Answer:
True both are 28/15
Step-by-step explanation:
Simplify the following:
5 + 2/3 - (3 + 4/5)
Put 3 + 4/5 over the common denominator 5. 3 + 4/5 = (5×3)/5 + 4/5:
5 + 2/3 - (5×3)/5 + 4/5
5×3 = 15:
5 + 2/3 - (15/5 + 4/5)
15/5 + 4/5 = (15 + 4)/5:
5 + 2/3 - (15 + 4)/5
15 + 4 = 19:
5 + 2/3 - 19/5
Put 5 + 2/3 - 19/5 over the common denominator 15. 5 + 2/3 - 19/5 = (15×5)/15 + (5×2)/15 + (3 (-19))/15:
(15×5)/15 + (5×2)/15 + (3 (-19))/15
15×5 = 75:
75/15 + (5×2)/15 + (3 (-19))/15
5×2 = 10:
75/15 + 10/15 + (3 (-19))/15
3 (-19) = -57:
75/15 + 10/15 + (-57)/15
75/15 + 10/15 - 57/15 = (75 + 10 - 57)/15:
(75 + 10 - 57)/15
| 7 | 5
+ | 1 | 0
| 8 | 5:
(85 - 57)/15
| 7 | 15
| 8 | 5
- | 5 | 7
| 2 | 8:
Answer: 28/15
______________________________________
Simplify the following:
1 + 13/15
Put 1 + 13/15 over the common denominator 15. 1 + 13/15 = 15/15 + 13/15:
15/15 + 13/15
15/15 + 13/15 = (15 + 13)/15:
(15 + 13)/15
| 1 | 5
+ | 1 | 3
| 2 | 8:
Answer: 28/15
We have been given that
and angle A is in quadrant 1. We are asked to find the exact value of
in simplest radical form.
We know that sine relates opposite side of right triangle with hypotenuse.

This means that opposite side is 12 units and hypotenuse is 13 units.
We know that cotangent relates adjacent side of right triangle with adjacent side.

Now we will find adjacent side using Pythagoras theorem as:




Let us take positive square root on both sides:

Therefore, adjacent side of angle A is 5 units.

Therefore, the exact value of cot A is
.
The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.
Step-by-step explanation:
The given is,
Given diagram is combination of Rectangle and Semi circle.
Step:1
Res the attachment,
Area of given diagram = Area of A + Area of B..............(1)
Step:2
For A,
The A section in the given diagram is semi circle,
Diameter of semi circle = Total distance - ( 2+3)
( ∵ 2, 3 are top distance in the given diagram)

Diameter, d = 5 cm
Radius, 

r = 2.5 cm
Area,
........................(2)


Step:3
For B,
Area of rectangle is,
.....................(3)
Where, l - Length = 10 cm
b - Width = 2 cm
Equation (3) become,


Area of B,
= 20 
Step:4
From the equation (1),
Area of given diagram = 20+ 9.81747
Area = 29.817 square centimeters
Result:
The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.