We know `log_(2)32 = 5` . Show that we get the same answer by writing 32 as `64/2` and then using the product rule. Verify your answer .

We have log_(2)32 = 5 . Show that we get the same result by writing 32 = 2^(5) and then using power rules. Verify the answer.

We know that log_(10)100000 = 5 Show that you get the same answer by writing 100000 = 1000 xx 100 and then using the product rule. Verify the answer.

Is 7 xx 5 xx 3 xx 2 + 3 a composite number? Justify your answer.

Consider the points A(3,2,-4),B(5,4,-6) and C(9,8,-10) . i. Find AB, BC and AC and show that A, B, C are collinear. ii. Find the ratio in which B divides AC using distance formula. iii. Verify the result using section formula.

A cylindrical pencil is sharpened to produce a perfect cone at one end with no over all its length. The diameter of the pencil is 1 cm and the length of the conical portion is 2 cm. Calculate the volume of the peels. Give your answer correct to two places if it is in decimal [use pi=(355)/(113) ]

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying onn it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts onit is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object anda buoyant force also acts on the object. Thus, true free fall is posible only in vacuum. For a freely falling object, the velocity on reachign the earth and the time taken for it can be calculated by using Newton's eqwuations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite ot the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. Write kinematic equations used in free fall?

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying onn it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts onit is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object anda buoyant force also acts on the object. Thus, true free fall is posible only in vacuum. For a freely falling object, the velocity on reachign the earth and the time taken for it can be calculated by using Newton's eqwuations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite ot the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. What is free fall?