Answer:
Step-by-step explanation:
Given:
x = 2cost,
t = (1/2)arccosx
y = 2sint
dy/dx = dy/dt . dt/dx
dy/dt = 2cost
dt/dx = -1/√(1 - x²)
dy/dx = -2cost/√(1 - x²)
Differentiate again to obtain d²y/dx²
d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)
At t = π/4, we have
(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)
A function that would represent profit based on the number of cups of lemonade is Profit = 1.5n - 14
<u>Solution:</u>
Given, Some kids are selling lemonade for $1.50 per cup at a high school baseball game.
They spent $14 on all of the items needed for the lemonade stand (cups, lemonade, table oth, sign, etc)
We have to create a function that would represent profit based on the number of cups of lemonade
Now, let the number of cups sold be "n"
Then , we know that,<em> profit = selling price – cost price </em>
Profit = number of cups sold x price per cup – cost price
Profit = n x $ 1.5 – $ 14
Profit = 1.5n – 14
Hence, the function is Profit = 1.5n - 14
Answer:
Volume: 3x2x4=24 so the volume is 24 Meter3
Surface area:
52 Square meter
At
, you have
The trick to finding out the sign of this is to figure out between which multiples of
the value of
lies.
We know that
whenever
, and that
whenever
, where
.
We have
which is to say that
, an interval that is equivalent modulo
to the interval
.
So what we know is that
corresponds to the measure of an angle that lies in the third quadrant, where both cosine and sine are negative.
This means
, so
is decreasing when
.
Now, the second derivative has the value
Both
and
are negative, so we're essentially computing the sum of a negative number and a positive number. Given that
for
, and
for
, we can use a similar argument to establish in which half of the third quadrant the angle
lies. You'll find that the sine term is much larger, so that the second derivative is positive, which means
is concave up when
.
