central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm is 0.9 radians
Step-by-step explanation:
We need to find the central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm.
arc length l== 7.2 cm
radius =r= 8 cm
central angle=Ф = ?
The formula used is:
![l=r\theta](https://tex.z-dn.net/?f=l%3Dr%5Ctheta)
Putting values:
![\theta=\frac{l}{r}\\ \theta=\frac{7.2}{8} \\\theta=0.9\,\,radians](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cfrac%7Bl%7D%7Br%7D%5C%5C%20%5Ctheta%3D%5Cfrac%7B7.2%7D%7B8%7D%20%5C%5C%5Ctheta%3D0.9%5C%2C%5C%2Cradians)
So, central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm is 0.9 radians
Keywords: central angle of circle
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Because the polynomial has degree 2, we can assume that there are 2 solutions (roots), whether real or imaginary.
You can subtract 60 in order to put this in standard form
48x^2+44x-60 = 0
From there, just put a,b, and c into the quadratic formula and you're good to solve for your answers.
(-b+-sqrt(b^2-4ac))/2a
(-44+-sqrt(44^2-4(48)(-60)))/2(48)
Then solve.
There is probably a better way, but this should give you the two roots/solutions.
Answer: ![x=-4](https://tex.z-dn.net/?f=x%3D-4)
Step-by-step explanation:
Remember that the line intersects the x-axis when
.Therefore, the zero of a linear function is the value of the variable "x" when the value of "y" is zero.
The equation of the line in Slope-Intercept form is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where "m" is the slope and "b" is the y-intercept.
In this case, given the graph of the function,you can identify that the y-intercept is:
By definition, the slope can be calculated with this formula:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Then, in order to find the slope, you can pick the points (4,2) and (-8,-1) and say that:
![y_2=-1\\y_1=2\\\\x_2=-8\\x_1=4](https://tex.z-dn.net/?f=y_2%3D-1%5C%5Cy_1%3D2%5C%5C%5C%5Cx_2%3D-8%5C%5Cx_1%3D4)
So, substituting these values into the formula, you get:
![m=\frac{-1-2}{-8-4}=\frac{1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1-2%7D%7B-8-4%7D%3D%5Cfrac%7B1%7D%7B4%7D)
Then the linear function has this form:
Finally, in order to find the x-intercept, you can substitute
into the function and solve for "x". This is:
![0= \frac{1}{4}x +1\\\\(-1)(4)=x\\\\x=-4](https://tex.z-dn.net/?f=0%3D%20%5Cfrac%7B1%7D%7B4%7Dx%20%2B1%5C%5C%5C%5C%28-1%29%284%29%3Dx%5C%5C%5C%5Cx%3D-4)
The equation of the vertical line passing through point -4,7 would be X = -4.