Answer:
85 tables
Step-by-step explanation:
1012 divided by 12 is 84 and 1/3. We want to have room for everyone, so we round up to 85.
For this equation, you want to do it in fractions/ratios to properly solve it. You would have his average misses out of every field goal and his real missed attempts over total. It would look like this
=
You want to solve for x since x is the total amount of field goals that he attempted. You can do this by doing cross multiplication:
(2)(x) = (8)(11)
From here you can get:
2x = 88
Divide each side by 2 to isolate x and you get:
x= 44
So he made a total of 44 field goals.
1) Yes, the relationship in the table is proportional. If, when you've been walking for 10 minutes, you are 1.5 miles away from home, and when you've been walking for 20 minutes, you are 1 mile away from home, and when you've been talking 30 minutes, you are 0.5 miles away from home, then we can see that there is a proportion that happens here. For every 10 minutes you walk, you get 0.5 miles closer to your home.
2) We know that you've been walking 10 minutes already at the start of this problem, and we know that you walk at a steady pace of 0.5 miles every 10 minutes, so we just need to add 0.5 miles to our starting point to get the distance from the school to home, which makes it 2 miles away.
3) An equation representing the distance between the distance from school and time walking could be something like this:
t = 20d
Where t is the amount of time it takes to get home (in this case, t = 40 minutes) and d is the distance you can walk in 10 minutes (in this case, 0.5 miles)
The equation is lame, but that's the best I could do :\
Hope that helped =)
Answer:
(a) square: L; triangle: 0.
(b) square: L·(-16+12√3)/11; triangle: L·(27-12√3)/11
Step-by-step explanation:
<u>Strategy</u>: First we will write each area in terms of its perimeter. Then we will find the total area in terms of the amount devoted to the square. Differentiating will give a way to find the minimum total area.
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In terms of its perimeter p, the area of a square is ...
A_square = p^2/16
In terms of its perimeter p, the area of an equilateral triangle is ...
A_triangle = p^2/(12√3)
Then the total area of the two figures whose total perimeter is L with "x" devoted to the square is ...
A_total = x^2/16 + (L-x)^2/(12√3)
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(a) We know when polygons are regular, the one with the most area for the least perimeter is the one with the most sides. Hence, the total area is maximized when all of the wire is devoted to the square.
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(b) The derivative of A_total with respect to x is ...
dA/dx = x/8 -(L-x)/(6√3)
This will be zero when ...
x/8 = (L-x)/(6√3)
x(6√3) = 8L -8x
x(8 +6√3) = 8L
x = L·8/(6√3 +8) = 8L(6√3 -8)/(64-108)
x = L·(12√3 -16)/11
The total area is minimized when L·(12√3 -16)/11 is devoted to the square, and the balance is devoted to the triangle.
