Answer:
The total surface are of the bowl is given by: 0.0532*pi m² (approximately 0.166533 m²)
Explanation:
The total surface area of the semi-spherical bowl can be decomposed in three different sections: 1) an outer semi-sphere of radius 12 cm, 2) an inner semi-sphere of radius 10 cm, and 3) the edge, which is a 2-dimensional ring with internal radius of 10 cm and external radius of 12 cm. We will compute the areas independently and then sum them all.
a) Outer semi-sphere:
A1 = 2*pi*r² = 2*pi*(12 cm)² = 288*pi cm² = 904.78 cm²
b) Inner semi-sphere:
A2 = 2*pi*(10 cm)² = 200*pi cm² = 628.32 cm²
c) Edge (Ring):
A3 = pi*(r1² - r2²) = pi*((12 cm)²-(10 cm)²) = pi*(144-100) cm² = 44*pi cm² = 138.23 cm²
Therefore, the total surface area of the bowl is given by:
A = A1 + A2 + A3 = 288*pi cm² + 200*pi cm² + 44*pi cm² = 532*pi cm² (approximately 1665.33 cm²)
Changing units to m², as required in the problem, we get:
A = 532*pi cm² * (1 m² / 10, 000 cm²) = 0.0532*pi m² (approximately 0.166533 m²)
Using the formula F=ma
500N=50kg (a)
a= 10 m/s^2
So, the angular frequency of the blades approximately <u>36.43π rad/s</u>.
<h3>Introduction</h3>
Hi ! Here I will discuss about the angular frequency or what is also often called the angular velocity because it has the same unit dimensions. <u>Angular frequency occurs, when an object vibrates (either moving harmoniously / oscillating or moving in a circle)</u>. Angular frequency can be roughly interpreted as the magnitude of the change in angle (in units of rad) per unit time. So, based on this understanding, the angular frequency can be calculated using the equation :
With the following condition :
= angular frequency (rad/s)
= change of angle value (rad)- t = interval of the time (s)
<h3>Problem Solving</h3>
We know that :
- = change of angle value = 1,000 revolution = 1,000 × 2π rad = 2,000π rad/s >> Remember 1 rev = 2π rad/s.
- t = interval of the time = 54.9 s.
What was asked :
- = angular frequency = ... rad/s
Step by step :
<h3>Conclusion :</h3>
So, the angular frequency of the blades approximately 36.43π rad/s.
Answer:
(a) convex mirror
(b) virtual and magnified
(c) 23.3 cm
Explanation:
The having mirror is convex mirror.
distance of object, u = - 20 cm
magnification, m = 1.4
(a) As the image is magnified and virtual , so the mirror is convex in nature.
(b) The image is virtual and magnified.
(c) Let the distance of image is v.
Use the formula of magnification.
Use the mirror equation, let the focal length is f.
Radius of curvature, R = 2 f = 2 x 11.67 = 23.3 cm
Answer:
2000 nickels
Explanation:
One way to solve proportionality problems, direct and inverse: the simple 3 rule.
If the relationship between the magnitudes is direct (when one magnitude increases so does the other), the simple direct rule of three must be applied.
On the contrary, if the relationship between the magnitudes is inverse (when one magnitude increases the other decreases) the rule of three simple inverse applies.
The simple 3 rule is an operation that helps us quickly solve proportionality problems, both direct and inverse.
To make a simple rule of three we need 3 data: two magnitudes proportional to each other, and a third magnitude. From these, we will find out the fourth term of proportionality.
In the simple three rule, therefore, the proportionality relationship between two known values A and B is established, and knowing a third value C, a fourth value D is calculated.
A -> B
C -> D
Calculation
1 nickel --> 5 g
X? nickel --> 10000g
X = (10000 g * 1 nickel) / 5 g
X = 2000 nickels
