Let f(x) = x2 − 16. find f−1(x). open study
2 answers:
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Given the following question:
We are given 12.4%
Answer:
see graph of y = 5x - 7
Step-by-step explanation:
If graphing is the task, you should rewrite the equation in a y = ax + b form. All straight lines can be described in this form, only the a and b determine which line it is.
Your equation 5x-y=7 has the 5x on the left side, so lets move it to the right. It will get a negative sign (this is the same as subtracting 5x like you did in your picture)
5x - y = 7
-y = 7 - 5x
Now we still have the -y which should be a +y. So we multiply left and right with -1 and get:
y = -7 + 5x
If we swap the -y and 5x (we can, because they are just an addition), we get:
y = 5x - 7
Now the equation is in its "normal" form. It's like the y = ax + b with a and b chosen as a=5 and b=-7.
The normal form is handy because you can immediately see the slope is 5 and the intersection with the y-axis is at y=-7.
Answer:
The size square removed from each corner = 32.15 cm²
Step-by-step explanation:
The volume of the box = Length * Breadth * Height
Let r be the size removed from each corner
Note that at maximum volume,
The original length of the cardboard is 119 cm, if you remove a size of r (This typically will be the height of the box) from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:
Length, L = 119 - 2r
Similarly for the breadth, B = 24 - 2r
And the height as stated earlier, H = r
Volume, V = L*B*H
V = (119-2r)(24-2r)r
V = r(2856 - 238r - 48r + 4r²)
V = 4r³ - 286r² + 2856r
At maximum volume dV/dr = 0
dV/dr = 12r² - 572r + 2856
12r² - 572r + 2856 = 0
By solving the quadratic equation above for the value of r:
r = 5.67 or 42
r cannot be 42 because the size removed from the corner of the cardboard cannot be more than the width of the cardboard.
Note that the area of a square is r²
Therefore, the size square removed from each corner = 5.67² = 32.15 cm²