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Here we need to compare the orders of magnitude of two measures.
We will see that the bacteria is<em> 300 times larger than the virus.</em>
We know that:
The diameter of the virus-cell is:
The diameter of the bacteria cell is:
So, to compare them, first notice that both are in the same units, meters, so we only need to <u>compare the numbers</u>.
Is common sense to identify the one with the largest exponent as the largest number, and the largest exponent is -7, thus <u>the bacteria should be the larger one.</u>
But let's prove this with math, remember the property:
Let's take the quotient between the diameters and see what we get, I will use the <u>diameter of the bacteria in the numerator</u>, thus <u>if the quotient is larger than 1, it would mean that the bacteria is greater and by how much.</u>
So we can say that the bacteria is 3*10^2 = 3*100 = 300 times larger than the virus.
If you want to learn more, you can read:
Answer:
w= 9
Step-by-step explanation:
Square both sides:
-4w +61= (w -4)²
Expand:
-4w +61= w² -2(w)(4) +4²
-4w +61= w² -8w +16
Simplify:
w² -8w +16 +4w -61= 0
w² -4w -45= 0
Factorize:
(w -9)(w +5)= 0
w -9= 0 or w +5= 0
w= 9 or w= -5 (reject)
Note:
-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.
<u>Why </u><u>do </u><u>we </u><u>use </u><u>negative </u><u>square </u><u>root?</u>
When solving an equation such as x²= 4,
we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.
In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.
However, back to our question, we did not introduce the square root so we should not consider the negative square root value.