To evaluate cot θ given that sinθ=√6/5 we shall have:
sin θ=opposite/hypotenuse
hence
opposite=√6
hypotenuse=5
thus the adjacent will be found using the Pythagorean theorem
c²=a²+b²
plugging in the value we get:
5²=(√6)²+b²
b²=25-6
b²=19
b=√19
thus
adjacent=√19
but
cotθ=1/tanθ
tanθ=√6/√19
hence:
cotθ=√19/√6
Answer:
See Below
Step-by-step explanation:
The surface area of cylinder is given by the formula:

Where
r is radius ( diameter is 4, so radius is 4/2 = 2)
h is height ( h = 9)
Lets find original surface are:

<u>Halving diameter:</u>
diameter would be 4/2 = 2, so radius would be 2/2 = 1
So, SA would be:

<u>Halving height:</u>
Height is 9, halving would make it 9/2 = 4.5
Now, calculating new SA:

Original SA is
,
Halving diameter makes it 
Halving height makes it 
So, halving diameter does not have same effect as halving height.
Mp. 146.54
dis . 15%
sp= 146.54 - 15 % of 146.54
=124.559
Answer:
Given that,
The number of grams A of a certain radioactive substance present at time, in years
from the present, t is given by the formula

a) To find the initial amount of this substance
At t=0, we get


We know that e^0=1 ( anything to the power zero is 1)
we get,

The initial amount of the substance is 45 grams
b)To find thehalf-life of this substance
To find t when the substance becames half the amount.
A=45/2
Substitute this we get,


Taking natural logarithm on both sides we get,







Half-life of this substance is 154.02
c) To find the amount of substance will be present around in 2500 years
Put t=2500
we get,




The amount of substance will be present around in 2500 years is 0.000585 grams