Certainly use the number line to work out half way, but children also need to be shown that by adding the two numbers and then halving the answer will also give them the correct answer.

At this stage we are keeping to smaller multiples of 10 but this method applies to finding halfway between any pair of numbers. For all that's new and revolutionary about the Jaguar XF, it's good to see that the company, in this period of transition, has found a way to pump genuine Lucas-brand electrical smoke back into the wires. The second XF is let out of its cage at the push of a button, one marked with a checkered flag and discreetly placed near the electronically actuated parking brake on the center console. What's even better than the insane power being churned by the rotor-type supercharger is that the chassis handles it so well.

When you consider the smaller size or higher price of other 420-hp machines out there, the $62,200 XF Supercharged is a pretty enticing deal. No photos, news stories, graphics, or logos may be used or reproduced without written permission.

Gears are easy to understand, make, and use, if you know the vocabulary and can space the gears at the correct distance apart.

Pressure Angle: The angle between the line of action (how the contact point between gear teeth travels as they rotate) and the line tangent to the pitch circle.

On the western side of Long Bay, just below the clubhouse of Randwick Golf Club, there is an ocean pool that was closed for over 25 years because of the pollution that used to cover the area. After you have estimated you have returned back to a point perpendicular to the entry point (depth about 6 metres), turn to the south-west. The best exit point, especially at or near high tide is the small channel adjacent to your entry point. Other fish to be seen here include Port Jackson sharks, bream, snapper, yellowtail, whiting and six-spined, reef, rough and velvet leatherjackets, as well as the occasional huge crayfish. Copyright © Michael McFadyen 1990 to 2016Non-commercial use of an article or photograph is permitted with appropriate URL reference to this site. That, or it's programmed a secret quirk machine and hidden it deep within the core of the car's structure.

The reservoir seemed to be full of orange cool-juice, but my reboot failed to make the message disappear. Like the way the hood curves up and stretches forward like a giant aluminum phallus, or the way the throttle response is just slow enough to allow deep V-8 vibrations without producing excess speed. In addition to firming up the CATS (now fully functional, by the way) the setting disables stability control and significantly tightens throttle response. With the XK coupe on which the XF is based, the naturally aspirated car feels just right but the supercharged XKR's chassis can feel strained. Think of it as the density of teeth — the higher the number, the smaller and more closely spaced the teeth on a gear.

It is also well known as the site of the wreck of the MV Malabar and the Malabar Sewage Treatment Plant. Take the small narrow slit on the south side of the hole and continue in a south-easterly direction.

These rocks have a number of overhangs which contain big numbers of bullseyes and eastern rock blackfish. Once again, it is probably easier to exit along the bottom, using your hands to assist your progress. It is a little more difficult to find a good spot to actually exit the water but you will be safe.

Dive shops, dive operators, publications and government departments cannot use anything without first seeking and receiving approval from Michael McFadyen. Not sure what else could account for my very British experience with the 2009 XF Supercharged. I soldiered on and promised the car I'd take a closer look the next morning when the engine was cold. But that's just half of the XF Supercharged experience — this is two cars in one modern, mostly attractive body. And by "tightens," I mean it cuts all 420 horses loose with the urgency of a starter pistol. That isn't the case with the XF, which just takes all that power and sets it gently onto the ground. Although rarely used to identify off the shelf gears, you may need this parameter when modeling gears in 2D and 3D software like we’re doing here.

On a gear with an odd number of teeth, if you draw a line from the center of one tooth straight through the center across the gear, the line will fall between two teeth. Since the opening of the new ocean outfall in 1990, the diving population of Sydney has been able to finally dive the area around Malabar, including Long Bay. This dive is able to be able to be done in all but the biggest easterly and southerly seas. Which I did, only to find this Jag had so much coolant that I could have scooped a Big Gulp out and it'd still be full.

Jaguar claims that 86 percent of the engine's torque (413 lb-ft) is available from 2000 rpm to redline, and there'll be no questioning the validity of that claim. So, just be careful using outside diameter in your calculations if you estimated it from a gear with an odd number of teeth.

It’s not important to understand this parameter, just to know that the pressure angle of all meshing gears must be the same. At the intersection of Bay Parade and Howe Street, Malabar, the golf club has a three tier carpark which is an ideal place to park your car.

More people have probably dived this area in that first year and a half than in the entire previous 30 years. After putting on all your gear, go down the steps to the pool and walk out along the edge closest to the water. Kelp patches appear regularly and I have seen common sea dragons hiding mixed up in the kelp. Follow the edge to the south-east (although in some spots it goes south, east and even north-east) past a large kelp bed. The reef disappears in some places, so if you find yourself over sand, head west until you meet rock again.

We may have forgotten it, but the knowledge is in there somewhere.First we make a table of values so we can graph some points, and then we see the shape we're getting and connect the dots. Swim out due east on the surface for about 15 metres until you see a small sand patch before submerging. Therefore, 0 is the only value of x we can plug into the equation y = x2 if we want to get 0 for y.

Un-coincidentally, the only point on the graph of y = x2 with a y-coordinate of 0 is the point (0, 0). He must be promoting a new film.Let's do some slightly more interesting, though more complicated, examples.

Of course, we could just graph these on the calculator, but we'd like to understand why we're getting the pictures we're getting.

So unless you have one of those calculators that blabs on and on about how it "got there, " let's go ahead and do the work ourselves.Sometimes we'll be asked to sketch a graph. Don't stress; no points will be taken off for less-than-perfectly-straight lines or a complete lack of artistic ability. The idea is to draw the rough shape of the graph and label a couple of easy values, but not to worry about pinpoint accuracy.

The only value we need to label on the sketch is y = 1.The examples we've done so far have been pretty straightforward, but now we'll get into some examples that are straightbackward.

The lowest or highest point of the parabola, depending on which way it opens, is called the vertex of the parabola.

Sample ProblemSketch a graph of y = x2 + 3x + 2.We need to find the intercepts, the vertex, and whether the parabola opens upwards or downwards. We should also find out how late it's going to be open, in case we need to make a late night run.1.

To find the roots, we factor the polynomial, set it equal to zero, and solve for x.x2 + 3x + 2 = 0(x + 2)(x + 1) = 0x = -2, x = -1These are the roots of the polynomial, and as a bonus, they're also the x-intercepts of the parabola. This is an equal opportunity graph.We now know the points (-2, 0) and (-1, 0) are on the graph:Where does the parabola cross the y-axis? What is the vertex?The vertex of a parabola occurs halfway between the roots, at least when the roots exist.

A parabola is no different.When x is outside the x-intercepts, the further away x gets from zero, the larger y gets, and it's not even taking growth hormones. In other words, the solutions to the quadratic equation0 = ax2 + bx + c.This may involve using the quadratic formula. Since not all quadratic equations have solutions, the graph might not have any x-intercepts. It could look like this, for example:The y-intercept is the value we get when we plug x = 0 in to the equation ax2 + bx + c. A parabola will always have a y-intercept, since c will always be some number (possibly 0). With all of this up-in-the-air x-intercept business, it's nice to know we can still rely on c and the y-intercept. Finding the vertex.When a parabola has x-intercepts, the vertex shows up halfway between them. Just like how you're halfway between the ages of your older brother and younger sister, which makes you totally average.

Deciding whether the graph opens upwards ("U'') or downwards (upside-down "U'').The coefficient a on the x2 term tells us whether the graph opens upward or downward. This should be easy to remember, because when you have a positive attitude your mouth forms a "U" shape, but when you're being negative it forms an upside-down "U" shape. Unless you're one of those people who can remain completely straight-faced at all times, in which case you're on your own with this one.Anyway, the reason for this is that as x gets farther from 0, y will be getting more and more negative.

At this stage we are keeping to smaller multiples of 10 but this method applies to finding halfway between any pair of numbers. For all that's new and revolutionary about the Jaguar XF, it's good to see that the company, in this period of transition, has found a way to pump genuine Lucas-brand electrical smoke back into the wires. The second XF is let out of its cage at the push of a button, one marked with a checkered flag and discreetly placed near the electronically actuated parking brake on the center console. What's even better than the insane power being churned by the rotor-type supercharger is that the chassis handles it so well.

When you consider the smaller size or higher price of other 420-hp machines out there, the $62,200 XF Supercharged is a pretty enticing deal. No photos, news stories, graphics, or logos may be used or reproduced without written permission.

Gears are easy to understand, make, and use, if you know the vocabulary and can space the gears at the correct distance apart.

Pressure Angle: The angle between the line of action (how the contact point between gear teeth travels as they rotate) and the line tangent to the pitch circle.

On the western side of Long Bay, just below the clubhouse of Randwick Golf Club, there is an ocean pool that was closed for over 25 years because of the pollution that used to cover the area. After you have estimated you have returned back to a point perpendicular to the entry point (depth about 6 metres), turn to the south-west. The best exit point, especially at or near high tide is the small channel adjacent to your entry point. Other fish to be seen here include Port Jackson sharks, bream, snapper, yellowtail, whiting and six-spined, reef, rough and velvet leatherjackets, as well as the occasional huge crayfish. Copyright © Michael McFadyen 1990 to 2016Non-commercial use of an article or photograph is permitted with appropriate URL reference to this site. That, or it's programmed a secret quirk machine and hidden it deep within the core of the car's structure.

The reservoir seemed to be full of orange cool-juice, but my reboot failed to make the message disappear. Like the way the hood curves up and stretches forward like a giant aluminum phallus, or the way the throttle response is just slow enough to allow deep V-8 vibrations without producing excess speed. In addition to firming up the CATS (now fully functional, by the way) the setting disables stability control and significantly tightens throttle response. With the XK coupe on which the XF is based, the naturally aspirated car feels just right but the supercharged XKR's chassis can feel strained. Think of it as the density of teeth — the higher the number, the smaller and more closely spaced the teeth on a gear.

It is also well known as the site of the wreck of the MV Malabar and the Malabar Sewage Treatment Plant. Take the small narrow slit on the south side of the hole and continue in a south-easterly direction.

These rocks have a number of overhangs which contain big numbers of bullseyes and eastern rock blackfish. Once again, it is probably easier to exit along the bottom, using your hands to assist your progress. It is a little more difficult to find a good spot to actually exit the water but you will be safe.

Dive shops, dive operators, publications and government departments cannot use anything without first seeking and receiving approval from Michael McFadyen. Not sure what else could account for my very British experience with the 2009 XF Supercharged. I soldiered on and promised the car I'd take a closer look the next morning when the engine was cold. But that's just half of the XF Supercharged experience — this is two cars in one modern, mostly attractive body. And by "tightens," I mean it cuts all 420 horses loose with the urgency of a starter pistol. That isn't the case with the XF, which just takes all that power and sets it gently onto the ground. Although rarely used to identify off the shelf gears, you may need this parameter when modeling gears in 2D and 3D software like we’re doing here.

On a gear with an odd number of teeth, if you draw a line from the center of one tooth straight through the center across the gear, the line will fall between two teeth. Since the opening of the new ocean outfall in 1990, the diving population of Sydney has been able to finally dive the area around Malabar, including Long Bay. This dive is able to be able to be done in all but the biggest easterly and southerly seas. Which I did, only to find this Jag had so much coolant that I could have scooped a Big Gulp out and it'd still be full.

Jaguar claims that 86 percent of the engine's torque (413 lb-ft) is available from 2000 rpm to redline, and there'll be no questioning the validity of that claim. So, just be careful using outside diameter in your calculations if you estimated it from a gear with an odd number of teeth.

It’s not important to understand this parameter, just to know that the pressure angle of all meshing gears must be the same. At the intersection of Bay Parade and Howe Street, Malabar, the golf club has a three tier carpark which is an ideal place to park your car.

More people have probably dived this area in that first year and a half than in the entire previous 30 years. After putting on all your gear, go down the steps to the pool and walk out along the edge closest to the water. Kelp patches appear regularly and I have seen common sea dragons hiding mixed up in the kelp. Follow the edge to the south-east (although in some spots it goes south, east and even north-east) past a large kelp bed. The reef disappears in some places, so if you find yourself over sand, head west until you meet rock again.

We may have forgotten it, but the knowledge is in there somewhere.First we make a table of values so we can graph some points, and then we see the shape we're getting and connect the dots. Swim out due east on the surface for about 15 metres until you see a small sand patch before submerging. Therefore, 0 is the only value of x we can plug into the equation y = x2 if we want to get 0 for y.

Un-coincidentally, the only point on the graph of y = x2 with a y-coordinate of 0 is the point (0, 0). He must be promoting a new film.Let's do some slightly more interesting, though more complicated, examples.

Of course, we could just graph these on the calculator, but we'd like to understand why we're getting the pictures we're getting.

So unless you have one of those calculators that blabs on and on about how it "got there, " let's go ahead and do the work ourselves.Sometimes we'll be asked to sketch a graph. Don't stress; no points will be taken off for less-than-perfectly-straight lines or a complete lack of artistic ability. The idea is to draw the rough shape of the graph and label a couple of easy values, but not to worry about pinpoint accuracy.

The only value we need to label on the sketch is y = 1.The examples we've done so far have been pretty straightforward, but now we'll get into some examples that are straightbackward.

The lowest or highest point of the parabola, depending on which way it opens, is called the vertex of the parabola.

Sample ProblemSketch a graph of y = x2 + 3x + 2.We need to find the intercepts, the vertex, and whether the parabola opens upwards or downwards. We should also find out how late it's going to be open, in case we need to make a late night run.1.

To find the roots, we factor the polynomial, set it equal to zero, and solve for x.x2 + 3x + 2 = 0(x + 2)(x + 1) = 0x = -2, x = -1These are the roots of the polynomial, and as a bonus, they're also the x-intercepts of the parabola. This is an equal opportunity graph.We now know the points (-2, 0) and (-1, 0) are on the graph:Where does the parabola cross the y-axis? What is the vertex?The vertex of a parabola occurs halfway between the roots, at least when the roots exist.

A parabola is no different.When x is outside the x-intercepts, the further away x gets from zero, the larger y gets, and it's not even taking growth hormones. In other words, the solutions to the quadratic equation0 = ax2 + bx + c.This may involve using the quadratic formula. Since not all quadratic equations have solutions, the graph might not have any x-intercepts. It could look like this, for example:The y-intercept is the value we get when we plug x = 0 in to the equation ax2 + bx + c. A parabola will always have a y-intercept, since c will always be some number (possibly 0). With all of this up-in-the-air x-intercept business, it's nice to know we can still rely on c and the y-intercept. Finding the vertex.When a parabola has x-intercepts, the vertex shows up halfway between them. Just like how you're halfway between the ages of your older brother and younger sister, which makes you totally average.

Deciding whether the graph opens upwards ("U'') or downwards (upside-down "U'').The coefficient a on the x2 term tells us whether the graph opens upward or downward. This should be easy to remember, because when you have a positive attitude your mouth forms a "U" shape, but when you're being negative it forms an upside-down "U" shape. Unless you're one of those people who can remain completely straight-faced at all times, in which case you're on your own with this one.Anyway, the reason for this is that as x gets farther from 0, y will be getting more and more negative.

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