Answer:
Here we have the relation:
m = 140*h
Where m is the distance in miles, and h is time in hours.
And we want to complete a table like:
![\left[\begin{array}{ccc}in, h&out, m\\&\\&\\&\\&\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Din%2C%20h%26out%2C%20m%5C%5C%26%5C%5C%26%5C%5C%26%5C%5C%26%5Cend%7Barray%7D%5Cright%5D)
The way to complete this, is to evaluate the function:
m = 140*h
in different values of h, and then record both values of h and m in the table.
Let's use values of h that increase by 0.5, then:
if h = 0.5
m = 140*0.5 = 70
We have the pair: h = 0.5, m = 70
if h = 1
m = 140*1 = 140
We have the pair: h = 1, m = 140
if h = 1.5
m = 140*1.5 = 210
Then we have the pair h = 1.5, m = 210
if h = 2
m = 140*2 = 280
We have the pair: h = 2, m = 280
Now we can complete the table, and it will be:
![\left[\begin{array}{ccc}in, h&out, m\\0.5&70\\1&140\\1.5&210\\2&280\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Din%2C%20h%26out%2C%20m%5C%5C0.5%2670%5C%5C1%26140%5C%5C1.5%26210%5C%5C2%26280%5Cend%7Barray%7D%5Cright%5D)
The dimensions of the square base after cutting the corners will be (40-2x). The depth of the box will be x, so its volume is given by
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The
dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deepThe
maximum volume is
(80/3 in)²(20/3 in) =
4740 20/27 in³
To find z, you have to divide -3 and 10, which you would get an odd number. That will be your answer for z :)
Answer:
Step-by-step explanation:
We know that:
Remember:
450°=360°+60°
and:
Thus:
Then:
By the Pythagorean Theorem:
L^2=20^2+15^2
L^2=400+225
L^2=625
L=25 m
