Answer:Refer to the image attached.
Given: and are congruent.
To Prove: ABC is an isosceles triangle.
Construction: Construct a perpendicular bisector from point B to Line segment AC.
Consider triangle BAD and BCD,
(given)
(By the definition of a perpendicular bisector)
(By the definition of a perpendicular bisector)
Therefore, by Angle Side Angle(ASA) Postulate.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent.(CPCTC)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
We know that trigonometric ratio as
- sin Ф = opposite/hypotenuse
- cos Ф = adjacent/hypotenuse
- tan Ф = opposite/adjacent
as
sin A = sin 40 = opposite/hypotenuse
From the diagram, it is clear that the opposite of angle A is a=8 and the hypotenuse is 'c'.
also the angle
sin A = sin 40 = opposite/hypotenuse = a/c = 8/c
sin 40 = 8/c
c = 8/sin 40
c = 8/0.745
c = 10.7
so the value of c will be: 10.7 units
so
tan B = opposite/adjacent
= b/a
= 0.9


Therefore, the value of B = 
As the sum of the angles of triangle ABC is 180.
i.e.
A+B+C = 180
(40)° + (42)° + C = 180°
C = 180° - 40° - 42°
= 98°
Therefore, the value of C = 98°
Hence,
Answer:
94.2
Step-by-step explanation:
circumference is d(pi)
20(3.14) = 94.2
Answer:
The general solution is

+ 
Step-by-step explanation:
Step :1:-
Given differential equation y(4) − 2y''' + y'' = e^x + 1
The differential operator form of the given differential equation
comparing f(D)y = e^ x+1
The auxiliary equation (A.E) f(m) = 0




The roots are m=0,0 and m =1,1
complementary function is 
<u>Step 2</u>:-
The particular equation is 
P.I = 
P.I = 
P.I = 



applying in integration u v formula

= 





again integration 
The general solution is 

+ 
Answer:
Absolute magnitude
Step-by-step explanation: Astronomy deals with the study of stars and other heavenly bodies. Astronomers use apparent magnitude to define how bright a star appears and shines from the earth.