Answer:
Volume of the sphere is 66.67r/h
Step-by-step explanation:
Hello,
Volume of a sphere = ⁴/₃πr³
Volume of a cylinder = πr²h
The volume of the cylinder = 50ft³
But the cylinder and sphere both have the same radius and height
Volume of a cylinder = πr²h
50 = πr²h
Make r² the subject of formula
r² = 50/πh
Volume of a sphere = ⁴/₃πr³
Put r² into the volume of a sphere
Volume of a sphere = ⁴/₃π(50/πh)r
Volume of a sphere = ⁴/₃ × 50r/h
Volume of a sphere = ²⁰⁰/₃ r/h
Volume of a sphere = 66.67r/h
The volume of the sphere is 66.67r/h
9514 1404 393
Answer:
5 seconds
Step-by-step explanation:
Suppose the front parts of the trains meet at point A. Since both are the same length and traveling the same speed, each will pass point A in time ...
time = distance/speed
time = (1/18 mi)/(40 mi/h) = (1/720 h) × (3600 s)/(1 h) = 5 s
That is, the rear part of each train will be at point A 5 seconds after the front part.
The rear parts will pass each other 5 seconds after the front parts meet.
{x-(-3/4)}^2=3^2
(x+3/4)^2=9
{(4x+3)/4}^2=9
(4x+3)^2/16=9
(4x+3)^2=9*16
16x^2+2*4x*3+3^2=144
16x^2+24x+9=144
16x^2+24x+9-144=0
16x^2+24x-135=0
Answer:5
Step-by-step explanation: 18-4K = -2
-18 -18
<u> -4K</u> =<u> -20</u>
-4 -4
K=5
The answer:
the main formula of the circle's equation is
(x-a)²+ (y-b)² = R²
where C(a, b) is the center of the circle
R is the radius
if a point A(x', y') passes through the circle, so the equation of the circle can be written as
(x'-a)²+ (y'-b)² = R², and that is a main formula.
<span>Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2), so we have exactly three equation:
</span>
(0-x)² + (0-y)² = R², circle O passes through A
x²+y²= R²
(-3 -x)² + (0-y)² = R², circle O passes through B
(-3 -x)² + (y)² = R²
(1-x)² + (2-y)² = R², circle O passes through A
(1-x)² + (2-y)² = R²
and we know that R= OA = OC= OB,
OA=R= sqrt( (0-x)² + (0-y)² ) = OB = sqrt((-3 -x)² + (0-y)²), this implies
x²+y² = (-3 -x)² + (0-y)² , it implies x² = 9+ x² + 6x , and then -9/6=x, x= -3/2
and when OA = OC
x²+y² =(1-x)² + (2-y)² so, x²+y² =1+x²-2x +4+y²-4y, therefore -5= -2x -4y
-5= -2x -4y, when x = -3 /2 we obtain y = 2
the center is C(-3/2, 2)
