Answer:
Klorina's rate in still water is 4.5 km/h
Current's rate is 0.5 km/h
Step-by-step explanation:
Let
x km/h = Klorina's rate in still water
y km/h = current's rate
<u>With the current (current helps):</u>
Distance = 10 km
Time = 2 hours
Rate = x + y km/h
![10=2(x+y)](https://tex.z-dn.net/?f=10%3D2%28x%2By%29)
<u>Against the current:</u>
Distance = 8 km
Time = 2 hours
Rate = x - y km/h
![8=2(x-y)](https://tex.z-dn.net/?f=8%3D2%28x-y%29)
Divide both equations by 2:
![x+y=5\\ \\x-y=4](https://tex.z-dn.net/?f=x%2By%3D5%5C%5C%20%5C%5Cx-y%3D4)
Add these equations:
![x+y+x-y=5+4\\ \\2x=9\\ \\x=4.5\ km/h](https://tex.z-dn.net/?f=x%2By%2Bx-y%3D5%2B4%5C%5C%20%5C%5C2x%3D9%5C%5C%20%5C%5Cx%3D4.5%5C%20km%2Fh)
Subtract these two equations:
![(x+y)-(x-y)=5-4\\ \\x+y-x+y=1\\ \\2y=1\\ \\y=0.5\ km/h](https://tex.z-dn.net/?f=%28x%2By%29-%28x-y%29%3D5-4%5C%5C%20%5C%5Cx%2By-x%2By%3D1%5C%5C%20%5C%5C2y%3D1%5C%5C%20%5C%5Cy%3D0.5%5C%20km%2Fh)
Due to the Triangle Angle Sum Theorem, we know that the sum of the interior angles of a triangle equals 180 degrees, therefore,
180 = m<1 + m<2 + m<3
180 - m<3 = m<1 + m<2
But, we also know that m<4 + m<3 = 180 degrees.
180 = m<3 + m<4
180 - m<3 = m<4
Both m<4 and m<1 + m<2 equals 180 - m<3
m<4 = m<1 + m<2
The answer
ellipse main equatin is as follow:
X²/ a² + Y²/ b² =1, where a≠0 and b≠0
for the first equation: <span>x = 3 cos t and y = 8 sin t
</span>we can write <span>x² = 3² cos² t and y² = 8² sin² t
and then </span>x² /3²= cos² t and y²/8² = sin² t
therefore, x² /3²+ y²/8² = cos² t + sin² t = 1
equivalent to x² /3²+ y²/8² = 1
for the second equation, <span>x = 3 cos 4t and y = 8 sin 4t we found
</span>x² /3²+ y²/8² = cos² 4t + sin² 4t=1
-29664 is the correct answer. This mostly deals with the zeros and crossing them off
6.b
7.d
8.a
9.c
see attached image. sorry that’s it’s all jumbled up weird, i could only figure out how to put them all together using photoshop. hope these help you out :))