Answer:
113.04
Step-by-step explanation:
Our formula for this circle is 3.14x6^2(6x6) and our formula is 3.14xr^2 so it equals 113.04
The intersecting arcs are created and connected.
Answer: The answer is the picture shown below
Step-by-step explanation:
To do this you will need to make a coordinate plane about 20 up and 20 down. So there is a formula that is y=mx+b which is called the slope intercept form and as you can see the problem given to you was already given in this formula. The variable m in the equation is the slope and slope is also known as rise (which basically means go up if positive and down if negative) over run (which is right if positive and left if negative) and as you can see in the equation the number 4/5 is the variable m. Since slope is rise over run 4 would be the rise and 5 would be the run, so you would go up 4 and right 5 because they are both positive. Now there is another variable that is b which would be the -1. In slope intercept formula b is the y intercept so -1 is where the line would cross the y axis. Now that you know all the parts to the slope you can put it together giving you the answer.
Hi there what you need is lagrange multipliers for constrained minimisation. It works like this,
V(X)=α2σ2X¯1+β2\sigma2X¯2
Now we want to minimise this subject to α+β=1 or α−β−1=0.
We proceed by writing a function of alpha and beta (the paramters you want to change to minimse the variance of X, but we also introduce another parameter that multiplies the sum to zero constraint. Thus we want to minimise
f(α,β,λ)=α2σ2X¯1+β2σ2X¯2+λ(\alpha−β−1).
We partially differentiate this function w.r.t each parameter and set each partial derivative equal to zero. This gives;
∂f∂α=2ασ2X¯1+λ=0
∂f∂β=2βσ2X¯2+λ=0
∂f∂λ=α+β−1=0
Setting the first two partial derivatives equal we get
α=βσ2X¯2σ2X¯1
Substituting 1−α into this expression for beta and re-arranging for alpha gives the result for alpha. Repeating the same steps but isolating beta gives the beta result.
Lagrange multipliers and constrained minimisation crop up often in stats problems. I hope this helps!And gosh that was a lot to type!xd
Answer:
180
Step-by-step explanation:
30 in 10 secs x6
180 in 60 secs.