Answer:
Step-by-step explanation:
The directional derivative of a function in a particular direction u is given as the dot product of the unit vector in the direction of u and the gradient of the function
g(x,y) = sin(π(x−5y)
∇g = [(∂/∂x)î + (∂/∂y)j + (∂/∂z)ķ] [sin(π(x−5y))
(∂/∂x) g = (∂/∂x) sin (πx−5πy) = π [cos(π(x−5y))]
(∂/∂y) g = (∂/∂y) sin (πx−5πy) = - 5π [cos (π(x−5y))]
∇g = π [cos(π(x−5y))] î - 5π [cos (π(x−5y))] j
∇g = π [cos (π(x−5y))] [î - 5j]
So, the question requires a direction vector and a point to fully evaluate this directional derivative now.
Let H represent hardcover
let P represent paperback
H + P = 20
H = P + 10
sub in H into the first eq’n
(P + 10) + P = 20
2P + 10 = 20
2P = 10
P = 5
sub P into eq’n 2
H + (5) = 20
H = 15
therefore there are 5 paperback books and 15 hardcover
Answer:
1 3/8.
Step-by-step explanation:
3 1/4 - 1 7/8
First convert to improper fractions:
3 1/4 = (3*4) + 1 / 4 = 13/4.
1 7/8 = (1 *8)+7 / 8 = 15/8. So we have:
13/4 - 15/8
The Lowest Common Multiple of 4 and 8 is 8 so we convert 13/4 to eighth's
13 / 4 = 13*2 / 4 *2 = 26/8
Finally: we have
26/8 - 15/8 = (26 - 15) /8
= 11 /8
= 1 3/8 (answer)
Answer:
B: Group A has less variability in the data.
Step-by-step explanation:
Group A's ages are around the same area while Group B's age is more spread out.
Answer:
240
Step-by-step explanation:
From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.
Fraction of men at the recital = 4/10
Fraction of women at the recital = 6/10
The number of men performers that were in the dance recital will be:
= 4/10 × 600
= 240 men