Answer:
Step-by-step explanation:
Given the functions z= (x+4y)e^y, x=u, and y =ln(v)
To get ∂z/∂u and ∂z/∂v, we will use the the composite rule formula:
∂z/∂u = ∂z/∂x•dx/du + ∂z/∂y•dy/du
∂z/∂x means we are to differentiate z with respect to x taking y as constant and this is gotten using product.
∂z/∂x = (x+4y)(0)+(1+4y)e^y
∂z/∂x = (1+4y)e^y
dx/du = 1
∂z/∂y = (x+4y)e^y+(x+4)e^y
dy/du = 0
∂z/∂u = (1+4y)e^y • 1 + 0
∂z/∂u = (1+4y)e^y
For ∂z/∂v:
∂z/∂v = ∂z/∂y• dy/dv
∂z/∂y = (x+4y)e^y+(x+4)e^y •(1/v)
∂z/∂y = {xe^y+4ye^y+xe^y+4e^y}•(1/v)
∂z/∂y = 2xe^y/v+4e^y(y+1)/v
Answer:
13/50
Step-by-step explanation:
#of original states/# of states now
Answer:
Step-by-step explanation:
look, area = length x width
so that means that the area of this rectangle is
= 11 1/2 * 8
= 23/2 * 8
= 23 * 4 (simplified)
= 92 in^2
The interquartile range is found by subtracting Q1 and Q2. We first need to identify the median to do this we cross out from each side until one or two are left in the middle.
<span>437, 456, 513, 650, 893 , 954, 1018, 1038, 1117, 1465
</span>
The median is <span>923.5 found by 893 + 954 / 2 = 923.5
</span>Now we identify the lower median and upper median.
<span>
</span>Lower set: 437, 456, 513, 650, 893
Upper set: 954, 1018, 1038, 1117, 1465
Lower set median or Q1: 513
Upper set median or Q3: 1038
We now would find the difference of the two to get the interquartile range.
Interquartile Range: 1038 - 513 = 525
Answer:
D. 62
Step-by-step explanation:
length = 5 in.
width = 3 in.
height = 2 in.
SA formula = 2(L×W) + 2(L×H) + 2(H×W)
2 (5×3) + 2(5×2) + 2(2×3)
PEMDAS
30+12+20
62