There are two ways to solve the problem: using calculus and algebra. For this, I'll be using the algebraic way. The function is parabolic, thus the minimum value is the ordinate of the vertex. Using completing the square, we could get the vertex of the parabola.
y = x^2 + 4x - 5y = x^2 + 4x + 4 - 5 - 4y = (x + 2)^2 - 9Vertex is (-2, -9).
Therefore, the minimum value is -9.
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Answer:
The length of each side of the cube is 
Step-by-step explanation:
we know that
The volume of a cube is equal to
but remember that in a cube
Length, width and height have the same value
so
Let
b-----> the length side of the cube
substitute in the formula
In this problem we have
substitute and solve for b
![b=\sqrt[3]{\frac{1}{512}}\\ \\b=\frac{1}{8}\ m](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B512%7D%7D%5C%5C%20%5C%5Cb%3D%5Cfrac%7B1%7D%7B8%7D%5C%20m)
therefore
The length of each side of the cube is
Answer:
The correct answer is 7.54 foot apart.
Step-by-step explanation:
The height of the Cap San Juan Lighthouse is 45 foot.
The angle of depression of the first boat is given to be 40°.
Distance between the first boat and the lighthouse is cos 40° × 45 = 34.47 foot.
The angle of depression of second boat is given to be 21°.
Distance between the second boat and the lighthouse is cos 21° × 45 = 42.01 foot.
Therefore the boats are 42.01 - 34.47 = 7.54 foot apart from each other.
The answer is A.
We know that p must be larger than d since a discount means something will be cheaper. Then we know that $2.50 is essentially what p-d should equal to (p-d =2.50)
Then you work through the various tables and find which values will consistently give you 2.50 as the difference between p and d.
For example in table A:
3.00-0.15=2.50
4.00-1.50=2.50
5.00-2.50=2.50
6.00-3.50=2.50
The x intercept would be -2
and the y intercept would be 21
