The intersection of the three equal squares is a regular triangle.

Question

(The entire shape has 3 axes of symmetry.) Each square has an area of 8. The triangle has an area of 1. The area of the entire shape is 16. What is the area of the black pentagon?

Answer 1

Let's denote the side length of each square as x. Since the area of a square is equal to the side length squared, we can write:

Area of each square = x^2 = 8

Taking the square root of both sides, we get:

x = √8 = 2√2

Since the intersection of the three equal squares is a regular triangle, we can calculate its area using the formula:

Area of a regular triangle = (s^2√3)/4

where s is the length of each side of the triangle. In this case, s is the side length of each square, so s = 2√2.

Area of the triangle = (2√2^2√3)/4 = 4√3

Given that the area of the entire shape is 16, and the area of the triangle is 1, we can calculate the area of the three black pentagons by subtracting the sum of the areas of the squares and the triangle from the total area.

Area of the three black pentagons = 16 - (3 * 8 + 1) = 16 - (24 + 1) = 16 - 25 = -9

The area of the black pentagon is -9. However, since area cannot be negative, there might be an error in the given information or calculations. Please double-check your question or provide additional information.

Answer 2

Please help in under 10 mins. Directions: Use the given rules to complete the table for each sequence and create the ordered pairs. Plot the ordered pairs on the coordinate plane and connect them in order. Then, write a short description of how the corresponding terms are related.

Answer 3

I apologize for the confusion, but I am unable to generate a table, plot coordinates, or connect them within the given timeframe. However, I can still assist you with understanding how the corresponding terms are related based on the given rules if you provide me with the sequence and the rules.

Answer 4

Solve sec(x) cos(3x)=0 from -pi/2,pi/2

Answer 5

To solve the equation sec(x) cos(3x) = 0 from -π/2 to π/2, we can start by considering the two factors:

1. sec(x) = 0
2. cos(3x) = 0

1. For sec(x) = 0, we know that sec(x) = 1/cos(x). Therefore, when sec(x) = 0, cos(x) must be equal to zero. However, we need to find the values of x that satisfy this condition within the given interval.

Looking at the values of cos(x) within the given interval (-π/2 to π/2), we find that cos(x) = 0 for x = -π/2 and x = π/2.

2. For cos(3x) = 0, we need to find the values of x that make cos(3x) equal to zero within the given interval.

We know that cos(3x) = 0 when 3x = π/2 + kπ/2 or 3x = 3π/2 + kπ/2, where k is an integer.

Solving for x in the first equation, we have:

3x = π/2 + kπ/2

x = (π/2 + kπ/2) / 3

Solving for x in the second equation, we have:

3x = 3π/2 + kπ/2

x = (3π/2 + kπ/2) / 3

We need to find these values of x within the given interval. Plugging in k = 0, 1, -1, 2, -2, we get the following values:

For k = 0:
x = (π/2) / 3 = π/6

For k = 1:
x = (π/2 + π/2) / 3 = π/3

For k = -1:
x = (π/2 - π/2) / 3 = 0

For k = 2:
x = (π/2 + 2π/2) / 3 = 5π/6

For k = -2:
x = (π/2 - 2π/2) / 3 = -π/6

Therefore, the solutions for cos(3x) = 0 within the interval -π/2 to π/2 are x = 0, π/6, π/3, 5π/6, and -π/6.

Now, we need to consider the solutions for sec(x) = 0 and cos(3x) = 0 together.

The solutions that satisfy both conditions are x = -π/2, π/2, and π/6.

Hence, the solutions to the equation sec(x) cos(3x) = 0 from -π/2 to π/2 are x = -π/2, π/6, π/2.