Answer:
The ratio 450 : 200 can be reduced to lowest terms by dividing both terms by the GCF = 50 :
450 : 200 = 9 : 4
Therefore:
450 : 200 = 9 : 4
basically 9/4
Step-by-step explanation:
Answer:

Step-by-step explanation:
A second order linear , homogeneous ordinary differential equation has form
.
Given: 
Let
be it's solution.
We get,

Since
, 
{ we know that for equation
, roots are of form
}
We get,

For two complex roots
, the general solution is of form 
i.e 
Applying conditions y(0)=1 on
, 
So, equation becomes 
On differentiating with respect to t, we get

Applying condition: y'(0)=0, we get 
Therefore,

Answer:
1041.6
Step-by-step explanation:
The volume of a pyramid is V=b x h x 1/3 . b is the area of the base and h is the height. V=124 x 25.2 x 1/3 This can simplify to V=3124.8 x 1/3 . You could also just divide by 3. You will get 1041.6
Let h = height of the box,
x = side length of the base.
Volume of the box is

.
So

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is


The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then

So the box is 4.86 in. wide and 4.87 in. high.
Answer:

Step-by-step explanation:
The magnitude of vector
is given by 
The magnitude of vector
is
.

The magnitude of vector
is
.

Therefore,
