Find the 30th term of the following sequence. 1, 7, 13, 19, ...
1 answer:
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By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
<h3>How to get the measures of the other two sides of the right triangle?</h3>Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
- sin(a) = (adjacent cathetus)/(hypotenuse).
- tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
- hypotenuse = AC
- opposite cathetus = AB.
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
If you want to learn more about right triangles:
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Given this equation:
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
<span>
<span>So, the tree is initially
tall.
</span>
Therefore this statement is false.
</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
<span>
</span>if x = 7 then:
So, between the 5th and 7th years the height of the tree remains constant
:
This is also a false statement.
<span>After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
approaches zero.
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
<span>
<span>So, the tree is initially
</span>
Therefore this statement is false.
</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
</span>if x = 7 then:
So, between the 5th and 7th years the height of the tree remains constant
:
This is also a false statement.
<span>After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.