Y=- \frac{7}{3}
.
To find the equation of a line, you need two things: the slope and the y-intercept.
The slopes of parallel lines are the same. So we can find the slope of the new line by finding the slope of the first line. To do that, we need to put it in y=mx+b format, where m is the slope. So we must rearrange the 7x+3y=10. First subtract 7x from both sides to make it look like:
Then divide both sides three:
b
So now that it's in y=mx+b format, we can now see that the m= - \frac{7}{3}
Now we know the m of the new equation, we need to find the b, or the y-intercept. To do this, we can plug the point we have and the m value into the y=mx+b format.
Solving this, we can subtract 7/3 from both sides:
Therefore, b=
Plugging the m= - \frac{7}{3} and the b=
back into the y=mx+b format, your parallel line is y=- \frac{7}{3}
.
Answer:
Step-by-step explanation:
Given
--- The radius of each
Required
The area between them
See attachment for illustration of the question. (figure 1)
First, calculate the height of the equilateral triangle formed by the 3 radii (See figure 2)
Using Pythagoras theorem, we have:
Collect like terms
Take square roots
Expand
Split
Now, the area of the equilateral triangle can be calculated using:
Where
Next, is to calculate the area of the sector formed by 2 radii in each circle (figure 3).
Since the radii formed an equilateral triangle, then the central angle will be 60. So:
For the three circles, the area is:
Subtract the areas of the sectors (A2) from the area of the equilateral triangle (A1), to get the area between them.
Approximate
When the balloon is on the ground, it is at point 0. It starts to go up at 5 f/m for a time of 4 minutes. So we will multiply 5 by 4 to get 20. At this point, the balloon is 20 feet off the ground. However, we now know that the balloon descends at 2 f/m at a time of 7 minutes. So we must multiply 2 by 7 to get 14. So we know it was at 20, and then it went down by 14.
20 - 14 = 6 feet
This means that the balloon is now 6 feet above the ground.
I hope I've helped! :)