Answer:
The probability that a randomly selected point within the circle falls in the white area is approximately 36.3%
Step-by-step explanation:
The given parameters of the area are;
The length of the radius of the circle, r = 4 cm
The length of the side of the inscribed quadrilateral, s = 4·√2 cm
The diagonals of the inscribed quadrilateral = 2 × The radius of the circle
∴ The diagonals of the inscribed quadrilateral are equal and given that the sides of the quadrilateral are equal, the quadrilateral is a square
The probability that a randomly selected point within the circle is white is given by the ratio of the white area to the brown square area as follows;
The white area = The total area - The area brown square
The total area, A = The area of the circle with radius, r = π·r²
∴ A = π·(4 cm)² = 16·π cm²
The area of the brown square, Asq = s² = 4·√2 cm × 4·√2 cm = 32 cm²
The white area, Aw = 16·π cm² - 32 cm² = 16·(π - 2) cm²
The probability that a randomly selected point within the circle falls in the white area is therefore;
By rounding to the nearest tenth of a percent, we have;
The probability that a randomly selected point within the circle falls in the white area, P(W) ≈ 38.3%.
Answer: x= 98°
Step-by-step explanation:
Concept:
Here, we need to know the concept of the "Exterior Angle theorem"
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite angles of the triangle.
If you are still confused, you may refer to the attachment below for a graphical explanation.
Solve:
x = 53 + 45 = 98°
Hope this helps!! :)
Please let me know if you have any questions
We want to find the domain of the following function:
This means that we want to find the x-values that it can take.
<h2>STEP 1: analyzing the simplies form of the function</h2>Let's analyze the simpliest form of the function:
Its graph is:
Then, for the simpliest form of the function, the x-values can only be higher than 0.
This means that its domain is
domain = x > 0
<h2>STEP 2: domain of the given function</h2>Based on the above we can deduce that for the <em>ln(x)</em> function, what is inside the parenthesis should be higher than 0 on this kind of functions.
This is that for
then
In order to find the values of x that make
we must factor it.
We want to find a pair of numbers that when multiplied give the last term (-55) and when added together give the second term (-6).
For the last term of the polynomial: -55, we have that
(-5) · 11 = 55
5 · (-11) = 11
If we add them:
-5 + 11 = 6
5 - 11 = -6
The pair of numbers that when multiplied give the last term (-55) and when added together give the second term (-6), are: 5 and -11
We use them to factor the polynomial:
Then,
In order to find them, we are going to separate the factors (x+5) and (x-11) and analyze when they are positive or negative:
Combining them:
Since we are going to multiply both factors:
We use the diagram to analyze the sign of their product:
Then
when x < -5 and when x > 11. This is the domain.
Therefore, expressed in set notation:
domain = {x|x∈(-∞, -5)∪(11, ∞)}
<h2>Answer: domain = {x | x ∈ (-∞, -5)∪(11, ∞)}</h2>