It is theoretically possible for a substance to have a negative value of cubical expansivity, which means that the substance would contract rather than expand when the temperature increases. However, it is very rare for a substance to have a negative value of cubical expansivity over a significant range of temperatures.
One example of a substance that has a negative value of cubical expansivity over a limited range of temperatures is water. Water has a positive value of cubical expansivity at...
The order of magnitude of a physical quantity is its magnitude in powers of ten when the physical quantity is expressed in powers of ten with one digit to the left of the decimal.
Orders of magnitude are generally used to make very approximate comparisons and reflect very large differences.
Here, the given equation of parabola is y2= 8x.
The equation of tangent to the parabola y2=8x is,
y= mx + 2/m
This tangent passes through the point (-2, 3)
So, 3 = -2m + 2/m
or, 3m + 2m2 = 2
or, 2m2+3m - 2= 0
or, 2m2 + (4 - 1)m -2 = 0
or, 2m2 + 4m - m - 2 = 0
or, 2m(m + 2) - 1(m+2) = 0
or, (m + 2) (2m - 1) = 0
Either, Or,
m = -2 m = 1/2
Required angle is,
Here, f(x)=x2 -6 logx-3=0
f(2)=4-6 log2-3=-0.806
f(3)=9-6 log3-3=3.1373
f(2).f(3)=-0.806*3.1373=-2.529422 which is negative.
Hence, the root lies between 2 and 3
c0 =(2+3)/2=2.5
f(2.5)=6.25-6 log 2.5-3=0.8623
Now
| n | a(-ve) | b(+ve) | cn | f(cn) |
| 0 | 2 | 3 | 2.5 | 0.8623 |
| 1 | 2 | 2.5 | 2.25 | -0.050595 |
| 2 | 2.25 | 2.5 | 2.375 | 0.38664 |
| 3 | 2.25 | 2.375 | 2.3125 | 0.1631658 |
| 4 | 2.25 | 2.3125 | 2.28125 | 0.05506 |
| 5 | 2.25 | 2.28125 | 2.265625 | 0.001925 |
From the table,
f(2.265625)=0.001928<10-2
Therefore, the...
