Answer:

Step-by-step explanation:



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Answer:the derivative of 1/x =-1/x^2
Step-by-step explanation:
1/x can also be written as x^-1
Therefore d/dx of x^-1
=-1*x^-1-1
=-1x^-2
Which can also be written as -1/x^2
Note: d/dx also means derivative of x
And d/dx (a/x^b) =(a*-b) /x^(b+1)
Where a and b represents a variable
Answer:
x (7+2x) = 372,
where 372 is the are of this rectangle, and
is its width.
Step-by-step explanation:
The width of this rectangle is
. Twice that width will be equal to
.
The length of this rectangle is seven more than twice the width of this rectangle, or seven more than
. The length of this rectangle will thus equal to
.
The area of a rectangle is equal to the product of its width and its length. The width of this rectangle times its length will be equal to
.
For this rectangle, this area is equal to 372. In other words,
.
This equation about
represents the relationship between the width, length, and the area of this rectangle.
Answer:
12 miles per hour
Step-by-step explanation:
Let speed of boat in still water be "x"
and speed of current be "c"
So, downstream rate would be "x + c"
And, upstream rate would be "x - c"
Now, given c = 4
We can use the distance formula, D = RT, where
D is distance, R is rate, and T is time
to solve this.
Downstream:
D = RT
92 = (x+4)(t)
Upstream:
D = RT
46 = (x-4)(t)
Both the times are same, we can equate both the times. Lets simplify first:
t = 92/(x+4)
and
t = 46/(x-4)
Equate:

Now, cross multiply and solve for x to get our answer:

Speed of Boat (in still water) = 12 mph
If the problem says "space", that usually means that they are talking about volume. The maximum length the box can be is 8.4 inches. To find volume, you do length * width * height. You know the length and height, as well as the volume. You can replace the width with "x". Your equation should be:
11.5 * 8.4 * x = 272.8
Then you can just solve for x by dividing both sides by (11.5 * 8.4). The answer should be about 2.82 inches.