3. {6,9,15)
for these u have use Pythagoras theorem
Related angle is 45 degrees, set up a triangle and use exact trig values to solve for x and y, then rationalise the denominators
Answer:
number of ways = 720
Step-by-step explanation:
The number of ways six people sit in a six-passenger car is given by the number of permutations of 6 elements in 6 different positions ( seats), then
number of ways = number of permutations of 6 elements = 6! = 6 * 5 * 4 *3 * 2 * 1 = 720
Since the first person that sits can be on any of the seats , but then the second person that sits can choose any of 5 seats (since the first person had already occupied one) , the third can choose 4 ... and so on.
Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.
The distances:
- from perihelion to the sun in terms of ellipse is a-c;
- from aphelion to the sun in terms of ellipse is a+c.
Then

Add these two equations:
and subtract first equation from the second:
Note that
thus

The equation for the planet's orbit is

Answer:

Step-by-step explanation:
The equation that will model this situation will be of the form
where
is the time in hours john has traveled since the gas station, and
is the distance.
Now we know that John has already traveled 20 miles when he is at the gas station, this means at
,
; or


Thus we have
.
Now we need to figure out 
When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have


Now we have the full equation:
