Answer:
3,105
Step-by-step explanation:
the answer is 3,105 because you simply take the total number that was eaten in 3 months and divide it by 3 since they only want to know what was eaten in 1 month
Answer:
m = -1
Step-by-step explanation:
m = change in y / change in x
m = ![\frac{10-(7)}{1-(4)}](https://tex.z-dn.net/?f=%5Cfrac%7B10-%287%29%7D%7B1-%284%29%7D)
Simplify.
m = ![\frac{3}{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B-3%7D)
m = -1
<h3>Answer:</h3>
![f'(x)=\dfrac{8x^4-2x^2-\left(28x^4+83x^2-3\right)\ln{\left(x^2+3\right)}}{2x^2\left(x^2+3\right)\left(4x^2-1\right)^4}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cdfrac%7B8x%5E4-2x%5E2-%5Cleft%2828x%5E4%2B83x%5E2-3%5Cright%29%5Cln%7B%5Cleft%28x%5E2%2B3%5Cright%29%7D%7D%7B2x%5E2%5Cleft%28x%5E2%2B3%5Cright%29%5Cleft%284x%5E2-1%5Cright%29%5E4%7D)
<h3>Explanation:</h3>
It can work well to consider the function in parts. Define the following:
... a(x) = (1/2)ln(x^2+3)
... b(x) = x(4x^2-1)^3
Then the derivatives of these are ...
... a'(x) = (1/2)·1/(x^2 +3)·2x = x/(x^2+3)
... b'(x) = (4x^2 -1)^3 + 3x(4x^2 -1)^2·8x = (4x^2 -1)^2·(4x^2 -1 +24x^2)
... = (4x^2 -1)^2·(28x^2 -1)
___
<em>Putting the parts together</em>
f(x) = a(x)/b(x)
f'(x) = (b(x)a'(x) -a(x)b'(x))/b(x)^2 . . . . . rule for quotient of functions
Substituting values, we have
... f'(x) = (x(4x^2 -1)^3·x/(x^2 +3) -(1/2)ln(x^2 +3)·(4x^2 -1)^2·(28x^2 -1)) / (x(4x^2 -1)^3)^2
We can cancel (4x^2 -1)^2 from numerator and denominator. We can also eliminate fractions (1/2, 1/(x^2+3)). Then we have ...
... f'(x) = 2x^2(4x^2 -1) -(x^2 +3)ln(x^2 +3)·(28x^2 -1)/(2x^2·(x^2 +3)(4x^2 -1)^4))
Simplifying a bit, this becomes ...
... f'(x) = (8x^4 -2x^2 -ln(x^2 +3)·(28x^4 +83x^2 -3))/(2x^2·(x^2 +3)(4x^2 -1)^4))
Answer:
DE = 20 units
Step-by-step explanation:
<u><em>GIVEN</em></u><em> :-</em>
- D & E are the mid-points of AB & BC respectively.
- DE = 4x + 4
- AC = x + 36
<u><em>TO FIND</em></u><em> :-</em>
<u><em>FACTS TO KNOW BEFORE SOLVING</em></u><em> :-</em>
- The midsegment of a triangle is a line constructed by connecting the midpoints of any two sides of the triangle.
- The Triangle Midsegment Theorem tells us that a midsegment is one-half the length of the third side (the base), and it is also parallel to the base.
<u><em>PROCEDURE</em></u><em> :-</em>
According to Triangle Midsegment Theorem ,
![DE = \frac{AC}{2}](https://tex.z-dn.net/?f=DE%20%3D%20%5Cfrac%7BAC%7D%7B2%7D)
![=> 4x + 4 = \frac{x + 36}{2}](https://tex.z-dn.net/?f=%3D%3E%204x%20%2B%204%20%3D%20%5Cfrac%7Bx%20%2B%2036%7D%7B2%7D)
Multiplying 2 on both the sides ,
![=> 2(4x + 4) = x + 36](https://tex.z-dn.net/?f=%3D%3E%202%284x%20%2B%204%29%20%3D%20x%20%2B%2036)
![=> 8x + 8 = x + 36](https://tex.z-dn.net/?f=%3D%3E%208x%20%2B%208%20%3D%20x%20%2B%2036)
![=> 8x - x = 36 - 8](https://tex.z-dn.net/?f=%3D%3E%208x%20-%20x%20%3D%2036%20-%208)
![=> 7x = 28](https://tex.z-dn.net/?f=%3D%3E%207x%20%3D%2028)
![=> x = \frac{28}{7} = 4](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%20%5Cfrac%7B28%7D%7B7%7D%20%3D%204)
∴ DE = 4×4 + 4 = 20 units
The answer is:
The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.Here's how:
The rate of change of the function is defined and calculated as (refer to the statement beloew):
r = [change in height] / {change in time]For the Table:
refer to the attached picture.
The table shows the calculations for the rate of change (r) for each interval given.
And for the Conclusion,
Refer to the table and notice that in the third ans fifth columns show that:
The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.