Doubling the side-lengths will multiply the area by four.
Proof:
Let the side-lengths of the rectangle by x and y. Clearly, the area will be x*y=xy. The new rectangle will have side-lengths 2x and 2y, and thus area 2x*2y=4xy. 4xy/xy=4 - hence, the new rectangle has four times the area of the old one.
What goes in goes out. This means none of the current is lost. So if 0.7amps+0.68amps+0.47amps = 1.85 amps comes in, then 1.85 amps goes out. So far we have 0.8 amps+0.55 amps going out= 1.35 amps. This means we need an additional 1.85-1.35amps going out= 0.5 amps for the third outgoing current. Cheers!
So what is the question??? If I understand correctly....
y = 3x
First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.
You'll basically complete the square for two equations at the same time. Set it up like this:
(16x^2 + 96x) + (9y^2 - 18y) = 9
Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.
(x^2 + 6x) + (y^2 - 2y) = 9/144
then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.
For instance the first one will be 6/2 = 3^2 = 9
The next one will be 2/2 =1^2 = 1
Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.
(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1
Then find a common denominator on the right side of the equals sign and add them all together to get:
(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144
Factor out the two polynomials
(x+3)^2 + (y-1)^2 = 1449/144
the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
23.
assuming you mean
first term is n=1, so 1²+3=1+3=4
2nd is n=2 so 2²+3=4+3=7
3rd is n=3 so 3²+3=9+3=12
the first 3 terms are 4,7,12
24.
5th term is 5²+3=25+3=28
10th term is 10²+3=100+3=103
difference is 103-28=75
