Step-by-step explanation:
Use double and triple angle identities:
sin(2x) + cos(3x)
2 sin x cos x + 4 cos³x − 3 cos x
Answer:
q≤7
Step-by-step explanation:
q+8≤15
1) Subtract 8 from both sides:
q≤7
Answer:
4x - 3y -18 = 0 or y = 4x/3 - 6
Step-by-step explanation:
We will have to find the slope of the line first
The formula for slope:

The standard form of equation of a line is:
y = mx + b
We know m,
So the equation will be:

We have to find the value of b, for that we will put any one of the point in the equation
So, putting (6,2)
2 = 4/3 * 6 + b
2 = 8 +b
b = -6
Putting the value of m and b in the standard form of equation of line,
..
Answer:
75
Step-by-step explanation:
Sea level is considered 0. To find 75 feet above sea level, we add 75 to 0. This gets us 75. Since 75 is an integer, it checks out.
Answer:
Area of pathway = 10.375 unit²
Step-by-step explanation:
Given - Peter has built a gazebo, whose shape is a regular heptagon, with
a side length of 1 unit. He has also built a pathway around the
gazebo, of constant width 1 unit, as shown below.
To find - Find the area of the pathway.
Proof -
Central angle =
= 51.43°
Now,
Central angle / 2 =
= 25.71°
And
height =
= 1.038
Now,
Inner area of gazebo = 7·
·1·(1.038) = 3.634 unit²
Outer area of gazebo = (
)²·(3.364) = 14.009 unit²
∴ we get
Area of pathway = Outer area - Inner area
= 14.009 - 3.634
= 10.375 unit²
⇒Area of pathway = 10.375 unit²