Note the binomial expansion,
(<em>a</em> + 1/<em>a</em>)³ = <em>a</em> ³ + 3<em>a</em> + 3/<em>a</em> + 1/<em>a</em> ³
so
<em>a</em> ³ + 1/<em>a</em> ³ = (<em>a</em> + 1/<em>a</em>)³ - 3 (<em>a</em> + 1/<em>a</em>)
Similarly,
(<em>a</em> + 1/<em>a</em>)² = <em>a</em> ² + 2 + 1/<em>a</em> ²
We're given <em>a</em> ² + 1/<em>a</em> ² = 79, so
(<em>a</em> + 1/<em>a</em>)² - 2 = 79
(<em>a</em> + 1/<em>a</em>)² = 81
<em>a</em> + 1/<em>a</em> = ±9
but <em>a</em> > 0, so we ignore the negative solution.
Then
<em>a</em> ³ + 1/<em>a</em> ³ = 9³ - 3×9 = 702
<h2><u>
PROPORTIONAL EQUATION</u></h2><h3>Exercise</h3>
Apply the means-extremes property of proportions: this allows you to cross multiply:
Apply the distributive property:
Add 24 to both sides:
Substract 3x to both sides
<h3><u>Answer</u>. The value of x = 24.</h3>
Answer:
Using sine ratio:
As per the statement:
The angle of elevation from Sara to kite in the sky is 53° and the length of the string is 32 feet. and Sara is 5 feet tall.
⇒Angle of elevation( 
) = 53° and
Hypotenuse side = 32 feet (As you can see the figure as shown below)
then;
Apply the sine ratio in triangle ACE we have;
Multiply both sides by 32 we get;
Simplify:
CE = 25.5563363215 feet.
Then:
DE = CD+CE = 5 + 25.5563363215 = 30.5563363215 ≈30.6 feet.
Therefore, 30.6 feet far off the ground is the kite.
4.29 + 97.2 + 0.687 = 102.177
In adding decimal numbers, make sure that the decimal points are aligned. Since each number has different counts of numbers after the decimal point, use 0 to pad the missing places.
4.290
97.200
<u> 0.687
</u> 102.177
The count of numbers after the decimal point is the same count of number of the decimal who has the greatest count of number after the decimal point.
4.29 only has 2 counts of places after the decimal point
97.2 only has 1 count of place after the decimal point
0.687 has 3 counts of places after the decimal point.
The sum of the decimals must also have 3 counts of places after the decimal point.
