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The Crusades were a series of religious wars initiated, supported, and sometimes directed by the Latin Church in the medieval period. The term refers especially to the Eastern Mediterranean campaigns in the period between 1096 and 1271 that had the objective of recovering the Holy Land from Islamic rule. The Crusades were organized by western European Christians after centuries of Muslim wars of expansion. Their primary objectives were to stop the expansion of Muslim states, to reclaim for Christianity the Holy Land in the Middle East, and to recapture territories that had formerly been Christian. Many participants also believed that undertaking what they saw as holy war was a means of redemption and a way of achieving expiation of sins.
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Meghna Thapar 5 years, 3 months ago
The inner glands produce adrenaline. Adrenaline is also known as the “fight-or-flight hormone.” It's released in response to a stressful, exciting, dangerous, or threatening situation. Adrenaline helps your body react more quickly. In response to acute stress, the body's sympathetic nervous system is activated due to the sudden release of hormones. The sympathetic nervous systems stimulate the adrenal glands triggering the release of catecholamines, which include adrenaline and noradrenaline.
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Yogita Ingle 5 years, 3 months ago
A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height.
For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.
Therefore, the cylinder’s volume of base radius ‘r’, and height ‘h’ = (area of base) × height of the cylinder
Since the base is the circle, it can be written as
Volume = πr2 × h
Therefore, the volume of a cylinder = πr2h cubic units.
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Yogita Ingle 5 years, 3 months ago
Autonomic nervous system is a part of peripheral nervous system which is responsible for involuntary actions i.e. it regulates all those actions or responses of our body that are not according to our will. Example - beating of heart.
It has two parts:
i. Sympathetic nervous system
ii. Parasympathetic nervous system
The nerve fibres of both these parts have opposing effects i.e. if one stimulates a particular response, the muscles of other system inhibits that response.
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Posted by Aadya Singh 5 years, 3 months ago
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Gaurav Seth 5 years, 1 month ago
Answer:
there are two methods to solve the problem which are discussed below.
Method 1:
Let us consider
a = n3 – n
a = n (n2 – 1)
a = n (n + 1)(n – 1)
Assumtions:
1. Out of three (n – 1), n, (n + 1) one must be even, so a is divisible by 2.
2. (n – 1) , n, (n + 1) are consecutive integers thus as proved a must be divisible by 3.
From (1) and (2) a must be divisible by 2 × 3 = 6
Thus, n³ – n is divisible by 6 for any positive integer n.
Method 2:
When a number is divided by 3, the possible remainders are 0 or 1 or 2.
∴ n = 3p or 3p + 1 or 3p + 2, where r is some integer.
Case 1: Consider n = 3p
Then n is divisible by 3.
Case 2: Consider n = 3p + 1
Then n – 1 = 3p + 1 –1
⇒ n -1 = 3p is divisible by 3.
Case 3: Consider n = 3p + 2
Then n + 1 = 3p + 2 + 1
⇒ n+1 = 3p + 3
⇒ n+1 = 3(p + 1) is divisible by 3.
So, we can say that one of the numbers among n, n – 1 and n + 1 is always divisible by 3.
⇒ n (n – 1) (n + 1) is divisible by 3.
Similarly, when a number is divided by 2, the possible remainders are 0 or 1.
∴ n = 2q or 2q + 1, where q is some integer.
Case 1: Consider n = 2q
Then n is divisible by 2.
Case 2: Consider n = 2q + 1
Then n–1 = 2q + 1 – 1
n – 1 = 2q is divisible by 2 and
n + 1 = 2q + 1 + 1
n +1 = 2q + 2
n+1= 2 (q + 1) is divisible by 2.
So, we can say that one of the numbers among n, n – 1 and n + 1 is always divisible by 2.
∴ n (n – 1) (n + 1) is divisible by 2.
Since, n (n – 1) (n + 1) is divisible by 2 and 3.
Therefore, as per the divisibility rule of 6, the given number is divisible by six.
n3 – n = n (n – 1) (n + 1) is divisible by 6.
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