Complete the square: bending movement in newton meters at a point

[par1996]

I have an a level maths question that i need answering:

The bending movement in newton meters at a point in a beam is given by:

M = 2.5x (15-x) over 2

Where x is the distance in metres from the point of support. You are required to find the values of X when the bending movement is 63Nm.

1) Write down a quadratic equation for this problem

2) Solve the quadratic equation to 3 decimal places.

3) Carry out 2 alternative methods to solve the equation and hence check your answer to question 2.

4) The height S metres of a mass thrown vertically upwards at time T seconds is given by:

S= 90t- 17t squared so the little 2 over the t.

Determine how long the mass will take, after being thrown, to reach a height of 84.1 metres:

part1) on the ascent and on the descent.
part2) Use an alternative method to check your answer to part 1
part3) Comment on your results.

 

[stapel]

I have split your post from the other thread in "Arithmetic". In future, kindly please post your new questions as new threads, rather than as replies to other student's questions; and post your questions to appropriate categories. Thank you.

The bending movement in newton meters at a point in a beam is given by:

M = 2.5x (15-x) over 2

Where x is the distance in metres from the point of support. You are required to find the values of X when the bending movement is 63Nm.

Is "X" meant to be "x", or have they really used both of the two different variables?

Also, what is the definition of "M"? Does it stand for the "bending movement" (or "torque")?

1) Write down a quadratic equation for this problem

You've been given a quadratic equation. What did you get when you copied it down? Did you multiply out the right-hand side? If "M" stands for "newton-meters", what did you get when you plugged the given value in for the specified variable? What did you get when you moved everything over to one side of the "equals" sign? What happened when you multiplied through by "2"?

2) Solve the quadratic equation to 3 decimal places.

Which methods did you use? What solution(s) did you get?

3) Carry out 2 alternative methods to solve the equation and hence check your answer to question 2.

What are the three (or more) methods they've given you? What did you get when you plugged into two of these?

4) The height S metres of a mass thrown vertically upwards at time T seconds is given by:

S= 90t- 17t squared so the little 2 over the t.

Did they really use the two different variables, "t" and "T"? If so, what is the definition of "t"? (If not, please use the given variable.)

Determine how long the mass will take, after being thrown, to reach a height of 84.1 metres:

What did you get when you plugged the given value into the appropriate variable? What two solutions did you obtain?

part1) on the ascent and on the descent.

Considering the shape of the upside-down parabola, which solution is "up" and which solution is "down"?

part2) Use an alternative method to check your answer to part 1
part3) Comment on your results.

Which method did you choose? What results did you obtain? What are your thoughts?

Please be complete, in accordance with what you saw in the "Read Before Posting" thread that you read before posting. Thank you!