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Answer:
Step-by-step explanation:
We are asked to find the circumference and area of a circle with a radius of 3 meters.
<h3>1. Circumference </h3>The circumference is the perimeter of a circle. It is calculated using the following formula:
We know the radius of the circle is 3 meters, but we must find the radius. The radius is the line from the center to the circle's edge, while the diameter is the line through the center from edge to edge. Therefore, the diameter is twice the radius.
- d= 2 r
- d= 2 * 3 m
- d= 6 m
The diameter is 6 meters and we are using 3.14 for pi. Substitute these values into the circumference formula.
Multiply.
The area is the size of the circle's surface. It is calculated using the following formula.
The radius is 3 meters are we are using 3.14 for pi. Substitute these values into the area formula.
Solve the exponent.
- (3 m)² = (3 m)(3 m)= 9 m²
The circumference is 18.84 meters and the area is 28.26 square meters.
Answer:
T = 3.967 C
Step-by-step explanation:
Density = mass / volume
Use the mass = 1kg and volume as the equation given V, we will come up with the following equation
D = 1 / 999.87−0.06426T+0.0085043T^2−0.0000679T^3
= (999.87−0.06426T+0.0085043T^2−0.0000679T^3)^-1
Find the first derivative of D with respect to temperature T
dD/dT =
Let dD/dT = 0 to find the critical value we will get
= 0
Using formula of quadratic, we get the roots:
T = 79.53 and T = 3.967
Since the temperature is only between 0 and 30, pick T = 3.967
Find 2nd derivative to check whether the equation will have maximum value:
Substituting the value with T=3.967,
d2D/dT2 = -1.54 x 10^(-8) a negative value. Hence It is a maximum value
Substitute T =3.967 into equation V, we get V = 0.001 i.e. the volume when the the density is the highest is at 0.001 m3 with density of
D = 1/0.001 = 1000 kg/m3
Therefore T = 3.967 C