Known that,
x = z
Also known that,
x + y = 10
Substituting value of x,
z + y = 10
Hence, proved.
Answer:
36 cm
Step-by-step explanation:
Because the plant is growing the same amount each week you would take 12(3) and get 36 cm at the end of the 12 weeks.
Answer: g > 7
Graph has an open circle at 7 on the number line, shading to the right
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Explanation:
Think of it like saying "I have a number, and I add on 5. The result is something larger than 12". You can guess and check your way to the answer, but the quickest way is to subtract 5 from both sides.
We subtract to undo the addition happening to the 'g'.
g+5 > 12
g+5-5 > 12-5
g > 7
So the number is larger than 7. For instance, if g = 8, then,
g+5 > 12
8+5 > 12
13 > 12
This is a true statement.
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If you need to graph the solution, then you'll have an open circle at 7 on the number line. The open circle says to the reader "don't include this value as part of the solution set". Shade to the right of the open circle to describe all values larger than 7.
In summary, the graph has an open circle at 7 and shading to the right.
To find the derivative of this function, there is a property that we should know called the Constant Multiple Rule, which says:
![\dfrac{d}{dx}[cf(x)] = cf'(x)](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%5Bcf%28x%29%5D%20%3D%20cf%27%28x%29)
(where 
is a constant)
Remember that the derivative of 
is 
. However, you may notice that we are finding the derivative of 
, not 
. So, we are going to have to use the chain rule. To complete the chain rule for the derivative of a trigonometric function (in layman's terms) is basically the following: First, complete the derivative of the trig function as you would if what was inside the trig function is 
. Then, take the derivative of what's inside of the trig function and multiply it by what you found in the first step.
Let's apply that to our problem. Right now, I am not going to worry about the 
at the front of the equation, since we can just multiply it back in at the end of our problem. So, let's examine 
. We see that what's inside the trig function is 
, which has a derivative of 2. Thus, let's first find the derivative of as if was just and then multiply it by 2.
The derivative of would first be 
. Multiplying it by 2, we get our derivative of 
. However, don't forget to multiply it by the that we removed near the beginning. This gives us our final derivative of .
Remember that we now have to find the derivative at the given point. To do this, simply "plug in" the point into the derivative using the x-coordinate. This is shown below:
![-\cot[2(\dfrac{\pi}{4})]\csc[2(\dfrac{\pi}{4})]](https://tex.z-dn.net/?f=-%5Ccot%5B2%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%29%5D%5Ccsc%5B2%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%29%5D)
Our final answer is 0.
