<h3>Given</h3>
tan(x)²·sin(x) = tan(x)²
<h3>Find</h3>
x on the interval [0, 2π)
<h3>Solution</h3>
Subtract the right side and factor. Then make use of the zero-product rule.
... tan(x)²·sin(x) -tan(x)² = 0
... tan(x)²·(sin(x) -1) = 0
This is an indeterminate form at x = π/2 and undefined at x = 3π/2. We can resolve the indeterminate form by using an identity for tan(x)²:
... tan(x)² = sin(x)²/cos(x)² = sin(x)²/(1 -sin(x)²)
Then our equation becomes
... sin(x)²·(sin(x) -1)/((1 -sin(x))(1 +sin(x))) = 0
... -sin(x)²/(1 +sin(x)) = 0
Now, we know the only solutions are found where sin(x) = 0, at ...
... x ∈ {0, π}
Answer:
b) 5:11
Step-by-step explanation:
count the orange squares and the white squares
Answer:
36 ft²
Step-by-step explanation:
Scale factor means the side length are multiplied by some value. Here, Jack takes 4 feet and multiplies it by a value of 1 1/2.
The side length he wants is one and a half times the length of his neighbor's.
The 'one' means the side length you started with, and the 'one half' means add half to the original length.
one and a half of four is six. (4 plus half of 4, which is 2, so 4 plus 2)
The box is square, so each side is 6 ft, so the area of the box is 6x6 = 36 ft²