Answer:
When we have a function f(x), the average rate of change in the interval (a, b) is:
In this case, we have the function:
f(x) = (x + 3)^2 - 2
(but we do not have the interval, and I couldn't find the complete question online)
So if for example, we have the interval (2, 4)
The average rate of change will be:
If instead, we want the rate of change in a differential dx around the value x, we need to differentiate the function (this is way more complex, so I will define some rules first).
Such that the rate of change, in this case, will be:
f'(x) = df/dx
For a function like:
g(x) = x^n + c
g'(x) = n*x^(n - 1)
And for:
h(x) = k( g(x))
h'(x) = k'(g(x))*g'(x)
So here we can write our function as:
f(x) = k(g(x)) = (x + 3)^2 - 2
where:
g(x) = x + 3
k(x) = x^2 - 2
Then:
f'(x) = 2*(x + 3)*1 = 2*x + 6
That is the rate of change as a function of x (but is not an "average" rate of change)
Trains depart after every 4 minutes.
Total time train takes to complete a circuit= 24 minutes
Evan sets off at 8:30 am, so he will be back at 8:54 am.
So time of trains coming in opposite direction:
8: 34 am
8:38 am
8:42 am
8:46 am
and 8:50 am
5 trains coming in opposite directions.
Now the trains started at 8:06 am from the stations are:
8:06 am
8:10 am
8:14 am
8:18 am
8:22 am
and 8:26 am.
So there are 6 trains started the circuit at 8:06 am.
Now total number of trains=6+5=11 trains
Answer: 11 trains will pass on complete circuit.
Answer:
2x + 10
Step-by-step explanation:
To expand (using the distributive property) <u>multiply</u> the number outside the bracket i.e. in this case '2', with the <u>values inside the brackets</u>.
So multiply '2' and 'x' and '2' and 5' and add or subtract on basis of whether the second value is positive or negative.
So
2(x + 5)
= (2*x)+(2*5)
=2x+10
<em>extention note:</em> <u>be careful</u> when the symbol within the equation within the brackets is a subtraction because it implies that the second value would instead be a negative number and should be treated as such.
an example
2(x-5)
= (2*x)+(2*-5)
=2x -10
Anyhow, I hope this helped!
Answer:
Question 675528: A ball is thrown vertically upward with an initial velocity of 48 feet per second. If the ball started its flight at a height of 8 feet, then its height s at time t can be determined by s(t)=-16t^2+48t+8 where s(t) is measured in feet above the ground and t is the number of seconds of flight.
Step-by-step explanation:
Step-by-step explanation:
slope=(y2-y1)/(x2-x1)
where (x1,y1)=(-8,-3)
(X2, y2)=(-12,-3)
slope=(-3+3)/(-12+8)=0
