Answer: Yes
Step-by-step explanation:
Though x and y can be achieved in a system of equations. The equation
x (t)=0.0411905(t^2)+(-0.164619)t+28.0114
And
y (t)=-0.024127(t^2)+(-0.591143)t+(-87.4403)
Are not system of equations but rather two different models of equations. Nevertheless
To find t in the first equation, x(t) has to be equal to zero.
When the t is substituted in the second equation, t will completely disappear. Given the value of y(t) and vice versa.
Answer:
Option B. ![6.75\ cm^{2}](https://tex.z-dn.net/?f=6.75%5C%20cm%5E%7B2%7D)
Step-by-step explanation:
we know that
The area of a circle is equal to
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
we have
![r=3\ cm](https://tex.z-dn.net/?f=r%3D3%5C%20cm)
substitute
![A=\pi (3^{2})=9 \pi\ cm^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%283%5E%7B2%7D%29%3D9%20%5Cpi%5C%20cm%5E%7B2%7D)
Remember that
radians subtends the complete circle of area ![9 \pi\ cm^{2}](https://tex.z-dn.net/?f=9%20%5Cpi%5C%20cm%5E%7B2%7D)
so
by proportion
Find the area of the related sector for a central angle of
radians
Let
x------> the area of the related sector
![\frac{9 \pi}{2\pi}\frac{cm^{2}}{radians} =\frac{x}{1.5}\frac{cm^{2}}{radians}\\ \\x=9*1.5/2\\ \\x= 6.75\ cm^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B9%20%5Cpi%7D%7B2%5Cpi%7D%5Cfrac%7Bcm%5E%7B2%7D%7D%7Bradians%7D%20%3D%5Cfrac%7Bx%7D%7B1.5%7D%5Cfrac%7Bcm%5E%7B2%7D%7D%7Bradians%7D%5C%5C%20%5C%5Cx%3D9%2A1.5%2F2%5C%5C%20%5C%5Cx%3D%206.75%5C%20cm%5E%7B2%7D)
<span>4x + 2y = 4
6x - 8 = -2y
Both equations are divisible by 2, so divide both sides of both equations by 2.
</span><span>2x + y = 2
3x - 4 = -y
Since the second equation has -y on one side, we can multiply both sides by -1 to solve for y.
y = -3x + 4
Now we substitute y of the first equation with -3x + 4.
This is the substitution method.
2x + y = 2
2x - 3x + 4 = 2
-x + 4 = 2
-x = -2
x = 2
Now we substitute 2 for x in the first original equation and solve for y.
4x + 2y = 4
4(2) + 2y = 4
8 + 2y = 4
2y = -4
y = -2
The solution is x = 2 and y = -2
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