What is the value of x in the equation −x = 4 − 3x + 6? 5 10 −5 −10
1 answer:
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1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is , so the measure of arc DF is
The inscribed angle theorem tells us that the central angle subtended by arc DF, , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so
so the measure of arc DF is also 64 degrees. So we have
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2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,
Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that
Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have
Here we want to have x on one side of equation so,
we put number 5 on right side of equation:
abx=5
then we divide both sides by ab to obtain x on left side:
Result:
x=<u />
we put number 5 on right side of equation:
abx=5
then we divide both sides by ab to obtain x on left side:
Result:
x=<u />
The formula for the radius r in terms of x . and for the maximum areas is x=2/+4
Given that,
y forms a circle of radius r
y=2r
r=y/2
(2-y)- forms Square Side x
(2-y) = 4x
x=(2-y)/4
Now Sum of Area's=Area of Square +Area of Circle
Sum = r² + x²
Substitute the r and x values in above equation,
A(y)= y²/4+(y-2)²/ 16
To maximize Area A(y)
A'(y)= 0
2y/4 + 2(y-2)/16 =0
y/2 + (y-2)/8 =0
y = 2/
+4
Y max will be max, x to be maximum.
for maximum sum of areas,
x=2/+4
Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/+4
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