Answer:
y=1/2x+2
Step-by-step explanation:
The equations come in the form of y=mx+c, where m is the gradient and c is the y-intercept. Looking at the graph we know that the y-intercept is (0,2), so that rules out options B and C.
To find the gradient is a little more tricky, but we can follow the formula:
, where rise is the vertical value and run is the horizontal value
So we sub in our values:
And simplify:
So now we sub in our new found values into y=mx+c:
y=1/2x+2
Answer: 3,140 radians per minute.
Step-by-step explanation:
We know that the wheel does 500 revolutions per minute.
This is called the frequency of the wheel, and this is written as:
f = 500 rev/min = 500 RPM
The angular speed (or Angular velocity) is written as
ω = 2*pi*f
And this quantity is in radians/unit of time.
where pi = 3.14
then:
ω = 2*3.14*500 (rev/min)*(rad/rev) = 3,140 rad/min
This means that the angular velocity (or angular speed) is 3,140 radians per minute.
Answer:
The number of possible choices of my team and the opponents team is
Step-by-step explanation:
selecting the first team from n people we have 
possibility and choosing second team from the rest of n-1 people we have 
As { A, B} = {B , A}
Therefore, the total possibility is 
Since our choices are allowed to overlap, the second team is
Possibility of choosing both teams will be
![\frac{n(n-1)}{2} * \frac{n(n-1)}{2} \\\\= [\frac{n(n-1)}{2}] ^{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%28n-1%29%7D%7B2%7D%20%20%2A%20%20%5Cfrac%7Bn%28n-1%29%7D%7B2%7D%20%20%5C%5C%5C%5C%3D%20%5B%5Cfrac%7Bn%28n-1%29%7D%7B2%7D%5D%20%5E%7B2%7D)
We now have the formula
1³ + 2³ + ........... + n³ =![[\frac{n(n+1)}{2}] ^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%20%5E%7B2%7D)
1³ + 2³ + ............ + (n-1)³ = ![[x^{2} \frac{n(n-1)}{2}] ^{2}](https://tex.z-dn.net/?f=%5Bx%5E%7B2%7D%20%5Cfrac%7Bn%28n-1%29%7D%7B2%7D%5D%20%5E%7B2%7D)
=![\left[\begin{array}{ccc}n-1\\E\\i=1\end{array}\right] = [\frac{n(n-1)}{2}]^{3}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dn-1%5C%5CE%5C%5Ci%3D1%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5B%5Cfrac%7Bn%28n-1%29%7D%7B2%7D%5D%5E%7B3%7D)
Answer:
The equation can define y as a function of x and it also can define x as a function of y.
Step-by-step explanation:
A relation is a function if and only if each value in the domain is mapped into only one value in the range.
So, if we have:
f(x₀) = A
and, for the same input x₀:
f(x₀) = B
Then this is not a function, because it is mapping the element x₀ into two different outputs.
Now we want to see it:
x + y = 27
defines y as a function of x.
if we isolate y, we get:
y = f(x) = 27 - x
Now, this is a linear equation, so for each value of x we will find an unique correspondent value of y, so yes, this is a function.
Now we also want to check if:
x + y = 27
defines x as a function of y.
So now we need to isolate x to get:
x = f(y) = 27 - y
Again, this is a linear equation, there are no values of y such that f(y) has two different values. Then this is a function.
2v=-68 I believe is the answer
