7. Tyrone is thinking of a number. In his number:
2 answers:
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Answer:
You could use the polygon area formula OR here's an easier solution
We draw the lines DC and DE
Angle ADC = 120°
Triangle ADC is a 30 60 90 triangle
In such a triangle Line AE = hypotenuse * sq root (3) /2
Line AE = 3 * 0.8660254038 = 2.5980762114
Line DE = 1.5
Area of Triangle ADE = .5 * 1.5 * 2.5980762114 =
1.9485571586 square meters and entire area of Triangle
ABC = 6 * 1.9485571586
which equals 11.6913429513 square meters
Step-by-step explanation:
Answer:
<em>1. A sperm whale is </em><em>3</em><em> </em><em>orders of magnitude</em><em> heavier than a La Plata river dolphin; 2. The radius of the larger ball is </em><em>one (1) order of magnitude</em><em> bigger than the radius of the smaller ball; 3. The volume of the larger ball is </em><em>3 orders of magnitude</em><em> bigger than the volume of the smaller ball</em>.
Step-by-step explanation:
If we expressed a number as:
(1)
Where
(2)
or
(3)
Then, <em>b</em> represents the <em>order of magnitude </em>of such a number (<em>Order of magnitude (2020), </em>in Wikipedia).
The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).
Having gathered all this information, we can proceed as follows:
<h3>First case</h3>The<em> La Plata river dolphin</em> weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.
Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the <em>scientific notation</em>):
Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):
Then
Thus
<em>A sperm whale is </em><em>3</em><em> </em><em>orders of magnitude</em><em> heavier than a La Plata river dolphin.</em>
<h3>Second case</h3>Following the same reasoning, we can conclude that <em>the radius of the larger ball is </em><em>one (1) order of magnitude</em><em> bigger than the radius of the smaller ball:</em>
For this case, we need to calculate <em>the volume of a sphere</em> for both radii (1cm and 10cm).
The volume of a sphere is
Then, the volume of the <em>ball of radius 1cm</em> is:
And, the volume of the <em>ball of radius 10cm</em> is:
Thus
As a result, <em>the volume of the larger ball is </em><em>3 orders of magnitude</em><em> bigger than the volume of the smaller ball</em>.