Thursday
July 2, 2015

Posts by Jai


Total # Posts: 1,862

Math
14 = 50 - 42/(3+4) * 6
October 8, 2013

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 ...
October 8, 2013

Calculus
s = t^6 * tan(t) - sqrt(t) ds/dt = t^6 (sec^2 (t)) + 6t^5 (tan(t)) - (1/2)(1/sqrt(t))
October 8, 2013

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
October 8, 2013

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
October 8, 2013

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 ...
October 8, 2013

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
October 8, 2013

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...
October 7, 2013

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...
October 7, 2013

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 ...
October 7, 2013

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
October 7, 2013

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
October 7, 2013

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...
October 7, 2013

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! (◕‿◕✿)
October 7, 2013

Science
1. Yep 2. Yep 3. It's magnetic attraction. Iron is attracted to magnet while Sulfur is not. 4. Yep
October 7, 2013

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 ...
October 7, 2013

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 ...
October 7, 2013

Calculus, please check my answers!
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 ...
October 7, 2013

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...
October 7, 2013

maths2
D. No solution
October 6, 2013

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...
October 6, 2013

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
October 6, 2013

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 = ...
October 6, 2013

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 ...
October 5, 2013

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, ...
October 4, 2013

Math PLEASE HELP!!!
letter D is false. For instance, 90 is divisible by 6 and 10, but not divisible by 60.
October 2, 2013

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
October 2, 2013

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
October 2, 2013

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.
October 2, 2013

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
October 2, 2013

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...
October 2, 2013

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...
October 2, 2013

math
15y^7 / 5y^4 = (15/5) * (y^7 / y^4) = 3y^3
October 2, 2013

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
October 2, 2013

math
10^1 - 10^0 = 10 - 1 = 9
October 2, 2013

math
(a+b)^9 / (a+b)^9 = 1
October 2, 2013

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
October 2, 2013

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 ...
October 2, 2013

8th Grade Physical Science
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
October 1, 2013

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 ...
October 1, 2013

Math
134n + 55
October 1, 2013

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...
October 1, 2013

Math
q + 49
October 1, 2013

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...
October 1, 2013

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 (...
October 1, 2013

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
October 1, 2013

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 + ...
October 1, 2013

maths
Substitute (a,a) to x and y: a = -2a + 27 3a = 27 a = 9 Hope this helps~ :3
September 30, 2013

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
September 30, 2013

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 ...
September 30, 2013

You're welcome! :)
You're welcome! (◕‿◕✿)
September 30, 2013

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...
September 30, 2013

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...
September 30, 2013

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...
September 30, 2013

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 ...
September 30, 2013

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
September 30, 2013

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
September 30, 2013

math
Yes, that's right, because notice that the numbers are in harmonic sequence.
September 29, 2013

math
Yes, that's correct. :)
September 29, 2013

math
Note that 3x / x = 3, thus 3 * (2x / 6) = 6x / 6 = x
September 27, 2013

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
September 27, 2013

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
September 27, 2013

Dma 040
Represent the unknowns with variables: Let x = width Let 2x + 7 = length (according to the first statement) Then we set up the equation. To set up, we need to recall that the perimeter of a rectangle is given by P = 2L + 2W where L is length and W is width. We know that P = ...
September 27, 2013

Algebra I
All answers are correct. :)
September 27, 2013

Calculus
limit of (sin^2 (x))/(x^2 - 1) as x -> infinity Note that the range of values of sin x is from -1 to 1, for all real values of x. Thus the range of sin^2 (x) is only from 0 to 1 (as any real number squared results to greater than or equal to zero). Now, for the denominator...
September 27, 2013

Calculus-correction
*oops I made a mistake on x->(pi)- means that x approaches pi (=3.14159) at the LEFT side (thus it is SMALLER than pi, for instance 3.140) But the answer & other explanations are still the same. :)
September 27, 2013

Calculus (first year uni)
First, we get the limit of cot(x) as x->(pi) only. Note that cot(x) is also equal to cos(x)/sin(x). Thus, lim cot(x) as x->pi lim (cos(x))/(sin(x)) = cos(pi) / sin(pi) = -1 / 0 = infinity Now we know that it approaches infinity, but we're not sure of the sign whether...
September 27, 2013

calculus
I think you mean f(x) = 3 + e^(4−x) To get the inverse, replace the f(x) by x, and the x by f'(x), then solve for f'(x): f(x) = 3 + e^(4−x) x = 3 + e^(4 - f'(x)) x - 3 = e^(4 - f'(x)) ln(x - 3) = 4 - f'(x) f'(x) = 4 - ln(x - 3) This is the ...
September 27, 2013

algebra
A < C A + C = 27 M = A + 19 Note that from the third relationship, to maximize M, we also have to maximize A. From the second relationship, we want A to be maximize in a way that it is still less than C. Thus the maximum possible integer for A = 13, so that C = 14. Thus, M...
September 27, 2013

algebra
There might have been some typos in your question, so I interpreted it as ((5x^2-16x+3)/(5x^2+24x-5))*((15x^2-8x+1)/(3x^2+14x-5)) We factor each quadratic equation inside the parenthesis, and simplify. ((5x^2-16x+3)/(5x^2+24x-5))*((15x^2-8x+1)/(3x^2+14x-5)) ((5x-1)(x-3)/(5x-1...
September 26, 2013

chemistry
First we get the amount (the mass, specifically) of calcium chloride needed. Mass is related to number of moles. Recall that molarity (M) is just number of moles (n) divided by the volume (V) in liters: M = n/V Therefore, n = MV n = (0.15 M)(0.2 L) n = 0.03 moles Now, to get ...
September 26, 2013

algebra
Note that when (8+9x) and (8-9x) are multiplied, (8+9x)(8-9x) = 64 + 72x - 72x - 81x^2 = 64 - 81x^2 Thus the least common multiple is 64 - 81x^2 hope this helps~ :3
September 26, 2013

Calculus
Both are correct. (The variation in the answers depends on what "u" to be substituted) Integral (sec^2 (x) tan x) dx This can be rewritten as: Integral (sec(x)*sec(x)*tan(x)) dx Here we use substitution. We let u = sec(x) du = sec(x)*tan(x) dx Substituting, Integral...
September 26, 2013

Algebra
Step 1 & 2 are right. She made the first mistake in Step 3, it should be 2 + 10 = 2y 12 = 2y And so the succeeding steps are wrong too. But the earliest was in step 3. hope this helps :3
September 25, 2013

Math
3a^3 + 4 - 4a - 2a^3 + 6 + 12a - b^3 Before we simplify this, I'll just write some terms: *Variable: in this case, the variables are a and b *Numerical coefficient: the number before the variables *Exponent: number raised to certain term *Constant: the numbers (w/o ...
September 25, 2013

Geometry
When it is rotated about its diameter, the shape formed is a sphere. :)
September 24, 2013

Calculus
Yep, not continuous at x = -8. If you graph the function, it approaches (+) and (-) infinity at x = -8. To prove, we get the lim as x -> (-8)+ (approaching -8 from the right side) and as x -> (-8)- (approaching -8 from the left side) lim |x−8| / (x+8) as x -> (-...
September 24, 2013

Calculus-correction
*oops sorry, I mean x = -8.
September 24, 2013

Calculus
f(x)= |x−8| / (x+8) The function is discontinuous only at x = 8 since it will yield a denominator equal to zero: f(8) = |8-(-8)| /-8+8 f(8) = 16/0 x = 8 is an asymptotic discontinuity. Hope this helps~ :3
September 24, 2013

Algebra II
The original function is k(x) = x^2. Provided that c cannot be equal to zero, we'll compare the following to the original position of the given function: 1. k(x+c) = (x+c)^2 The graph moves c units to the left is c is (+) and c units to the right if c is (-). 2. k(x) + c...
September 24, 2013

Math!!!
#32. n is any nonzero number. n*n = n^2 Therefore it is always (+), regardless of the sign of n. #33. If y is (-), (-y)(-y)(-y) = (-1)^3 * (y^3) = -(y^3) Therefore the sign is (-). #41. Since it is depth (it went down), from the origin it is: -40,230 I think you can do the ...
September 24, 2013

chemistry
First, we get the molar masses to the CuCl2 and H2O. Just get a periodic table and add the individual masses of elements in the chemical formula: CuCl2: 63.55 + 2*35.45 = 134.45 H2O: 2*1 + 1*16 = 18 Then we get their moles. We divide the mass by the molar mass to get the moles...
September 24, 2013

Pre algebra
Let x = number It was said in the first statement that the number is multiplied by itself and then by itself again. Thus, it was multiplied by itself thrice: x*x*x = -1000 x^3 = -1000 We get the cuberoot of this, so that we can get x alone on the left side: cuberoot(x^3) = ...
September 24, 2013

math
Formula for getting an interior angle of a regular polygon with n sides: I = 180(n-2)/n Substituting, I = 180(18-2)/18 I = 160 degrees Hope this helps~ :3
September 24, 2013

Calculus
Your answer is actually correct. :) d/dx (6/ln(x)) d/dx (6*(ln(x))^(-1)) = 6(-1)(1/x)(ln(x))^2 = -6/(x*(ln(x))^2)
September 24, 2013

chemistry
First, we have to get the molar mass of aniline. Just get a periodic table and add the individual masses of the elements in the chemical formula: C6H5NH2: 6*12 + 5*1 + 1*14 + 2*1 = 93 g/mol Then we get the mass of aniline using the given density and volume. Recall that density...
September 23, 2013

Chemistry
Nope, you can't directly convert the 1.27 g sample to moles of Mg because it is impure or not 100% Mg. Since there is some HCl left after the reaction, the impure Mg is the limiting reactant and HCl is in excess. Note that the Mg used was impure. To get the number of moles...
September 22, 2013

Math
#1. Not necessarily. For example, a = -5 and b = -3 |a| = 5 |b| = 3 |a| is greater than |b|, but -5 is NOT greater than -3. #2. Opposites are numbers which have the same distance (numerical value) from zero but different in directions (opposite signs). An example would be -5 ...
September 22, 2013

Calculus
lim (x^4-5x^3+7x^2-6x+3)/(x-1) as x->1 Note that if we substitute 1 to the function, the denominator becomes zero (and we don't want that). But take note that the numerator can be factored: lim (x-1)(x^3 - 4x^2 + 3x - 3) / (x-1) Thus the x-1 will be cancelled, and we&#...
September 22, 2013

math
If that's already the question, then yes. :3
September 22, 2013

8th G-Math
This means that the number of students did not exactly fill the total capacity of the 7 buses, because there are 6 who had to travel in cars. What we'll do here is first, we subtract the 6 "extra" students from the 405, so that we'll know the exact, total ...
September 22, 2013

Math
Represent the unknown with variable. Let x = time that Steve's brother travelled Recall that distance is equal to speed multiplied by time. We get their distances travelled and equate them (since it's said that they followed the same route and they'll overtake at ...
September 22, 2013

maths
Note that you can factor out a(a+b) from the two terms: a(a+b) * (a+b - 2b) Thus, a(a+b)(a-b) Hope this helps~ :3
September 22, 2013

Algebra Answer Check
Yup, they are all correct. :)
September 21, 2013

Chemistry stoch1
First we write the balanced chemical reaction involved: 3Fe + 4H2O -> Fe3O4 + 4H2 Since we have 18 g of steam, we have to convert this to moles and use the stoich ratios from the reaction to get amount of Fe needed to react with it. To convert mass to moles, we get the ...
September 21, 2013

a
0 > x^2 + 5x - 2 We can also rewrite this as x^2 + 5x - 2 < 0 First thing to do is find the roots of the equation. Since the quadratic equation is not factorable in just one look, we use the quadratic formula: x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a Therefore, x = ( -5 +/- ...
September 21, 2013

Math
Note that when two lines are parallel, their slopes are equal. The given equation is 4x - 5y = 8. To get its slope, we change it to the form y = mx + b where m is the slope and b is the y-intercept. Therefore, 4x - 5y = 8 -5y = -4x + 8 y = (4/5)x - 8/5 The slope is equal to 4/...
September 20, 2013

Geometry
Note that we can form a right triangle here, with base equal to 100 ft and angle between hypotenuse and base equal to 48°. Let h = height of triangle, which is also equal to total height of statue minus the 5 ft elevation of the device. Thus, tan 48° = h / 100 h = 100...
September 20, 2013

Geometry
To get the distance, use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) Assuming the point where the home lies is at the origin (0,0), thus the beach lies at (120, -30). Substituting, d = sqrt((120 - 0)^2 + (-30 - 0)^2) d = sqrt(14400 + 900) d = sqrt(15300) d = 123....
September 20, 2013

Geometry
Angle of depression is the angle below the horizontal that an observer must look in order to see an object below him. If you draw the figure, you can actually see that the hot-air balloon is located 25° above the horizontal. We actually formed a triangle here, with height ...
September 20, 2013

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