Here, we want to find the diagonal of the given solid
To do this, we need the appropriate triangle
Firstly, we need the diagonal of the base
To get this, we use Pythagoras' theorem for the base
The other measures are 6 mm and 8 mm
According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides
Let us have the diagonal as l
Mathematically;
![\begin{gathered} l^2=6^2+8^2 \\ l^2\text{ = 36 + 64} \\ l^2\text{ =100} \\ l\text{ = }\sqrt[]{100} \\ l\text{ = 10 mm} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20l%5E2%3D6%5E2%2B8%5E2%20%5C%5C%20l%5E2%5Ctext%7B%20%3D%2036%20%2B%2064%7D%20%5C%5C%20l%5E2%5Ctext%7B%20%3D100%7D%20%5C%5C%20l%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B100%7D%20%5C%5C%20l%5Ctext%7B%20%3D%2010%20mm%7D%20%5Cend%7Bgathered%7D)
Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above
Thus, we calculate this using the Pytthagoras' theorem as follows;
![\begin{gathered} d^2=5^2+10^2 \\ d^2\text{ = 25 + 100} \\ d^2\text{ = 125} \\ d\text{ = }\sqrt[]{125} \\ d\text{ = }11.2\text{ mm} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20d%5E2%3D5%5E2%2B10%5E2%20%5C%5C%20d%5E2%5Ctext%7B%20%3D%2025%20%2B%20100%7D%20%5C%5C%20d%5E2%5Ctext%7B%20%3D%20125%7D%20%5C%5C%20d%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B125%7D%20%5C%5C%20d%5Ctext%7B%20%3D%20%7D11.2%5Ctext%7B%20mm%7D%20%5Cend%7Bgathered%7D)
Answer:
-4
Step-by-step explanation:
[√2(cos(3π/4) + i sin(3π/4))]⁴
(√2)⁴ (cos(3π/4) + i sin(3π/4))⁴
4 (cos(3π/4) + i sin(3π/4))⁴
Using De Moivre's Theorem:
4 (cos(4 × 3π/4) + i sin(4 × 3π/4))
4 (cos(3π) + i sin(3π))
3π on the unit circle is the same as π:
4 (cos(π) + i sin(π))
4 (-1 + i (0))
-4
Let
denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by
, each independently and identically distributed with distribution
.
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
, then the sampling distribution
with
being the size of the sample.
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to
A simple method is to square all the answers
now arrange them
