I'll solve B, and then challenge you to do A and C on your own!
If the line passes through (-3,4) and (5, -4), then the slope is the change in y over the change in x, which is (4-(-4))/(-3-5)=8/-8=-1 in this scenario, meaning that in the equation y=mx+b (with m as the slope), we have y=-x+b so far.Note that we only have to find b, as y and x can stay as variables. Plugging (-3,4) in for y and x (to find B), we get 4=-(-3)+b=3+b. Subtracting 3 from both sides, we get b=1 and the equation being y=-x+1
The rate of change is the slope.
f(x) is the same as y...
f(x) = 3x + 9.....y = 3x + 9....and in y = mx + b form, the rate of change(slope) can be found in the m position.
y = mx + b
y = 3x + 9....so the slope or rate of change is 3...not 9...so answer is false
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.
Answer:
150 minutes
Step-by-step explanation:
1 hour is 60 minute, 2 hours are 120 minutes. You have also one half of hour, which is 30 minutes.
2.5hrs = 60 + 60 + 30 = 150 minutes
I believe the answer is letter A
