An airplane has a speed of 400 km/h with no wind. The airplane flies 2140 km with the wind. The airplane can only fly 1860 km against the wind in the same time. If w equals the speed of the wind, which equation would be used to find w?
a) 2140/(w+400) = 1860/(w-400)
b. 2140/(400+w) - 1860/(w-400)=2140-1860/w
c) 2140/(400+w) = 1860/(400-w)
d) 2140/(400+w) - 1860/(400-w) = 650
2. What is the average rate of change of f(x)= (x-5)/(x+3) from x=-2 to x =4?
a) 24/7
b) 8/7
C) -25/21
D) -11/3
Can someone explain to me what to do with the denominators? that's the only thing I am confused about. I know that you plug in -2 for x, f(x)= (x-5)/(x+3)
Y2-Y1/X2-X1
anyone?? D:
I assume you got C for #1.
Time = distance/speed
The two times are equal
#2.
f(-2) = -7/1
f(4) = -1/7
So, over an interval of 6 units, y changed from -7 to -1/7 = +48/7
So, the average change per unit is (48/7)/6 = 8/7
How did you get the denominator 1 and 7? That is what I am confused :3
To find the equation that is used to find the speed of the wind, we need to set up an equation based on the given information.
First, let's consider the airplane's speed with no wind, which is 400 km/h.
When the airplane flies with the wind, the effective speed is increased by the speed of the wind. So the effective speed can be expressed as 400 + w km/h, where w is the speed of the wind.
When the airplane flies against the wind, the effective speed is decreased by the speed of the wind. So the effective speed can be expressed as 400 - w km/h.
Now let's set up the equation based on the distances traveled in each case.
The airplane travels 2140 km with the wind, so the time taken can be expressed as 2140/(400 + w) hours.
The airplane travels 1860 km against the wind, so the time taken can be expressed as 1860/(400 - w) hours.
Since the times taken are the same in both cases, we can set up the equation:
2140/(400 + w) = 1860/(400 - w)
Therefore, the correct equation to find the speed of the wind would be option a) 2140/(w+400) = 1860/(w-400).
Now, let's move on to the second question about finding the average rate of change of f(x) = (x-5)/(x+3) from x = -2 to x = 4.
To find the average rate of change, we can use the formula:
Average rate of change = (f(x2) - f(x1))/(x2 - x1)
Here, x2 and x1 represent the two x-values between which we want to find the average rate of change. In this case, x2 = 4 and x1 = -2.
Let's plug in these values and evaluate the expression:
f(4) = (4-5)/(4+3) = -1/7
f(-2) = (-2-5)/(-2+3) = 7
So, the average rate of change is:
(-1/7 - 7)/(4 - (-2)) = (-1/7 - 49/7)/(4+2) = (-50/7)/(6) = -25/21
Therefore, the correct answer for the average rate of change is option C) -25/21.
Remember, to solve these types of problems, it's important to carefully analyze the given information and set up the appropriate equations or formulas to find the desired result.
You're kidding, right?
f(x)= (x-5)/(x+3)
f(-2) = (-2-5)/(-2+3) = -7/1
f(4) = (4-5)/(4+3) = -1/7