<span> the equation of this circle is (x - 3)² + (y + 1)² = 4²</span>
Answer:
0.1187
Step-by-step explanation:
A = P (1 + k)^t
where A is the final amount,
P is the initial amount,
k is the monthly growth rate,
and t is the number of months.
70 = 50 (1 + k)^3
1.4 = (1 + k)^3
∛1.4 = 1 + k
k = -1 + ∛1.4
k = 0.1187
The original width would be 19 and the original length would be 32.
Let w be the width. Then 2w-6 would be the length. However, after cutting a 3-inch square from each corner, both the width and length left over to fold into a box would be 6 inches smaller; thus the dimensions would be w-6 and 2w-6-6 or 2w-12.
Since the section cut out is 3 inches long, 3 will be the height of the box.
Volume is found by multiplying the length, width and height of the box; thus we have:
1014=(w-6)(2w-12)(3)
We multiply the binomials and have:
1014 = [w*2w-12*w-6*2w-6(-12)](3)
1014 = (2w²-12w-12w+72)(3)
1014 = (2w²-24w+72)(3)
1014 = 6w² - 72w + 216
When solving a quadratic equation, we want it set equal to 0. Subtract 1014 from each side:
1014-1014 = 6w² - 72w + 216 - 1014
0 = 6w² - 72w - 798
We will use the quadratic formula to solve this:

Since we cannot have a negative number for a measurement, 19 has to be the width; then 2(19)-6 = 32 would be the length.
Answer:
3729.5521 exact 3729.55 rounded
Step-by-step explanation:
Rule: second differences are 2.
Selection C is appropriate.
_____
First differences are the sequence of differences of the given numbers:
.. 3 -8 = -5
.. 0 -3 = -3
.. -1 -0 = -1
.. 0 -(-1) = 1
Second differences are the sequence of differences of these:
.. -3 -(-5) = 2
.. -1 -(-3) = 2
.. 1 -(-1) = 2
All of these are 2, so the sequence can be described by a *second* order polynomial (because *second* differences are a non-zero constant).