Answer:
danny
Step-by-step explanation:
Danny charges $11 a hour while martin charges $18 a hour
Answer:
f = xy²-2x² satisfies that F = ∇f.
Step-by-step explanation:
F(x,y) = (y² - 4x) i + 2xy j
We want f(x,y) such that
Lets find a primitive of y²-4x respect to the variable x. We need to think y (and y²) as constants here, so a primitive of y² would be xy² the same way that a primitive of k is xk (because we treat y² as constant). A primitive of x is x²/2, thus a primitive of 4x is 2x². Thus, a primitive of y²-4x is xy² - 2x². We can obtain any other primitive by summing a constant, however since we treated y as constant, then we have that
where c(y) only depends on y (thus, it is constant repsect with x).
We will derivate the expression in terms of y to obtain information about c(y)
Thus, is constant. We can take f(x,y) = xy²-2x². This function f satisfies that F = ∇f.
(1+tan²x)/(tan²x) =
1/tan²x + tan²x/tan²x =
cos²x/sin²x + 1 =
cos²x/sin²x + sin²x/sin²x =
(cos²x + sin²x) / sin²x =
1/sin²x =
csc²x.
QED
Approximately 3365 students will score less than 66.
The z-score is calculated using the formula
z=(X-μ)/σ, where μ is the mean and σ is the standard deviation.
For this problem, we have
z=(66-57)/9 = 9/9 = 1.00
Using a z-table (http://www.z-table.com) we see that the area to the left of, or probability less than, this is 0.8413.
To find the number of students out of 4000 that will score in this range, we multiply this probability by 4000:
0.8413(4000) = 3365.2 ≈ 3365
X = 2, y = 1. Tell me if it’s correct