Answer:
Solution: ,
Step-by-step explanation:
<u>System of Equations</u>
Solve the system:
x + 4y = 14
3x - 2y = 7
using the elimintation method.
To use the elimination method, we must add or subtract both equations in such a way that one of the variables goes away, and only one remains.
It requires to multiply one of them by a specific factor to match the coefficients. For example, multiply the first equation by -3:
-3x - 12y = -42
And add it to the second:
3x - 2y = 7
To result:
-14y = -35
Divide by -14:
Simplifying:
Now calculate x:
Solution: ,
Answer:
This is the interval from -9 to 16. Exclude -9 but include 16.
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Work Shown:
The idea is to multiply all sides by 5, then add 1 to all sides
This converts to the interval notation
note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.
Answer:
If , the slang height of the cone is approximately 23.521 inches.
Step-by-step explanation:
The surface area of a cone (A) is given by this formula:
Where:
- Base radius of the cone, measured in inches.
- Slant height, measured in inches.
In addition, the slant height is calculated by means of the Pythagorean Theorem:
Where is the altitude of the cone, measured in inches. If
, then:
And:
Given that , the following second-order polynomial is obtained:
Roots can be found by the Quadratic Formula:
As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.