A 30−60−90 triangle has a longer leg with length 53√4 and a hypotenuse with length 5/2 . What is the length of the shorter leg?
1 answer:
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Answer:
Step-by-step explanation:
When we throw a die , Total outcomes =6
When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]
Given : Three fair dice are rolled, one red, one green and one blue.
Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed
By Permutations , the number of favorable outcomes =
The probability that the upturned faces of the three dice are all of different numbers =
The probability that the upturned faces of the three dice are all of different numbers is .
<h2>Answer:</h2>
0 - 17i
<h2>Step-by-step explanation:</h2>Given expression;
i⁸⁰ + i³⁸ - i17
To express the expression in the form a+bi;
<em>i. Rewrite the expression such that it contains terms in i²</em>
(i²)⁴⁰ + (i²)¹⁹ - i17
<em>ii. Solve the result from (i) above using the identity i² = -1</em>
We know that the square root of -1 is i. i.e
<em>Squaring both sides gives</em>
<em>=> </em><em />
=> -1 = i²
Therefore,
i² = -1
<em>Substitute i² = -1 in step (i) above</em>
(-1)⁴⁰ + (-1)¹⁹ - i17
<em>(iii) Solve the result in (ii)</em>
We know that the when a negative number is raised to the power of an even number, the result is a positive number. If it is raised to the power of an odd number, the result is a negative number. Therefore,
(-1)⁴⁰ + (-1)¹⁹ - i17 becomes
1 + (-1) - i17
0 - i17
<em>(iv) Write the result from (iii) in the form a+bi</em>
0 - 17i