1. -15(-9)=
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
We khow that the equation of a circle is written this way :
(x-a)²+(y-b)²=r² where (x,y) are the coordinates of the cercle's points and (a,b) the coordinates of the cercle's center and r the radius .
Our task is to khow the values of a and b :
- We khow that the center is lying on the line 3x+2y=16⇒ 2y=-3x+16⇒ y=
x+8
- We khow that the points P and Q are two points in the cercle
- Let Ω be the center of this cercle
- we can notice that : PΩ AND QΩ are both equal to the radius ⇒ PΩ=QΩ= r
- So let's write the expression of this distance using vectors KHOWING THAT Ω(a,b)
- Vector PΩ(a-4,b-6) and Vector QΩ(a-8,b-2)
- PΩ=
and QΩ=
- Let's substitute a by x and b by y
- PΩ=QΩ we substitute each distance by its expression
- After simplyfying the expressions we get finally : -12+8x-8y=0
- now we have -12x +8x-8y=0 and the line equation 3x+2y-16=0
- these are simultanious equations so after solving them we get x=3.8 wich is approximatively 4 and y=2
- we substitute a by 4 and y by 2 in PΩ to get the radius
- we get r =
= 4
- so r²= 16
- then the equation is : (x-4)²+(y-2)²=16
<u>First Train:</u>
Time taken = 9 hours (2pm to 11pm)
Let the speed be x
Distance = Time x Speed = 9x
<u>Second Train:</u>
Time taken = 5 hours (6pm to 11pm)
Speed = x + 48
Distance = Time x Speed = 5(x + 48)
Since both the distance they traveled are the same, we equate the distance to solve for x.
<u>Solve for x:</u>
9x = 5(x + 48)
9x = 5x + 240
4x = 240
x = 60
<u>Find the speed:</u>
x = 60 mph
x + 48= 108 mph
Answer: The spend of the two trains are 60 mph and 108 mph.