Joaquin buys white shirts for $12 each. after he dyes and paints each shirt he plans to sell them at a 65% markup Joaquin wants
1 answer:
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Step-by-step explanation:
We are to get the expression for the following statements;
1) The difference of nine times a number x and the quotient of that number and 5.
The product of nine and a number x is expressed as;
The quotient of that number and 5.
The difference between both expression;
Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as
2) Eight more than the quotient of twelve and a number n
Quotient of twelve and a number n is expressed as:
Eight more than the resulting function is;
Hence eight more than the quotient of twelve and a number n is expressed as
3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.
Let the number be x:
six minus the number is expressed as;
product of a number x and the quantity 'six minus the number is;
quotient of eight and the number is;
Taking the resulting sum of the last two expression
Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;
4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).
Let the first even number be 2x
The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2
the sum of three consecutive even integers is expressed as;
A) 
is continuous, so 
is also continuous. This means if we were to integrate 
, the same constant of integration would apply across its entire domain. Over 
, we have 
. This means that
For to be continuous, we need the limit as 
to match 
. This means we must have
Now, over
, we have 
, so 
, which means 
.
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,
c) is increasing when 
, and concave upward when 
, i.e. when is also increasing.
We have
over the intervals 
and 
. We can additionally see that 
only on and .
d) Inflection points occur when
, and at such a point, to either side the sign of the second derivative 
changes. We see this happening at 
, for which 
, and to the left of we have decreasing, then increasing along the other side.
We also have along the interval 
, but even if we were to allow an entire interval as a "site of inflection", we can see that to either side, so concavity would not change.
For
Now, over
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,
c)
We have
d) Inflection points occur when
We also have