What is the completely factored form of the expression 16x2 + 8x + 32?
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From what I imagine in the problem description, the toy is located on the ground. Then, Belkis is pulling on the string to keep the toy moving just like how you put a leash on a dog. My illustration is shown in the picture. The F arrow is where Belkis pulls it. Its component vectors are Fx and Fy, as shown.
From the figure, we can see that it forms a right triangle. So, it makes it easy because the pythagorean theorems are applicable and we can easily use trigonometric functions. First, let's determine Fy which is located opposite to the angle. Since we know the hypotenuse F to be 1.5 N, so we use the sine function:
sin 52° = Fy/F = Fy/1.5
Fy = 1.182 N
For the horizontal component, Fx is parallel to the adjacent side with respect to the angle. Thus, we use the cosine function.
cos 52° = Fx/F = Fx/1.5
Fx = 0.923 N
From the figure, we can see that it forms a right triangle. So, it makes it easy because the pythagorean theorems are applicable and we can easily use trigonometric functions. First, let's determine Fy which is located opposite to the angle. Since we know the hypotenuse F to be 1.5 N, so we use the sine function:
sin 52° = Fy/F = Fy/1.5
Fy = 1.182 N
For the horizontal component, Fx is parallel to the adjacent side with respect to the angle. Thus, we use the cosine function.
cos 52° = Fx/F = Fx/1.5
Fx = 0.923 N
Take partial derivatives and set them equal to 0:
We find one critical point within the boundary of the disk at
. The Hessian matrix for this function is
which is positive definite, and incidentally independent of
and 
, so 
attains a minimum 
.
Meanwhile, we can parameterize the boundary by
with 
, which gives
with critical points at
At these points, we get
so we attain a maximum only when
, which translates to 
.
We find one critical point within the boundary of the disk at
which is positive definite, and incidentally independent of
Meanwhile, we can parameterize the boundary by
with critical points at
At these points, we get
so we attain a maximum only when