Answer:
The volume of the cylinder is <em>approximately</em> 1570.8 cm³.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Geometry</u>
Volume Formula [Cylinder]:
- <em>r</em> is radius
- <em>h</em> is height
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given variables</em>.
<em>h</em> = 5 cm
<em>r</em> = 10 cm
<u>Step 2: Find Volume</u>
- [Volume Formula - Cylinder] <em>Substitute</em> in variables:
- [Order of Operations] Evaluate:
- Approximate:
∴ the volume of a cylinder whose height is 5 cm and radius is 10 cm is <em>approximately</em> 1570.8 cm³.
___
Learn more about Geometry: brainly.com/question/9774838
___
Topic: Geometry
Answer:
Magnitude: 121.35 pounds
Direction: 21.64°
Explanation:
1) Decompose each force into its x - y components.
2) Force 1, F1: 140 pounds at angle of 30°
x-component: F1,x
F1, x = F1 *cos(30°) = 140 pounds * cos(30°) = 121.24 pounds
y-component: F1,y
F1,y = F1 * sin(30°) = 140 pounds * sin(30°) = 70 pounds.
3) Force 2, F2: 75 poounds at 150°
x-component: F2,x
F2,x = F2 * cos(150°) = 75 pounds * cos(150°) = - 64.95 pounds
y-component: F2,y
F2,y = F2 * sin(150°) = 75 pounds * sin(150°) = 37.5 pounds
4) Resultant Force, Fr
x-component: Fr,x
Fr,x = F1,x + F2,x = 121.24 pounds - 64.95 pounds = 56.29 pounds
y-component: Fr,y
Fr,y = F1,y + F2,y = 70 pounds + 37.5 pounds = 107.5 pounds
4.1) magnitude
|Fr| = √ [ (56.29 pouns)^2 + (107.5 pounds)^2 ] = 121.35 pounds.
4.2) direction
tan(α) = Fr,y / Fr,3 = 56.29 pounds / 107.5 pouns = 0.5236
=> α = arctan(0.5236) = 27.64 °
Let the two required numbers be x and 100 - x, then
Sum of its squares is given by S = x^2 + (100 - x)^2
For the sum of the squares to be minimum, dS/dx = 0
dS/dx = 2x - 2(100 - x) = 0
2x - 200 + 2x = 0
4x = 200
x = 50.
The two numbers is 50 and 50.
