The slope of the line CD is (12 - 11)/(5 - 0) = 1/5 The slope of the perpendicular bisector is the negative reciprocal of this (that is -5) The midpoint of line CD is (5/2 , 23/2) The point-slope formula can be used to get...

The slope of the line CD is (12 - 11)/(5 - 0) = 1/5 The slope of the perpendicular bisector is the negative reciprocal of this (that is -5) The midpoint of line CD is (5/2 , 23/2) The point-slope formula can be used to get...

My assumption is that equation is : (x2 +20)1/2 = 3 z1/2 The first step is to square both sides: x2 + 20 = 9 x Rearrange this as" ...

Since point A and point B have the same y coordinate, this line is horizontal. The point P will also have y coordinate of 2. The remaining problem is to find the x coordinate of P. One way to do this is as follows. For some...

There are standard formulas for this type of problem. However, it can also be solved by a combination of simple steps. First, the shortest distance from the point (3,5) to the line y = x +4 (line1) will be along a straight line perpendicular to line1. ...

This problem can be solved using the principle that external work done on a system is equal to the change in energy of the system. In symbols Wext = ΔE = Ef - Ei (here E is KE +PE) I am going to assume...

The rotational kinetic energy, Krot, is (1/2) I ω2 For a disk I = (1/2) m R2 For the case of rolling without frictions ω = vcm/R Putting this together Krot = (1/4) m vcm2 This is one half the translational...

One way to solve this kind of problem is to use a description of lines drawn from formal linear algebra. The line (which will be referred to as Line1): y = x +7 can be described by the ordered triplet (x,y,z) (0, 7, 0) + α (1 , 1 ,0) = ...

It looks like you are on the right track with this one. However, you have a factor of 2 in your equations that I don't understand. Since ρ is quoted in the SI unit (kg/m3) and ultimately one would like to used g = 9.8 m/s2 , it is a good idea to convert the...

How do I work this problem? (answer)

For a fixed value of d, this set is over determined. There are three equations but only two unknowns. One approach is to solve the first two equations for x and y. This can be done by standard methods. The result is: ...

6.43 g water = 0.357 moles water. The balanced chemical equation is 4 HH3 + 5 O2 --> 4 NO + 6 H2O So it takes 5/6 mole of O2 to get 1 mole of water. Since we got 0.357 moles of water, ...

-2tantheta=2√3 (answer)

This is easy with a graphing calculator such as the TI-84 (in degree mode). theta = arctan(-√3) = -60 deg. Other approaches involve using a unit circle chart or Remembering that sin(60) = √3/2...

Absolute value question help (answer)

The solution set is just x = -1/2. The value x = -1/2 can be easily checked to be a solution. A way to see that it is the only solution is to use a graphing calculator such as the TI-84. Put abs(x) into Y1 and abs(x+1) into Y2.

Since the denominator is 3 sqrt(3) =sqrt(7), multiply both top and bottom by 3sqrt(3) + sqrt(7) this results in (2 sqrt(3) +sqrt(7) )( 3 aqrt(3) + sqrt(7) ) /(27 -7) = (18 +5 sqrt(21) + 7 ) / 20 = ( 25 + 5 sqrt(21) ) / 20

The payoff for one punch = 150 /100 + 5/15 = 1.8333 or $1.83 . So you should pay $1.83 (or less) if you want to come out ahead. However, this amount ($1.83) , is the correct amount only if you get a fresh card each time you take that one punch.

Since the x intercepts are 1 and 3, the parabola must have the form: f(x) = A (x-1)( x-3) for some value of A. The bit of information that f(0) = 6, can be used to find A 6 = A (0 -1) (0-3) ...

f(x)=x^2-x-6 (answer)

The function f is a parabola. The standard quadratic form is a x2 + b x +c. So for this case a =1, b= -1, c = -6 The x coordinate of the vertex is -b/2a = 1/2. The y coordinate of the vertex can...

This is an optimization problem in differential calculus. For a can of height, h, and radius, r, the formulas for volume and surface area are: V= pi r2 h A = 2 pi r h + pi r2 + pi r2 (side...

Quadratics (answer)

Since this is a two dimensional system (x,y), gradient just means slope. Call the slope of a tangent line m. The equation of the tangent line is then y = m x +1 Call a candidate point of tangency (x0,y0). Then we require ...

Lagrange Multipliers (answer)

Introduce a Legrange multiplier, λ. The function to be studied is then: h(x,y,z) = xyz + λ (z - exp(-x2-y2)) Denote the partial derivatives with subscripts ( for example hx is the partial derivative of h wrt x) Then the conditions...

Since the standard molar volume is 22.4 L , 6.5 / 22.4 = 0.29 moles of H2 are required. The chemical equation says the one mole of H2 is produced from each mole of Ca. Thus 0.29 moles of Ca must react. The molar mass of Ca is approximately...

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