Find the attachment photo for complete solution
Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)
Answer:
the largest interval of x values where f(x) is increasing is (-1,1).
Step-by-step explanation:
the domain of f(x) is all real numbers.
As we can conclude from the table that the function f(x) is decreasing from (-3, -1) and the function is increasing from (-1, 1) .
Graphically we can also show this that for the x-values in (1,-1) function is increasing.
Answer:
x=0, y=1.
Step-by-step explanation:
-8x+12y= 12
-2x-12y= -12 Adding these 2 equations:
-10x = 0
x = 0.
Plug this into equation 1:
-8(0) + 12y = 12
12y = 12
y = 1.
Hello there,
Since there are 6 sides to one cube and 6 choices to choose from there is a 1/6 chance of rolling a 2.
Answer: 1/6
Hope this helps!