Answer:
a.)x² + y² = 900
b.)y = √900 - x²
Step-by-step explanation:
P.S - The exact equation is as follows :
As given,
The shape of the roller coaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
a.)
Equation of circle be x² + y² = r²
As given , leg of the roller coaster is 30 feet above the ground.
⇒ r = 30
⇒x² + y² = 30²
⇒x² + y² = 900
∴ we get
Equation of height of Roller coaster - x² + y² = 900
b.)
As we have, x² + y² = 900
⇒y² = 900 - x²
⇒y = √900 - x²
This is the area of a trapezoid and the formula for that is:
.5(h)(b1 + b2) where h is height and b1 and b2 are the base length or the length of the parallel sides. therefore, our area is:
.5(16)(6+12)
8(18)
144
if you're wondering why the area formula works, construct another trapezoid but this time upside-down. now flip it along it's height axis so you can align one of the side lengths of the 2 trapezoids and you have a parallelogram.
the base of this parallelogram is b1+b2 of the original trapezoid and the height still remains h so the area of this parallelogram is (h)(b1 + b2). however, we want to find the area of the trapezoid but we find that the parallelogram is twice the area of our trapezoid so the area of the trapezoid is half the area of the parallelogram. so area = .5(h)(b1 + b2).
let me know if you have any questions!
Answer:
The monthly expense is $244.16
Step-by-step explanation:
Given:
automobile insurance= $400
health insurance = $140
life insurance = $450
To find:
The monthly expense =?
Solution:
The automobile insurance is Semiannual premium . so it is paid twice a year
So for a year the total automobile insurance paid is = = $800
The health insurance is monthly premium. it is paid for all 12 months.
Thus the health insure for a year is = = $1680
The life insurance is annual premium. so it is paid once in a year
So for a year the life insurance paid is = $450.
The total expense for a year = 800+ 1680 + 450 = 2930
Then for one month the expense will be = = $244.16
Answer:
The radius of the duct is or
Step-by-step explanation:
The picture of the question in the attached figure
we know that
At the point of tangency, the tangent to a circle and the radius are perpendicular lines
so
In the right triangle formed
Applying the Pythagorean Theorem
Remember that
substitute
solve for r
Multiply by 16 both sides
convert to mixed number
----> exact value
The approximate value is