The first one is 10ab + 20
The standard form of the equation of a circle of radius r, with (assuming centre h, k) is given as:
(X-h)^2 + (y-k)^2 = r^2
As we are required to write an equation in standard form for the circle with radius 9 centred at the origin.
Centre(h,k)=(0,0), r=9
Substituting these values into the standard form of the equation of a circle given above:
(X-0)^2 + (y-0)^2 = 9^2
X^2 + y^2 =81
The standard form is x^2 + y^2 =81
I’m pretty sure this is right
Answer:
4 feet
Step-by-step explanation:
We start by subtracting the 6 from the 14, to get the leftover space on the wall, 8 feet. We then divide that by two, since if the painting is centered there will be two equally-sized spaces on either side of it. This means that X = 4 feet.
<span> To get an explicit formula, we need to find an expression which gives the n-th term without having to compute earlier terms in the sequence. Looking at the numbers, and from the recursive formula, we see that the sequence is built by subtracting n from the previous term. This is similar to the triangular number sequence 1,3,6,10,15,... which has the explicit formula a_n = n(n+1)/2. In our case we are subtracting n from the previous term, so we multiply by -1/2 instead of 1/2. However, we also need to add a constant term to reproduce the numbers of the sequence. We can write a_1 = -1(2)/2 + c = 8. Therefore, c = 9.
So the explict formula is:
a_n = -n(n+1)/2 + 9</span>
