Suppose that y varies directly with x and y3 when x = 9. What is y when x = 18? y = [?]
1 answer:
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What will the radius of your cake be?
This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.
How many slices will you be able to cut?
The total area of a circle is given by:
We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:
Let's name n the number of slices, if we divide the total area by n this result, each area must equal, then:
Finally, we will be able to cut:
Slices
This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.
How many slices will you be able to cut?
The total area of a circle is given by:
We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:
Let's name n the number of slices, if we divide the total area by n this result, each area must equal, then:
Finally, we will be able to cut:
The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:
So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
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