Dwayne is throwing a summer kick-off party. He is making 25 bags of candy as party favors for his guests. Dwayne plans to put at
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Answer:
215.20 ft^2
Step-by-step explanation:
The figure has 2 semi-circles.
First we find the area of each circle using the formula because that is the area formula for a circle.
The semi-circle to the left gives the diameter which is 22 feet. The radius would be half the diameter thus r=11 for semi-circle one.
Then we are to find the diameter of the second semi-circle. Given the entire length to be 30 feet, 30-22 leaves us with 8 feet as its diameter thus r=4.
Left: r=11
Right: r=4
Then, plugging both into the formula for area of a circle, we get
Left: 380.1327
Right: 50.26548
We must divide each by two because we are only looking for semi-circle which is exactly half the area of a full circle.
Then,
Left: 190.066
Right: 25.1327
190.066+ 25.1327= 215.199 = 215.2ft^2
Answer:
I) f + g = 10/3
II) 4f + 2g = 20/3
III) f = 2 and g = 4/3
Step-by-step explanation:
From the chart,
P = 25
q = 40
The total number of one centimeter lines in the first n diagrams is given by the expression
2/3n^3 + fn^2 + gn.
When n = 1, the total number of line = 4. So,
2/3(1)^3 + f(1)^2 + g(1) = 4
2/3 + f + g = 4
Make f+g the subject of formula
f + g = 4 - 2/3
f + g = (12 - 2)/3
f + g = 10/3 ......(1)
When n = 2
Total number of line = 12
2/3(2)^3 + f(2)^2 + g(2) = 12
2/3×8 + 4f + 2g = 12
16/3 + 4f + 2g = 12
4f + 2g = 12 - 16/3
4f + 2g = (36 - 16)/3
4f + 2g = 20/3 ......(2)
(iii) To find the values of f and g, solve equation 1 and 2 simultaneously
f + g = 10/3 × 2
4f + 2g = 32/3
2f + 2g = 20/3
4f + 2g = 32/3
- 2f = - 12/3
f = 12/6
f = 2
Substitutes f in equation 1
f + g = 10/3
2 + g = 10/3
g = 10/3 - 2
g = (10 - 6)/3
g = 4/3
