Solve for x. 2(4x+9)=98
2 answers:
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a. The percentage of the circle occupied by the hexagon is 82.7%
b. The percentage of the circle not occupied by the hexagon is 17.3%
Step-by-step explanation:
a regular hexagon inscribed in a circle is approximately 0.827 times the
area of that same circle
1. Assume that area the circle is x
2. Find the ratio of area hexagon to area circle
3. Change The ratio to percentage
4. Subtract area hexagon from area circle to find the area not occupied
by the hexagon and do the same steps 2 and 3 with the area not
occupied and the circle
∵ The regular hexagon inscribed in a circle
∴ Area the circle > area of the hexagon
∵ Area the circle is x
∵ Area the hexagon is 0.827 times the area of the circle
∴ Area hexagon = 0.827(x)
∵ The ratio between area hexagon and area circle =
- Cancel x up with x down
∴ The ratio between area hexagon and area circle = 0.872
- Change the ratio to percentage by multiply it by 100%
∴ The percentage of area hexagon to area circle = 0.827 × 100%
∴ The percentage of area hexagon to area circle = 82.7%
a. The percentage of the circle occupied by the hexagon is 82.7%
∵ Area the circle is x
∵ Area the hexagon is 0.827 x
∴ The area not occupied by the hexagon = x - 0.827 x
∴ The area not occupied by the hexagon = 0.173 x
The ratio between area not occupied by the hexagon and area circle
=
- Cancel x up with x down
∴ The ratio between area not occupied by the hexagon and area
circle = 0.173
- Change the ratio to percentage by multiply it by 100%
∴ The percentage of area not occupied by the hexagon to area
circle = 0.173 × 100%
∴ The percentage of area not occupied by the hexagon to area
circle = 17.3%
b. The percentage of the circle not occupied by the hexagon is 17.3%
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Answer:
Month 4
Step-by-step explanation:
To solve this problem we must propose an equation that models the number of kilometers of bicycle trails made monthly in Charles City and in Tinsel Town
<em>For Charles City </em>we know that the number of kilometers built in the first month is 5, and it doubles every month. Then we have an exponential equation, in base 2, whose initial value is 5.
This equation has the following form:
Where:
is the number of kilometers built in month 1
x is the number of months: {1, 2, 3, 4, 5 ... x}
x = 1 represents month 1.
So:
<em>For Tinsel Town</em> we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.
Where x is the number of months. x: {1, 2, 3, 4, 5 ...}
We want to know at the end of what month the total length of the cycle lanes in Charles City first exceeds the length in Tinsel Town
Then we equal both equations and clear x.
Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.
For x = 3
For x = 4
<em>The value must be between x = 3 and x = 4</em>
For x = 3.8
Then x ≈ 3.8 months.
Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town