Answer:
111 m²
Step-by-step explanation:
A rectangle is a quadrilateral (has four sides and four angle) with two pairs of parallel sides. Opposite sides of a rectangle are equal to each other. Also all the angles of a rectangle are 90° each.
The area of a rectangle = length * width
For rectangle 1, length = 12 m, width = 3 m
Therefore area of rectangle 1 = length * width = 12 m * 3 m = 36 m²
For rectangle 2, length =(12 m - 3 m - 3 m) = 6 m, width =(15 m - 10 m) =5 m
Therefore area of rectangle 2 = length * width = 6 m * 5 m = 30 m²
For rectangle 3, length = 15 m, width = 3 m
Therefore area of rectangle 3 = length * width = 15 m * 3 m = 45 m²
Area of composite shape = Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3
Area of composite shape = 36 m² + 30 m² + 45 m² = 111 m²
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
<h3>What is the composite function of f(x) and g(x)?</h3>
The composite function of f(x) and g(x) is given as follows:

In this problem, the functions are:
.
The composite function is of the given functions f(x) and g(x) is:

The square root has to be non-negative, hence the restriction relative to the square root is found as follows:


The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:





Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
More can be learned about composite functions at brainly.com/question/13502804
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Answer:
162-x=180
x=342
Step-by-step explanation:
Answer:
The volume of the metal used is 5277.9 cm³.
Step-by-step explanation:
The volume of a cylinder is given by:

Where:
r: is the radius
h: is the height = 50 cm
The volume of metal (
) can be found by subtracting the internal volume (
) from the external volume (
):

The external radius is given by the sum of the internal radius with the tickness:

Hence, the volume is:

Therefore, the volume of the metal used is 5277.9 cm³.
I hope it helps you!
Answer:
The practical domain of the function is [30,32].
Step-by-step explanation:
The given function is

where, p(h) represents the Vonda's weekly pay as a function of hours worked.
She pays a one time $250 chair rental fee, and earns $40 per hour that she works.
Domain is the set of all possible inputs.
The possible domain of the given function is all real numbers but the number of hours can not be negative, therefore h>0.
It is given that Vonda works between 30 and 32 hours per week at a hair salon. So,

Therefore practical domain of the function is [30,32].