13.292 might be the right answer :)
Salad and pbj: 24 students
Turkey sandwich and school lunch: 30 students
30
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24
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6
What we know:
12 hour period from 8pm to 8am
temperature dropped from 8°F to 16°F from 8pm to 8am
We need to find temperature at 4 am.
We can start by setting up points:
8pm is are starting point with 8°F, we can express it as (0,8), 0 represents initial time from 0 to 12 hour span.
8am is the ending point with 16°F, we can express it as (12,16), 12 represents the end time of 0 to 12 hours span.
We will use these points to find slope.
slope=m=(16-8)/(12-0)=8/12=2/3
Now, we can set up an expression to find any temperature at a specific time. Aslo, x represents the hours not the the specific time of 4am. We will use 8 since 4am is the 8th hour of the 12 hour span. Using slope of 2/3 and the y intercept of (0,8) since we were already at 8°F at the initial time of 0 we have the function:
f(x)=2/3x+8
f(8)=2/3(8)+8= 40/3≈13.3°
Step-by-step explanation:
f(x) = -16x² + 22x + 3
Factor:
f(x) = (8x + 1) (-2x + 3)
The x-intercepts are (-1/8, 0) and (3/2, 0).
The leading coefficient is negative, so the parabola points down. Therefore, the vertex is a maximum. The x-coordinate is halfway between the x-intercepts.
x = (-1/8 + 3/2) / 2
x = 11/16
f(11/16) = 169/16
So the vertex is at:
(11/16, 169/16)
Graph the x-intercepts and the vertex, then draw a curve through the 3 points.
Answer:
Using Green's theorem we have:
int F.dr =
int int d/dx ((y^2-x^2)/(x^2+y^2)^2) - d/dy (2xy/(x^2+y^2)^2) =
(2x^3 - 6xy^2) / (x^2+y^2)^3 - (2x^3 - 6xy^2) / (x^2+y^2)^3 =
0
Therefore:
int F.dr = 0
Step-by-step explanation: