6 - 34 + 96 - 384 +...
a 1 = 6 , a 2 = a 1 * ( - 4 ) , a 3 = a 2 * ( - 4 ), a 4 = a 3 * ( - 4)...
a 5 = - 384 * ( - 4 ) = 1,536
a 6 = 1536 * ( - 4 ) = - 6,144
a 7 = - 6,144 * ( - 4 ) = 24,576
This is a sum of a geometric sequence:
S 7 = 6 - 24 + 96 - 384 + 1,536 - 6,144 + 24,576 = 19,662
Another way to solve this:
S 7 = a 1 * ( r^n - 1) / ( r - 1 ) = 6 * (( - 4) ^7 - 1 )/ (- 4 - 1)=
= 6 * (-16,385) / (-5 ) = 19,662
Part A. To solve for the distance travelled during the
interval, all we have to do is to plug in values of t = 3 and t = 3.5 in the
equation and the difference would be the answer:
when t = 3: s = 16 (3)^2 = 144 m
when t = 3.5: s = 16 (3.5)^2 = 196 m
Therefore the distance travelled within the interval is:
196 m – 144 m = 52 m
<span>Part B. The velocity is calculated by taking the 1st
derivative of the equation. v = ds / dt</span>
s = 16 t^2
ds / dt = 32 t = v
when t = 3: v = 32 (3) = 96 m / s
when t = 3.5: v = 32 (3.5) = 112 m / s
Therefore the average velocity is:
(96 + 112) /2 = 104 m / s
Part C. We can still use the formula v = 32 t and plug in
the value of t = 3
v = 32 t = 32 (3)
v = 96 m / s
<span> </span>
9514 1404 393
Answer:
rectangle: 2x+2 wide by 2x high
triangle: 2 high
Step-by-step explanation:
Usually, a problem like this is asking you to find dimension expressions that combine to give you the given expression. There are usually a number of possibilities. Using the designators in the attached, we would generally like to have B > C and A about the same as C. That doesn't seem possible with the given factors.
__
The given quadratic expression factors as ...
area = 4x^2 +6x +2 = (2x+2)(2x +1)
This might be written to match the area formula as ...
(2x +2)(2x +2/2)
This would give A=2, B=2x+2, C=2x, as shown in the attachment.
The data is a positive correlation
