My kids are stuck on this they've no idea what to do and I can't help them out either!
Darren throws a stone from the top of a vertical cliff into the sea below.
The trajectory of the stone can be modelled by the quadratic equation
y = -(x^2/3)+2x+24
where y represents the height in metres of the stone above sea level, and x is the horizontal distance of the stone from the bottom of the cliff
measured in metres.
We don't see a question here!
the demand y for a commodity when its price is ,3x-15/2x+7 find the elasticity of demand when price is 10
Well, you’re ****IT’S SO EASy
I’m sorry for ‘it’s’ reaction
To help your kids understand what to do, let's break down the problem step by step.
Step 1: Understand the Problem
The problem provides a quadratic equation that models the trajectory of a stone thrown by Darren. The equation is y = -(x^2/3) + 2x + 24. Here, y represents the height above sea level, and x represents the horizontal distance from the bottom of the cliff.
Step 2: Analyze the Equation
In this quadratic equation, we have three terms: -(x^2/3), 2x, and 24. The equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. Comparing this with the equation, we can infer that a = -1/3, b = 2, and c = 24.
Step 3: Interpret the Equation
The equation helps us visualize the trajectory of the stone. It tells us how the height (y) of the stone changes with respect to the horizontal distance (x) from the bottom of the cliff. By rearranging the equation, we can find the x-intercepts (where the stone hits the ground) and the vertex (the highest point the stone reaches).
Step 4: Find the x-intercepts
To find the x-intercepts, we set y equal to zero and solve for x. So, we substitute y = 0 into the equation:
0 = -(x^2/3) + 2x + 24
Now we can solve this quadratic equation to find the values of x where the stone hits the ground.
Step 5: Find the Vertex
The vertex represents the highest point the stone reaches. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients from the quadratic equation.
Step 6: Determine the Answer
Using the results from steps 4 and 5, your kids can determine where the stone hits the ground and the highest point it reaches. They can also plot the graph of the equation to visualize the trajectory of the stone.
By following these steps, your kids should be able to analyze and understand the problem regarding the quadratic equation that models the stone's trajectory.