isolating b2 in A= h1/2(b1+b2) trapezoid formula?
610797
A=h 1/2 (b1 + b2)     \n2A= h (b1 + b2)       mult. both sides by 2\n2A= hb1 + hb2         distribute the "h"\n2A - hb1= hb2         move "hb1" to the other side\n(2A)/h - b1= b2           divide both sides by "h"
741293
the expression of your equation is confusing. It has 2 interpretation but I will solve the two for sure.\n\n your equation is      s=H/b-a    \n\n 1. consider that variable a is not included in the fraction.\n            first, transpose the term H/b to the left that will be\n\n                                s -  H/b = -a \n\n            then, divide both sides by -1 to make the variable a   \n                     positive  that will give you :\n\n                                  a = H/b - s\n\n  2. consider that a is included in the fraction  \n             your equation will be:\n\n                                   s = H/(b - a) \n\n                   first, by cross multiplication  you will get\n\n                               sb - sa = H\n\n                   next, transpose the term sb to the right\n\n                                   - sa = H - sb\n \n                   then divide by  - s  to get the value of a\n\n                       you will get       a =  (sb - H)/s\n\n   Im sure any of the two interpretation I get from it  \nit is in you to decide what you are going to choose.
950045
Correct formula should be as follows:\n\nE = 1/2*I*w^2
66380
You have to use the formula -\nm1s1(t3-t1)=m2s2(t2-t3)\n=>191(4.184)(30.5-25)=38s2(192-30.5)\n=>s2=191(4.184)(5.5)/((38)(161.5)\n=>s2=0.716 J/g.k
791337
1) (1/2 i+2bj) - (bi-b^2 j) + ((7/2 +b)i-bj) = 4i+20j\n\nNow separate the equation into two equations.\n\n1/2 i - bi + (7/2 + b)i = 4 i\n2bj + b^2 j - bj = 20j\n\ni and j are no longer needed so get rid of them too\n\n1/2 - b + 7/2 + b = 4 => 0 = 0 (Not a big help)\n2b + b^2 - b = 20 \n\nb^2 + b - 20 = 0\n\nTime for the quadratic formula.\n\nb = (-1 +- sqrt(1 + 80)) / 2 = -1/2 +- 9/2 = -5, 4\n\n2) x = 1/2 i+2bj\n\nBasically you need to find where b makes the length of the vector equal to one. The Pythagorean Theorem helps here.\n\n(1/2)^2 + (2b)^2 = 1^2\nb = sqrt(3/4) / 2
787829
SOHCAHTOA\nsinθ = O/H = a/c\ncosθ = A/H = b/c\ntanθ = O/A = a/b
521217
The only formula necessary is the definition of the area of a parallelogram, which is width*height (Choose one side as the width. The height is the length of a line segment perpendicular to this side that connects this side to its parallel).\nNote that every triangle forms a parallelogram with a copy of itself. Thus the area of a triangle is half the area of that parallelogram. Note that two sides of the triangle coincide with the two unique sides of the parallelogram, so follow the same instructions as above, choosing one side of the triangle as the width (in this case called a "base") and measuring a line segment drawn perpendicular to this base to the opposite vertex of the triangle as the height of the triangle (really the height of the parallelogram). Take the product and divide by 2.\nA trapezoid has only two parallel sides. Choose one of these sides as the "base", and it is easy to see that you can divide the trapezoid into two (possibly different) triangles and a rectangle (a parallelogram), all of the same height. Simply add these areas together keeping in mind what they have in common to get the formula for the area of a trapezoid.
55347
That's the answer, but that doesn't tell you how:\n\nwrite out the equation like such:\n\n(a+b)(a+b)\n\nNow use a method called the FOIL method.\n\nmulitply the FIRST part of each unit (F from foil)\n\na*a = a^2 (or a squared)\n\nNow multiply the OUTER part of each unit (O from foil)\n\na*b = ab\n\nNow muliply the INNER part of each unit (I from foil)\n\na*b= ab\n\nFinally mulitply the last part of each unit (L from foil)\n\nb*b = b^2 \n\nNow combine all the like terms: \n\nab = ab = 2ab\n\nLeaving  you with:\n\na^2 + 2ab + b^2   (or a squared plus 2ab plus b squared)
797921
"A trapezoid is a 4-sided figure with one pair of parallel sides. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2." The height is the perpendicular distance between the two parallel bases.\n\nArea (trapezoid) = 1/2 h (b1 + b2) , where b1 and b2 are the lengths of the two parallel sides, and h is the perpendicular distance between them.
565612
Take all the terms that include H to one side.\n\nS - 2LW = 2LH + 2WH.\n\nNow, factor out the H from the right side to get:\n\nS - 2LW = (2L + 2W)*H.\n\nNow, divide both sides by what it takes to leave H by itself.  In this case, get rid of the (2L + 2W)\n\n(S - 2LW)/(2L + 2W) = H
829618
1.find the midpoint of BC usingthe midpoint formula\n(x1+x2/2,y1+y2/2) say (x,y)\n2.find the slope os BC using theformula \ny2/y1/x2-x1 say m\n3.the slope of the perpendicular bisector will be the negative inverse of this -1/m\n4. now use the point (x,y) and slope (-1/m) and find the equation of the perpendicular bisector
690597
Using DeMorgan's law, it is A' ∩ B'.\n\nAnother way?  I guess S-A-B?
974937
please complete the equation
1143772
er that formula is false and you cant prove it. i can disprove it for ya.\nyou have a trapezoid with legs a and b, and c and d being the bases. you know that a formula for a trapezoid is the average of the bases times the height: (h)(b1+b2)/2. (c+d)/2 is already the average of the bases, since c = b1 and d = b2. now you have to multiply it by the height. if the formula you're supposed to prove is true, then (a+b)/2 has to be equal to the height. how can that be possible? that will never happen unless you have BOTH of the of the legs are perpendicular to the bases. think about it. if they arent perpendicular to the bases, no matter how you draw the trapezoid, the average of the non parallel legs (a+b)/2 will always be greater than the height.
119628
So, usually the best way to do these is to just fiddle with them until you get them right, but for the sake of it, let's go with a systematic approach using algebra.  First we assign a variable in front of each of the terms on the left and right like:\n\nx Pb  +  y H2O  +  z O2  -->  a Pb(OH)2\n\nSo now we'll write down equations to make sure that we have the same numbers of both sides of each *element*.  I'll do this by writing down the variable in front of each compound in your equation (so x, y z and a) and then multiplying those by the number of times an element exists in that compound.  (So when I'm writing the equation for hydrogen, the H20 term will be 2*y, because y is the coefficient in front of H20 and H occurs twice in that compound).\n\nRemember, the number of any element on the reactants (left) side equals the number of that element on the products (right) side.\n\nFor Pb: x = a, because Pb shows up only once on each side with a subscript of 1, those two compounds will have to be present in the same molar amounts.\n\nFor Hydrogen: 2y = 2a\n\nFor Oxygen: y + 2*z = 2 * a\n\nSo now we have three equations:\n\nx = y\ny = a\ny + 2z = 2a\n\nBut four unknowns, which is fine because we'll just solve for them in terms of one of the variables and then simply choose the last variable to make all the numbers nice.  So solving the equations in terms of a:\n\nx = a\ny = a\nz = (2a - y)/2 = (2a - a)/2 = a/2\n\nSo now we have x, y and z in terms of a free parameter, a.  We'll just choose a = 2, for example, to make x, y and z all turn out as integers.  So now we've chosen:\n\nx = 2\ny = 2\nz = 1\na = 2\n\nSo the balanced equation is:\n\n2 Pb + 2 H2O + O2 --> 2 Pb(OH)2\n\nMake sense?
975170
If the top side represents a and the bottom side represnts b. The height is h. The formula is (a+b)h/2.
868179
2Rb + 2 H20 --> 2RbOH + H2