Answer:
Equation of given circle :- x² + y² = 4
Step-by-step explanation:
The equation of the circle with center (0, 0) and radius r is given by,
x² + y² = r²
It is given that, a circle with center (0,0) and (-1,-3) a point on the circle
To find the radius of circle
radius r = √[(0 - - 1)² + (0 - -3)²] =√(1 + 3) =√4 = ±2
r = 2
<u>To find the equation of circle</u>
x² + y² = r²
x² + y² = 2²
x² + y² = 4
Answer:
85 nails
Step-by-step explanation:
First, we need to calculate the volume of a single nail. It consists of a circular cylinder and hemispherical part.
The volume of the cylinder πr^2 • h. We are given the diameter of the cylinder (14 mm), so radius is half of that (r = 7 mm) and we are given the height (h = 20 mm).
So, the volume of the cylinder is:
V1 = π • 7^2 • 20
V1 = 3077.2 mm^3
Now for the volume of the hemisphere part. Its volume is half of the sphere:
V2 = (4/3 • πr^3) / 2
Diameter of the sphere is given and it is 21 mm, so the radius is 10.5 mm. So, the volume is:
V2 = (4/3 • π • 10.5^3) / 2
V2 = 2423.3 mm^3
So, the volume of the nail is V1 + V2 which is 5500.5 mm^3
Now let's convert volume of the metal used for making nails. It's given that it is 550.55 cm^3 which is 550550 mm^3.
It is also said that 15% of the volume is wasted, so we are left with 85% of the volume, which is 550550 • 0.85 and that equals to 467967.5 mm^3. So to find a number of nails made from this volume, we divide:
467967.5 / 5500.5 = 85 nails
This is a special right triangle called a 30-60-90 triangle. It has a special property the relates the ratio of side lengths. That ratio is 1:
:2
What does this mean? If you know the shortest side of a 30-60-90 triangle, you can find the longer leg by multiplying it by
, and you can find the hypotenuse by multiplying the short leg by 2.
In the picture, note that the short leg of the triangle has a length of 9. Therefore, the long leg(or n) is simply 9
Answer: bag of 50 penguins for 795.95.
Step-by-step explanation:
