Q1. The answer is <span>1 over 5 to the 3rd power.
</span>5 to the 5th is 5⁵
5 to the 8th is 5⁸
5 to the 5th over 5 to the 8th is
To simplify, we will use two rules:
Therefore:
is the same as 1 over 5 to the 3rd power.
Q2. The answer is <span>(53)−4.
The exponents are multiplied when are expressed in the form:
</span>
So,
Other choices are incorrect:
<span>one third to the 4th times one third to the 7th is </span>
3 to the 7th over 3 to the 15th is
<span>45 ⋅ 42 is </span>
Answer:
17
Step-by-step explanation:
Look at any 2 adjacent numbers and find the difference between them.
Starting with numbers 1 and 2, subtract the first from the second:
That's a difference of 8, meaning the second number increased by 8.
Check the next numbers, 2 and 3:
It increased by 8 again. Now that we know for sure that each term in the sequence increases by 8 over the previous one, we can find the number in the green box. Just add 8 to the number before it:
Using vector concepts, it is found that:
The component form is of approximately (-9.58, 7,22). It means that the ship is about 9.58 miles to the west and about 7.22 miles to the north of where the ship left the port.
<h3>How can a vector be represented in component notation?</h3>
Given a magnitude M and angle 
, then a vector V can be represented as follows in component notation:
In this problem, the magnitude and the angle are given, respectively, by:
Hence:
V = [12cos(143º), 12sin(143º)] = (-9.58, 7,22).
Which means a displacement of 9.58 miles to the west(negative x = west) and 7.22 miles to the north(positive y = north).
The component form is of approximately (-9.58, 7,22). It means that the ship is about 9.58 miles to the west and about 7.22 miles to the north of where the ship left the port.
More can be learned about vectors at brainly.com/question/24606590
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The circumference would be 53.38 because the formula on finding the circumference is pi times the diameter.
