Answer:
a) d²y/dx² = ½ x + y − ½
b) Relative minimum
Step-by-step explanation:
a) Take the derivative with respect to x.
dy/dx = ½ x + y − 1
d²y/dx² = ½ + dy/dx
d²y/dx² = ½ + (½ x + y − 1)
d²y/dx² = ½ x + y − ½
b) At (0, 1), the first and second derivatives are:
dy/dx = ½ (0) + (1) − 1
dy/dx = 0
d²y/dx² = ½ (0) + (1) − ½
d²y/dx² = ½
The first derivative is 0, and the second derivative is positive (concave up). Therefore, the point is a relative minimum.
Answer:
C) 4
Step-by-step explanation:
Given equation:

The above equation represents proportional relationship.
To find the constant of proportionality.
Solution:
<em>The equation representing proportional relationship is given by:</em>
<em>
</em>
<em>where
represents constant of proportionality.</em>
So, in order to find the value of
for the given proportionality relationship, we will solve for 
We have:

Solving for 
Dividing both sides by 2.


∴ 
Thus, the constant of proportionality = 4.
2.20 rounded to the nearest tenth is 2.2 it is already rounded if it was 2.29 it would be 2.3
Answer:
19°
Step-by-step explanation:
I have attached an image showing this elevation.
From the image, let's first find the angle A by using cosine rule.
Thus;
8.1² = 5.5² + 13.1² - 2(5.5 × 13.1)cos A
65.61 = 30.25 + 171.61 - 144.1cos A
144.1cos A = 171.61 + 30.25 - 65.61
144.1cosA = 136.25
cosA = 136.25/144.1
cosA = 0.9455
A = cos^(-1) 0.9455
A = 19°