To check for continuity at the edges of each piece, you need to consider the limit as approaches the edges. For example,
has two pieces, and , both of which are continuous by themselves on the provided intervals. In order for to be continuous everywhere, we need to have
By definition of , we have , and the limits are
The limits match, so is continuous.
For the others: Each of the individual pieces of are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
If the point P(x, y) partitions the segment AB in the ratio 1 : 1, then the point P is midpoint of segment AB.
The formula of a midpoint of segment:
We have:
Answer: C. (4, -1)
Answer:
This is an example of impulse purchase
Step-by-step explanation:
This is an impulse purchase since Ronnie didn't plan to by the stereo before entering the store. An impulse purchase comes from the word impulse I.e sudden urge leading to a prompt action. An impulse purchaser does not budget for whatever they buy rather are influenced by their emotions. If they're attracted to that item, they'll buy it instantly.
B- the volume of a cone is pi(r^2)(h/3) where r=radius and h= height.
When you plug in r &h you get pi(6^2)(19.6/3) =
pi(36)(6.53)=738.9
The formula for an area of a regular parallelogram is:
A = l * w
Where,
l = length
w = width
We are given that the total measurement of fence is only
60 feet and one side of the house is used as one side of the pen. Therefore,
l + 2 w = 60
<span>or simplifying to make an explicit expression for
one variable, say l:</span>
l = 60 – 2 w
<span>Substituting to the 1st equation:</span>
A = (60 – 2 w) * w
A = 60 w – 2 w^2
<span>The maxima are obtained by getting the 1st
derivative then equating dA/dw = 0:</span>
dA/dw
= 60 – 4 w
60 –
4 w = 0
4 w
= 60
w =
15
Since
l = 60 - 2w
l =
60 – 30
l =
30
<span>Therefore
the dimension that will make the largest pen is 15 ft by 30 ft.</span>
<span>ANSWER: C</span>