Answer:
Domain : 0° < x <90°
Range: 90° < y < 180°.
Step-by-step explanation:
When we have a function:
f(x) = y
the domain is the set of the possible values of x, and the range is the set of the possible values of y.
In this case we have:
x + y = 180°
such that x < y
Let's analyze the possible values of x.
The smallest possible value of x must be larger than 0°, as we are workin with suplementary angles.
Knowing this, we can find the maximum value for y:
0° + y = 180°
y = 180° is the maximum of the range.
Then we have:
0° < x
y < 180°
To find the other extreme, we can use the other relation:
x < y.
Then, we can impose that x = y (this value will not be either in the range nor the domain)
if x = y then:
x + y = x + x = 180
2*x = 180
x = 90°
This will be the maximum of the domain and the minimum of the range.
Then we have that the domain is:
0° < x <90°
And the range is:
90° < y < 180°.
Answer: 5,984 ÷ 32 = 0,187
Ok done. Thank to me :>
Answer:
B = 1.875
Step-by-step explanation:
given that A varies directly as B and inversely as C then the equation relating them is
A = 
← k is the constant of variation
to find k use the condition A = 12 when B = 3 and C = 2 , then
12 = 
( multiply both sides by 2 to clear the fraction )
24 = 3k ( divide both sides by 3 )
8 = k
A = 
← equation of variation
when A = 10 and C = 1.5 , then
10 = 
( multiply both sides by 1.5 )
15 = 8B ( divide both sides by 8 )
1.875 = B
Answer: first option 392.699 square feet.
Explanation:
1) The shape of the sidewalk is an ring with exterior radius equal to the radious of the fountain + 5 feet and inner radius equal to the radius of the fountain.
2) The area of such ring is equal to the area of the outer circle less the area of the inner circle (the fountain)
Area of a circle = π × r²
Area of the outer circle: π (10ft + 5 ft)² = π (15 ft)² = 225 π ft²
Area of the inner circle = π (10ft)² = 100 π ft²
Area of the ring (sidewald) = 225π ft² - 100π ft² = 125π ft² = 392.699 ft²
