Which sum is rational? A. π + 18 B. √25 + 1.75 C. √3 + 5.5 D. π + √2
1 answer:
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Answer:
a. and 41.6
b. 52.1
Step-by-step explanation:
a.
Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.
<u>Note:</u> the exact value of tan 60 is
Thus, we can write
Approximate value (rounded to nearest tenth):
b.
Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.
Thus we can write and solve:
<h2>Explanation:</h2><h2></h2>
Here we need to set a system of two linear equations in two variables. So:
- <em>The sum of digits in a two digit number formed by two digits from 1 to 9 is 8:</em>
Let be those digits, then:
- <em>If 9 is added to a number then both the digits become equal. find the number:</em>
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But from eq 1:
Substituting y into the expression 1:
The x-value will be found by hit and trial, so:
- Let x = 1:
We have to reject this solution because digits are different.
- Let x = 2:
We have to reject this solution because digits are different.
- Let x = 3:
<em>Then this is a two digit number formed by two equal digits. </em>
Finally, the number is:
44