Consider the relationship 7r+4t=14. a. Write the relationship as a function r=f(t).
1 answer:
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First we are going to draw the triangle using the given coordinates.
Next, we are going to use the distance formula to find the sides of our triangle.
Distance formula:
Distance from point A to point B:
![d_{AB}= \sqrt{[6-(-9)]^2+(10-5)^2}](https://tex.z-dn.net/?f=d_%7BAB%7D%3D%20%5Csqrt%7B%5B6-%28-9%29%5D%5E2%2B%2810-5%29%5E2%7D%20)
Distance from point A to point C:
![d_{AC}= \sqrt{[2-(-9)]^2+(-10-5)^2}](https://tex.z-dn.net/?f=d_%7BAC%7D%3D%20%5Csqrt%7B%5B2-%28-9%29%5D%5E2%2B%28-10-5%29%5E2%7D)
Distance from point B from point C
Now, we are going to find the semi-perimeter of our triangle using the semi-perimeter formula:
Finally, to find the area of our triangle, we are going to use Heron's formula:
We can conclude that the perimeter of our triangle is 140.13 square units.
Next, we are going to use the distance formula to find the sides of our triangle.
Distance formula:
Distance from point A to point B:
Distance from point A to point C:
Distance from point B from point C
Now, we are going to find the semi-perimeter of our triangle using the semi-perimeter formula:
Finally, to find the area of our triangle, we are going to use Heron's formula:
We can conclude that the perimeter of our triangle is 140.13 square units.
See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
