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2 answers:
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We need to find the base x in the following equation:
First, lets convert 365 from base 7 to base 10. This is given by
where the upperindex denotes the position of eah number. This gives
that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:
where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives
Now, we have all number in base 10. Then, our first equation can be written in base 10 as
For simplicity, we can omit the 10 and get
so, we can solve this equation for x. By combining similar terms. we have
and by moving 197 to the right hand side, we obtain
Finally, we get
Therefore, the solution is x=5
Answer:
The height of the tree is is 60m
Step-by-step explanation:
Let's answer a, as it is the only complete question.
We know that the angle of elevation of the top of a tree observed from a point 60m away, is 45°.
We can model this with a triangle rectangle, a sketch of it can be seen below (assuming that you are looking it from the ground).
You can see that the adjacent cathetus to the 45° angle is equal to 60m
And the opposite cathetus is the measure we want to find.
Now you can remember the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
So to find the height of the tree we need to solve:
tan(45°) = H/60m
This is just:
tan(45°)*60m = H =60m
The height of the tree is is 60m
