# Posts by Jai

Total # Posts: 1,998

**math**

3 x 20° = 60°

**Chemistry**

A gas 'collected over water' is a mixture of water vapor and the gas. So P,total = P,gas + P,water vapor You'll solve for P,gas and to do that, you'll need data for vapor pressure of water at 23 C. P,water vapor = 21.1 mm Hg (different sources may show ...

**Math 222**

Yes that's right. `u` Domain is all real numbers or (-infinity, +infinity). And range is (-infinity, 4] since the highest value of g(x) occurs when x^2 is zero. Yes, the graph is a parabola with a maximum (its vertex) which is at point (0,4)

**Math 222**

You take some values of x. Then substitute them to the equation to get the corresponding y values. Plot the points. For instance, y = -x^2 at x = 0, y = -0^2 y = 0 So a point on the graph is (0,0) at x = 1, y = -1^2 y = -1 So a point on the graph is (1,-1) at x = -1, y = -(-1...

**physics**

Assuming ideal gas, use the formula P1 * V1 / T1 = P2 * V2 / T2 Substitute the given, and don't forget to convert temperature to absolute temperature (K units). Celsius to Kelvin conversion: K = C + 273

**Precal**

f(g(x)) = 4(8x+1) - 4 f(g(x)) = 32x + 4 - 4 f(g(x)) = 32x as x ---> 0, = 32(0) = 0

**chemistry**

The dilute acid we're talking about here is H2SO4. So the reactants involved are Cu and H2SO4. The product of this reaction is CuSO4·5H2O. This is the pale blue solution.

**algebra**

A. Well you just substitute a and b: √a * √b √18 * √10 To combine them, we just multiply the terms inside the radical sign and retain the radical sign: √180 √(36*5) √(6^2)(5) 6√5 B. Well we know that 6√5 is also equivalent ...

**algebra(???)**

What's the question...? `u` But I'm assuming that these values of x are roots, and you need to find the polynomial which has these roots. If that's the case, you substitute the values of roots here: (x - root1)(x - root2)(x - root3) = 0 (x + 7)(x - 7)(x - 5/6) = 0 ...

**algebra**

#1. It's not in simplified form because there's a radical sign in the denominator. to remove the radical sign, we multiply both numerator and denominator by √3: (3 / √3) * (√3 / √3) = 3√3 / 3 = √3 #2. Yeah, it's already in ...

**physics**

We use the formula g = GM / r^2 where g = acceleration due to gravity (m/s^2) G = gravitational constant = 6.673 x 10^-11 N-m^2-kg^2 M = mass of larger body (kg) r = distance from center of mass of the body Here, the total distance from the center of earth to the satellite is ...

**MATH**

Use distance formula (point-to-point): d = sqrt((y2 - y1)^2 + (x2 - x1)^2) where (x1,y1) and (x2,y2) are the points involved. In the problem, it was said that the distances from A -> B and A -> C are equal. Therefore, sqrt((4 - 2)^2 + (3 - a)^2) = sqrt((1 - 2)^2 + (-2 - ...

**Math**

Let x = number of quarters since she has twice as many dimes as quarters, Let 2x = number of dimes The total value in $ is 0.25x + (0.10)(2x) And it was said that when the numbers of quarters and dimes are interchanged, she would have $1.20 more than the original. So, (New ...

**Chemistry**

In the balanced chemical reaction, SO2 + 2 Cl2 ---> SOCl2 + Cl2O We make a mole ratio of the species involved, which is Cl2O : Cl2. That is, for every 2 moles of Cl2 reacted, 1 mole of Cl2O is produced, or 1 mol Cl2O / 2 mol Cl2 We are given 0.400 moles of Cl2, and it was ...

**Chemistry**

Density is simply mass per unit volume. ρ = m / V Useful conversions: 1 L = 1000 mL 1 g = 1000000 µg Substitute the values to the formula, and convert.

**Chemistry**

Dilution formula: M1 * V1 = M2 * V2 where M = molarity V = volume Substitute: 8.25 M * 25 mL = 2.40 M * V2 Now solve for V2 and don't forget to convert it to Liters.

**chemistry**

#1. Balance the chemical reaction first. 2 Na2O2 + 2 H2O −--> 4 NaOH + O2 #2. Then calculate the molar mass of Na2O2 and O2. From the periodic table, Na - 23 and O - 16. Thus, Na2O2 : 2*23 + 2*16 = 78 g/mol O2 : 2*16 = 32 g/mol #3. Get the moles of Na2O2 from the ...

**Algebra**

The English alphabet consists of 26 letters, but since x, y and z are not used, we'll have 23 letters to choose from. From 0 to 9, there are 10 numbers total, but there's restriction that the last digit cannot be 0 or 9, so that's 8 numbers total to choose from for...

**algebra 2**

The term with highest degree of x is 10x^3. The degree is 3 (exponent of x), and the leading coefficient is 10 (the numerical coefficient of 10x^3).

**Math**

Area of triangle: A = (1/2)bh Area of circle: A = (π/4)d^2 The remaining area is therefore, (1/2)bh - (π/4)d^2 Substituting, (1/2)(8)(7) - (π/4)(3)^2 = ? Units in in^2. Hope this helps~ `u`

**Math**

14/165

**math**

Volume of rectangular box is length x width x height: V = l*w*h Area of the base is also length x width, so V = (area of the base)*h 18 = (4.5)*h h = 18 / 4.5

**Chemistry**

Ammonium Nitrate is NH4NO3 We need the get the molar mass of this. From the periodic table, the masses of each element in the chemical formula N - 14 H - 1 O - 16 So for NH4NO3, 14 + 4*1 + 14 + 3*16 = 80 g/mol To get the number of moles, we simply divide the given mass by its ...

**math**

4/8 + 3/8 To add this fraction, first make sure their denominators are equal. Their denominators are already equal (which is 8). And so we can combine now their numerators while denominator stays the same: (4 + 3)/8 = 7/8

**math**

Yes. `u`

**Math**

Area of rectangle is length x width. A = l * w substitute and convert: A = (15 ft * (0.305 m / 1 ft)) * (6 ft * (0.305 m / 1 ft)) A = ?

**Inequalities Interval Notation**

#1. (2 + x)(5 + x)(4 - x) < 0 Equate each term inside the parenthesis to zero: 2 + x < 0 x < -2 5 + x < 0 x < -5 4 - x < 0 4 < x x > 4 When x > 4, only the term (4 - x) is negative while the others are positive, so it satisfies the inequality. When x...

**Math**

In a deck of cards, there are 4 different card suits (Hearts, Diamonds, Spades, Clubs) 13 cards in each suit 3 face cards (Jack, Queen, King) in each suit, so 12 face cards total 10 cards which are not face cards, so 40 cards total with no face 1. P(card is not face) = 40/52 2...

**Algebra**

sqrt(x - 11) = sqrt(x) - 1 Well you already have a hint. We square both sides: x - 11 = x - 2sqrt(x) + 1 Simplify it first. And take all terms with radical sign to the right side of equation: x - x - 11 - 1 = -2sqrt(x) -12 = -2sqrt(x) 6 = sqrt(x) Square both sides for the ...

**Algebra**

Place all terms to left side of equation: x^4 + 6x^2 = -8 x^4 + 6x^2 + 8 = 0 This is factorable. But how do you factor this? What we'll do is list all the factor pairs of 8 and from these, we choose the pair which has a sum of 6. 1 x 8 | 2 x 4 | -1 x -8 | -2 x -4 Here, we ...

**science**

We need to find the specific heat capacity of water. This can be found in google or textbooks. specific heat of water = 4.184 J/g-K Then we use the formula Q = m*c*(T2 - T1) where Q = energy (J) m = mass (g) c = specific heat capacity (J/g-K) T = temperature I'm not sure ...

**math, if i have correct answer**

Well if you're doing a proving of trigonometric expressions, you only modify or simplify one side of the equation. Usually it's left side of the equation. So after you're done with proving, you should arrive at an answer sin^2 (θ) = sin^2 (θ)

**Math**

| t - 24 | ≤ 30 There are two cases here: positive and negative: case I: positive t - 24 ≤ 30 t ≤ 30 + 24 t ≤ 54 case II: negative -(t - 24) ≤ 30 -t + 24 ≤ 30 24 - 30 ≤ t -6 ≤ t We get the intersection of these solution: -6 &#...

**Math 222**

(x - root1)(x - root2) = 0 Substitute the given roots: (x - (-1))(x - (-2)) = 0 Now expand this.

**algebra**

Substitute the values for x and y to the given equation, and if it equals to 8, then that point is a solution. For instance take the first point (-1,3): 2x + 3y = 8 2(-1) + 3(3) = 8 -2 + 9 = 8 7 = 8 They aren't equal so that means that point (-1,3) is not a solution to the...

**critical numbers**

I'm assuming that's f'(x) = (x-3)^3 * (x + 4) * (x^2 + 1) instead of f'(x) = (x-3) ^ 3(x + 4)(x^2 + 1) Critical numbers occur at f'(x) = 0 or does not exist. Let f'(x) = 0: 0 = (x-3)^3 * (x + 4) * (x^2 + 1) Will be true if the terms inside the ...

**Algebra 222**

-5x + 2y = 16 y = 2x + 7 To do substitution, choose an equation and from that equation, choose a variable and express it in terms of the other. Then substitute that expression to the other equation. Here, let's choose the second equation. y = 2x + 7 Then let's choose ...

**math**

Volume of rectangular prism: V = lwh Substitute the values: V = 6.5 * 2.5 * 4 V = 65 in^3 Since the juice fills 90% of the box's volume, Volume of juice = 0.90 * 65 = ? hope this helps~ `u`

**Calc 1**

lim [ ln (x)/(sin (5πx)) ] as x → 1 Use L'hopital's rule. Differentiate numerator and denominator separately: lim [ (1/x) / 5π(cos(5πx)) ] as x → 1 Substitute x = 1: = (1/1) / 5π(cos(5π(1))) = 1 / 5π(-1) = -1 / 5π

**math**

Two points make a line. So what we'll do is get any 2 values for x, and get their corresponding y-value. For instance, take x = 3. Substituting this to the linear equation, y = 1/3x - 4 y = 1/3 * 3 - 4 y = 1 - 4 y = -3 Therefore, a point on the line is (3,-3) Another point...

**chemistry**

There are symbols which I don't understand in this problem that you typed, like these ¡æ and ¥ÄH¡Æ. But I understand the reactions. :3 We need to find the ΔH for this reaction: N2H4 + H2 ---> 2 NH3 using the data for these reactions...

**math**

Let tan(θ) = x So that, 2tan^2 (θ) = 3tan(θ) - 1 becomes 2x^2 = 3x - 1 Solving, 2x^2 - 3x + 1 = 0 (2x - 1)(x - 1) = 0 2x = 1 x = 1/2 : first root x = 1 : second root Substitute back tan(θ): tan(θ) = 1/2 θ = tan^-1 (1/2) θ = 26.6 degrees tan...

**PHYSICS**

Your solution for acceleration is correct, but I don't know why you changed units from m/s^2 to N. They aren't the same units, since Newton is force units. Numerically, it's correct as well. Anyway, now that you have acceleration (which is -10.316 m/s^2), we'll...

**Physics**

Formula for open-pipe: f = nv / (2L) Formula for closed-pipe: f = (2n-1)v / (4L) where n = harmonic number v = speed L = length of pipe Just substitute the given values to these equations for n = 3. Units in Hz

**math**

If that's (-3,3) instead of (-3x,3), then the slope is -2. m (slope) = (y2 - y1) / (x2 - x1) m = (-5 - 3) / (1 - (-3)) m = -8 / (1 + 3) m = -8 / 4 m = -2

**Math 222**

I understood it as [ (2x + 7y) / 8x ] - [ (2x + 5y) / 2x ] + 2 We can combine them as long as their denominators are the same. Their LCD is 8x. For the first term, its denominator is already 8x so it stays the same. For the second term, to make 2x become 8x, we multiply the ...

**chemistry**

Assuming ideal gas, we use ideal gas law formula: PV = nRT where P = pressure (atm) V = volume (L) n = moles T = absolute temperature (K) R = universal gas constant = 0.0821 L-atm/mol-K At Standard Temperature & Pressure (STP), T = 273 K and P = 1 atm. Xenon has molar mass of ...

**Physics**

Acceleration is change in velocity over time, or: a = (v2 - v1)/t Initial velocity (v1) and time (t) is given, and final velocity (v2) is zero since it eventually comes to rest. Convert first the initial velocity units to ft/s, then solve for acceleration. Finally, substitute ...

**Math- Probability Please Help!**

(1) Yes it's 24, because, 4 x 3 x 2 x 1 = 24 ways (2) You'll choose 2 pairs of jeans from 7 pairs. Order of the items does not matter, so we'll use combinations: nCr = n! / ( r! (n - r)! ) Thus, 7C2 = 7! / (2! (7 - 2)! ) 7C2 = 21

**Math**

(1) Yes :) (2) No, it's not B. slope: m = (y2 - y1) / (x2 - x1) m = (-35 - (-17)) / (5 - 2) m = -18 / 3 m = -6 slope-intercept form: y - y1 = m(x - x1) y - (-17) = -6(x - 2) y + 17 = -6x + 12 y = -6x + 12 - 17 y = -6x - 5 (3) No, it's not A. If the point is reflected ...

**Heat and properties of matter**

(1) Pressure is force (N) per unit area (m^2): P = F/A P = mg/A P = (5 kg * 9.8 m/s^2) / (0.0001 m^2) P = ? (2) Heat is simply the flow of energy. (3) If there are no more net flow of energy between them. (4) Heat capacity units is J/K. Specific heat capacity units is J/kg-K

**Math**

nPr = n! / (n - r)! So, 6P3 = 6! / (6 - 3)! 6P3 = (6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) 6P3 = (6 x 5 x 4) 6P3 = 120

**Math - Probability**

There are six even numbers from 0 to 10: 0, 2, 4, 6, 8, 10 And there are 11 numbers total. So P(even) = 6/11

**algrebra**

1 meter = 1000 millimeters So, 1.3 meter * (1000 millimeters / 1 meter) = ? Units are in millimeters.

**Algebra**

Multiply numerator by numerator, and denominator by denominator: x/5 * y/z = (x*y) / (5*z) = xy / (5z) I guess that's it. `u`

**Heat and property matter**

density = mass / volume Since mass is constant, when volume is halved, density must be doubled.

**Heat and property matter**

Its volume.

**physics**

Acceleration is change in velocity over time: a = (v2 - v1)/t Initial velocity (v1) is given as 63 km/h. Final velocity (v2) is zero, since it came to rest in 40 s (time). Note that we should convert km/h to m/s too. Thus, a = [ 0 - (63 km/h * (1 h / 3600 s) * (1000 m / 1 km...

**Heat and property matter**

Because pressure is larger at the bottom than at the top.

**physics**

Acceleration is change in velocity over time: a = (v2 - v1)/t Initial velocity (v1) is given as 63 km/h. Final velocity (v2) is zero, since it came to rest in 40 s (time). Note that we should convert km/h to m/s too. Thus, a = [ 0 - (63 km/h * (1 h / 3600 s) * (1000 m / 1 km...

**college math**

If it said, 3.32 ÷ 4 * 10 without brackets and written in one line then, yes, your answer is correct. However if it is, 3.32 ÷ (4 * 10) then the answer is 0.083

**Physics**

Find these values in textbooks or google: Hv = latent heat of vaporization Hf = latent heat of fusion c,water = specific heat of liquid water Formula for energy: Q = m*c*(T2 - T1) Summation of all energy is zero: m,steam*Hv + m,steam(c,water)(T2-100) + m,ice(c,water)(T2-0) + m...

**Chemistry**

Write the balanced reaction: Ca(OH)2 + 2HCl ---> CaCl2 + 2H2O Then we get the moles of HCl by multiplying the given concentration by the volume. I'm assuming that the given concentration, 0.0704 m, is the molarity: M = n/V n = M*V n = 0.0704 M * 18.2 mL n = 1.28128 mmol...

**math**

Let x = number of days Let y = height cleared after x days If they can clear 11.5 ft per day, the height cleared in x days is: y = 11.5x

**calc**

Let x = base of triangle Let y = height of triangle Area of triangle is (1/2) base times height, so A = (1/2)xy 24 = (1/2)xy 48 = xy : eqn(1) If the angle between the two equal sides is 166°, then the remaining angles are: 1/2(180° - 166°) = 7° each In your ...

**math calc**

It's easier to solve if you draw the figure. If you're not sure what 'angle of elevation' or 'angle of depression' is about, I suggest you read some lectures about it first. In your drawing, you can separate them into two right triangles. One triangle ...

**6th grade math**

Let n = number of girls Since there are 11 more boys than girls, Let n+11 = number of boys Since the total number of children in the class is 24, girls + boys = total n + n + 11 = 24 2n + 11 = 24 2n = 24 - 11 2n = 13 n = 6.5 girls n+11 = 17.5 boys ...which cannot be, since ...

**Chemistry**

If the stoichiometric coefficients are multiplied by some number, then the value for ∆H (in kJ/mol) is also multiplied by that number. We got earlier the ∆H formation for CO with fraction stoichiometric coefficients: C + 1/2 O2 ---> CO ; ∆H = -110.4 kJ/mol...

**Chemistry**

∆H for what reaction...? Write the balanced reactions: C + O2 ---> CO2 ; ∆H = -393.7 kJ/mol C CO + 1/2 O2 ---> CO2 ; ∆H = -283.3 kJ/mol CO If the problem asks for ∆H of formation for CO, we can make the second reaction become: CO2 ---> CO + 1/2...

**Algebra**

Represent the unknowns: Let x = one piece Since according to the problem, the other piece is 5 times as long as the first one, Let 5x = other piece Since their total length must be 24 ft, x + 5x = 24 6x = 24 x = 24/6 x = 4 ft. 5x = 20 ft.

**Science**

One of the formulas for uniformly accelerated motion (UAM): h = vo*t - (1/2)gt^2 Ball falls freely, so initial velocity (vo) is zero: h = 0 - (1/2)(-9.8)(0.5^2) h = 1.225 meters Since we're looking for the terminal velocity (vf) we can use the formula, vf^2 - vo^2 = 2gd vf...

**Algebra**

Let x = Meg's age According to the problem, Jill is 2 years younger than Meg: Let x - 2 = Jill's age And it was also said that Beth is half as old as Meg: Let (1/2)x = Beth's age

**Algebra**

Let x = suggested amount of donation If b is the number of bracelets given away, and every person who makes the suggested donation amount will be given one bracelet, then b is also the number of people donated. Therefore, the total collected amount is the number of people ...

**Science (Chemistry)**

"Like dissolves like" is a general rule in solubility. Water is a polar molecule. Its structure is not symmetric, and there is polarity between its elements that compose it - the electronegativity difference between H and O is significantly large. Ionic molecules are...

**Math**

No it's not 8. But you're almost correct, you just forgot to divide it by 2. :) From your solution, p = 2l + 2w 30 = (2 * 11) + 2w 30 = 22 + 2w Put the 22 (from the right side of equation) to the left side, but by doing so, you must change its sign to its opposite. It...

**algebra**

Let x = width Let y = length Area of rectangle is length x width, so A = xy 912 = xy Perimeter of rectangle is 2*(length + width), so P = 2(x + y) 124 = 2(x + y) 62 = x + y Now that you have two equations tow unknowns, we can solve for x and y. From the second equation, we can...

**physics**

P = ρgh where P = pressure (in Pa) g = acceleration due to gravity = 9.8 m/s^2 h = height (in meters) Note that 1 bar = 100000 Pa. Substituting, 100000 = (600)(9.8)(h) h = ? Hope this helps~ `u`

**Redox Reaction**

Write the redox reaction: Mn2+ + BiO3- --→ Bi3+ + MnO4− Balance this redox reaction. Write first the half-reactions: Reduction: BiO3- ---> Bi3+ (charge is changed from 5+ to 3+) Oxidation: Mn2+ ---> MnO4- (charge is changed from 2+ to 7+) Balance them by ...

**Algebra (check my work?)**

1. Yes 2. Yes 3. Let n = number of 4th grade swimmers The ratio of 4th grade swimmers to the total swimmers is 5:16 or 5/16. The total number of swimmers is 80. Therefore, n/80 = 5/16 If you solve this, you'll have n = 25 swimmers (4th grade) hope this helps~ `u`

**pre-calc - JAI**

Sn = n(1+3n)/2 Therefore, S1: 2 = 1(1 + 3(1))/2 S2: 2+5 = 2(1 + 3(2))/2 S3: 2+5+8 = 3(1 + 3(3))/2 They are all true/equivalent for S1, S2, and S3.

**math**

If you want an aquarium in shape of a cube with volume of 8000, then use the formula for volume of cube to find the length of one side: V = s^3 where s = side length Substitute, 8000 = s^3 s = cuberoot(8000) s = 20 inches Well, if you have to draw this on a graphing paper, you...

**pre-calc**

It's difficult to show Gaussian elimination process here. But the answers should be, x = 1, y = -4 and z = -2

**phyiscs**

Modified/simplified continuity equation: S1*v1*ρ1 = S2*v2*ρ2 where S1 and S2 = entrance and exit cross-sectional area v1 and v2 = entrance and exit velocity ρ1 and ρ2 = initial and final density Assuming density of water is constant, we can cancel ρ1 ...

**Science**

Let's have some definitions: Element - the simplest substance made up of one type of atom that cannot be broken down by any chemical means. It can be converted to other elements by nuclear methods, though. Examples are Na, Ca, Mg. Molecule - group of atoms bonded together...

**Math**

Separate them as such: 6x + 5y = 7x + 3y and 7x + 3y = 2(x + 6y - 1) Simplify both equation: Eqn(1): 6x + 5y = 7x + 3y 6x - 7x = 3y - 5y -x = -2y x = 2y Eqn(2): 7x + 3y = 2(x + 6y - 1) 7x + 3y = 2x + 12y - 2 7x - 2x = 12y - 3y - 2 5x = 9y - 2 We can multiply Eqn(1) by -5 so ...

**physics class**

Pressure is force (in Newton) per unit area (in m^2): P = F/A The force here is the weight of the ball, so we must find first the weight of the ball: W = mg where m = mass (kg) g = acceleration due to gravity = 9.8 m/s^2 Substitute the values: W = 5 * 9.8 W = 49 N Therefore ...

**analytical geometry**

Use distance formula: d = sqrt[(y2 - y1)^2 + (x2 - x1)^2] Their distances from one point to (-3,p) must be the same, so sqrt[(-1 - p)^2 + (7 - (-3))^2] = sqrt[(-4 - p)^2 + (4 - (-3))^2] Square both sides: (-1 - p)^2 + (7 + 3)^2 = (-4 - p)^2 + (4 + 3)^2 1 + 2p + p^2 + 100 = 16...

**math**

There are a lot of ways doing these. Mine might be a long way, there might be a shorter way. Anyway, let the contents of each gallon be represented in this format: (12-gallon bucket) - (7-gallon bucket) - (6-gallon bucket) Fill the 12-gallon bucket. Leave the others empty. So...

**Math**

(1) In arithmetic sequence, we just add the common difference, d = 0.25, to a term to get the next term. Therefore, a1 = 16.5 a2 = 16.5 + 0.25 = 16.75 a3 = 16.75 + 0.25 = 17.0 ...and so on. (2) General formula for arithmetic sequence: an = ao + (n-1)d where an = nth term ao = ...

**Math**

F = S/w

**math plz help**

Yes, both are correct. `u`

**ALGEBRA 2 (LOGARITHMIC FUNCTIONS)**

For the next questions, they are all solved with the same method. So I'll guide you to solving #1, then try solving the others by following these steps. We need to find an equation in the form y = ab^x that passes through the points (1,6) and (2,36). What we'll do is ...

**ALGEBRA 2 (LOGARITHMIC FUNCTIONS)**

I'll solve for the first five problems. You have to recall some laws of exponents for these. (1) 3^(x+1) = 27^(x+3) Note that we can rewrite 27 as power of 3: 27 = 3^3. Thus, 3^(x+1) = (3^3)^(x+3) You can distribute the '3' in 3^3 to (x+3). 3^(x+1) = 3^(3(x+3)) 3^(...

**Algebra 2**

(a) "Z" is distinctly different than the other: I think that means you have to count both of them, as if they're different letters. There are five letters in total. Therefore, 5! = 120 ways (b) "Z" is repeated twice in the word FUZZY. Thus, 5! / 2! = 60...

**math -check**

Yes, all the equations you wrote are correct. :) I don't know what window setting means too, and I don't have a graphing calculator. But I think window setting looks like in table (rows,columns) format? I'm not really sure. ^^;

**Math**

Yes it's B. This is another example of conditional probability. Note that there are four vowels here: U, I, O, E. And there are six letters total. So, P(vowel) = 4/6 Then you spin again. The probability of getting a P: P(P) = 1/6 Thus, P(vowel, then P) = 4/6 * 1/6 = 4/36...

**Math**

No it isn't. It was said that time varies inversely as the rate: t = k/r where t = time (hours) r = rate (mph) k = some constant If we solve for the constant, k, k = r*t and this k is the same for all. Therefore if we have two different values for time and rate, r1 * t1 = ...

**Math**

Mass, m, is varies inversely as acceleration, a: m = k / a where k some constant. since f is the constant of variation, we substitute f for k: m = f / a

**integral**

Well the derivative of sec(x) = sec(x) tan(x) dx, as it's one of the formulas usually memorized. So the integral of sec(x) tan(x) dx = sec(x). But if you want a longer method, we let sec(x) = 1/cos(x) and tan(x) = sin(x) / cos(x). Substituting, ∫ sec(x) tan(x) dx &#...

**Precalculus**

Yeah, you have to draw two different triangles for them. It's easier to solve this if you draw them. Anyway, we let arcsin(8/17) be equal to some angle, A. And we let arctan(4/3) be equal to some angle, B. In your drawing of two triangles, label these angles as A and B. We...