2)(w + 4) = 0 w = -2 w = 2 w = -4 Hope this helps :3

Calculus Area between curves
Actually your answer is correct if it's indefinite integral. :) Now that you got the answer, we can now evaluate it at the given bounds: -(1/3)(8-2x)^(3/2) , at x = -7 to 0 = -(1/3)(8-2(0))^(3/2) - [-(1/3)(8-2(-7))^(3/2)] = -(1/3)(8)^(3/2) - [-(1/3)(22)^(3/2)] = (22/3)*(22...

Science
Yes.

Science
Red has the longest wavelength, while violet has the shortest. Arranging the colors from shortest to longest wavelength: VIBGYOR

cal
f(x) = x^2 + √x We can rewrite this as: f(x) = x^2 + x^(1/2) Therefore, the first derivative is f'(x) = 2x + (1/2)*(x^(-1/2)) And the second derivative is f''(x) = 2 + (-1/4)*(x^(-3/2)) Hope this helps :3

chemistry
Let m = mass of NaCl in grams Since the given is in 22% mass/mass, 0.22 = m / 250 m = 0.22 * 250 m = 55 grams NaCl Hope this helps :3

Geometry (math)
I suggest you draw the figure, it's easier to see that way. The planes that intersect are: (1) the plane containing the cross-sectional area (one triangle) and the plane containing one lateral surface area (one rectangle); and (2) the planes containing two lateral surface ...

math
cot x - tan x = 2 cot 2x I will be solving the left side and make it look like the right side. Note that cot x = cos(x) / sin(x) and tan x = sin(x) / cos(x): cos(x) / sin(x) - sin(x) / cos(x) Combining, cos^2 (x) - sin^2 (x) / cos(x)*sin(x): Note that the numerator cos^2 (x) -...

science
Recall that speed is distance travelled over a certain period of time, or v = d/t Since we know the distance (5000 m) and the speed (25 m/s), we can solve for the time: 25 = 5000/t 25t = 5000 t = 5000/25 t = 200 s Hope this helps :3

science
Acceleration is the change in velocity over a certain period of time, or a = Δv / t Substituting, a = (3 m/s) / 4 s a = 0.75 m/s^2 Hope this helps :3

Trigonometry
It would be a lot easier if you draw the figure. What you would do is just a summation of Forces. Since the system is at equilibrium (forces cancel out), the sum of forces should be zero. Sum of forces at x-direction: (T1)*cos(28) - (T2)*cos(35) = 0 Sum of forces at y-directio...

Algebra
If you mean ln (x) = negative number, yes, they can. If you mean ln (negative number) = y, no it's not possible. If you plot ln x, the plot is asymptotic to y-axis from the right (positive values of x only), therefore the plot will never reach x equal to zero nor the negat...

Math
The area of circle is given by, A = pi*(D^2)/4 where D = diameter Substituting, A = ( 3.14 * (5/2)^2 )/4 A = 4.90625 ft^2 In mixed number, this is 4 29/32 ft^2. Hope this helps :3

math
Solve for w: 100w + 10000 = 220w + 7000 100w - 220w = 7000 - 10000 -120w = -3000 w = 3000/120 w = 25 weeks hope this helps :3

Geometry
Concurrent lines are lines that intersect at a single point. Well, a figure cannot be shown here, but try to draw/imagine. For instance, in an x-y plane, you have the three concurrent lines that intersect at the origin. Now, in order to have one pair of parallel lines, the fou...

math
Let x = length. Do ratio & proportion: 10 / 19 = 38 / x Cross-multiplying, 10x = 19 * 38 10x = 722 (10/10)x = 722/10 x = 72.2 in Hope this helps :3

physics
I suggest you draw the figure. Note that if you draw the figure, you'll have a scalene triangle (a triangle with no sides equal). Two of its sides are given (51 and 45), and the angle between them is 180 - 30 = 150 degrees. Since you have two given sides and an angle oppos...

science
Thus, it's a rational number. Note that integer and whole number are the same.

physics
If x is the displacement, note that v (velocity) = dx/dt, and a (acceleration) = dv/dt Therefore, we get the derivative of the given equation: dx/dt = 6t - 3t^2 = velocity Note that this is just the equation for velocity, and we need to maximize it. Thus, we differentiate it a...

Pre-Calculus
D = √(x^2 + 8x + 12) We can also rewrite this as D = (x^2 + 8x + 12)^(1/2) Now we have to get dD/dt. To get the derivative, recall that if x is raised to a certain constant, the derivative is x^n = n*x^(n-1) * dx We multiply the exponent to x, which is jow raised to 1 le...

math
0.875

chemistry
Assuming the gas is ideal, we use the ideal gas law: PV = nRT where P = pressure V = volume n = number of moles R = universal gas constant T = temperature Note that there are two different species involved, but their P and T are the same (of course, R also). Rewriting the equa...

chemistry-correction
*In the second one, I mean you don't usually make solutions of defined volume and concentration in beakers, because these glasswares are not accurate in volume. (sorry about this, I misread ^^;) Also, using volumetric pipettes or simply pipettes are more accurate than grad...

chemistry
The dilution formula is M1*V1 = M2*V2 Substituting, 0.02 * 100 = 0.4 * V2 V2 = 2 / 0.4 V2 = 5 mL The volume of stock solution used is correct. And we need 95 mL of water to make the target solution. One mistake here is adding water to acid. Note that you should NOT add WATER t...

CHEMISTRY
Yes it does. From the problem, it says that 50 cm^3 of AgNO3 and 50 cm^3 of HCl are mixed. Therefore, the total volume of the solution is 50 + 50 = 100 cm^3. Then an assumption is that the density of the solution is 1 g/ cm^3. We have the volume, we have the density, we can ge...

math
a. I'm not sure about this ^^; sorry. b. We add the number of steps to each coordinate. The initial point is (-2,-5). Here, the x-coordinate is -2 and the y-coordinate is -5. When the drummer moved: 1 step right means plus one to the x-coordinate 3 steps up means plus thre...

algebra
Let n = cost of refreshments for 26 people. We can do ratio and proportion here. For every 18 people, the cost of refreshments is $45, while for every 26 people, the cost of refreshments is $ n. Thus, 18 / 45 = 26 / n We cross-multiply: 18n = 45 * 26 18n = 1170 Divide both sid...

Math-Algebra
The pressure of a gas varies directly as its temperature: P = kT Note that the temperature must be absolute (in Kelvin units). To convert, just add 273 to the degree Celsius. Substituting the given, 200 lb/in^2 = k (65.5 + 273) k = 200 / 338.5 k = 0.5908 Now that we know the k...

Math - Algebra
Are you sure it's 81.5 N on the surface of the moon? #1. Anyway, what we'll do is first get the mass of the man. Note that mass is constant, and in physics, it is different from the term 'weight' (though in other cases, they are interchangeable, like in chemist...

math
Because it lies in the x axis.

math
Substitute the pints to the function: at (0,b): f(x) = 2^x / a b = 2^0 / a b = 1/a at (2,0.8): f(x) = 2^x / a 0.8 = 2^2 / a 0.8 = 4 / a a = 4 / 0.8 a = 5 Substituting to the equation for b, b = 1/a b = 1/5 Hope this helps :3

Chemistry
This is a colligative property problem. Note that when an solute is dissolved in a solvent, the freezing point of the solvent decreases. This is called freezing depression, and the change in temperature can be calculated by (T,orig - T,new) = Kf * m where T,orig = original fre...

Math!
Yes it is.

chemistry
Recall that the formula for root mean square speed is given by v,rms = (3RT/M)^(1/2) where R = universal gas constant = 8.314 J/mol-K T = temperature in K M = molar mass in kg/mol We know that the molar mass of O2 is 32 g/mol or 0.032 kg/mol, and the v,rms is equal to 475. Sub...

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