The thousandth place is the 3rd digit after the decimal.
So your answer is 93.013
Answers:
x = 2√2 units
y = 2√6 units
Explanation:
The given diagram is a right-angled triangle. This means that the special trig functions can be applied.
These functions are as follows:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
For getting x and y, we can choose to either work with θ = 30 or θ = 60.
I will work with 30.
1- For x:
We have:
θ = 30
x is the opposite side to θ
4√2 is the hypotenuse
Therefore, we can apply the sine function as follows:
sin θ = opposite / hypotenuse
sin (30) = x / 4√2
x = sin (30) * 4√2
x = 2√2 units
2- For y:
We have:
θ = 30
x is the adjacent side to θ
4√2 is the hypotenuse
Therefore, we can apply the cosine function as follows:
cos θ = adjacent / hypotenuse
cos (30) = y / 4√2
y = cos (30) * 4√2
y = 2√6 units
Hope this helps :)
Answer:
5
Step-by-step explanation:
Let the smallest integer equal x - 1, the next one equal x, and the last one equal x + 1.
4(x-1) = 3(x-1) + 6
x-1 = 5
x = 6
The smallest integer is x - 1, which is equal to 5. Thus, the smallest of the three integers is 5.
Since g(6)=6, and both functions are continuous, we have:
![\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%20%3D%2045%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2B6f%28x%29%5D%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B9f%28x%29%5D%20%3D%2045%5C%5C%5C%5C9%5Ccdot%20lim_%7Bx%20%5Cto%206%7D%20f%28x%29%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20f%28x%29%3D5)
if a function is continuous at a point c, then
,
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
, f(6) = 5
Answer: 5
