A food scientist is developing a new recipe. He needs it to have between 3 and 5 teaspoons of sugar per serving and between 3 an
d 6 grams of fiber. Each teaspoon of sugar has 5 carbohydrates. Each gram of fiber counts as a carbohydrate when counting total carbohydrates. If the recipe already has 10 carbohydrates per serving from other sources, create a linear programming feasible region to minimize the total carbohydrates in the recipes nutrition profile.
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Let
x-------> the number of hours
y------> the temperature in degrees Fahrenheit
we know that
For
For
The domain of the function is the interval---------->
The range of the function is the interval---------->
therefore
<u>the answer is</u>
The domain is all real numbers 0 through 30
Answer:
m < A = 60º
m < B = 30º
Step-by-step explanation:
The given sides on this triangle are: 6, , and 12
Any triangle with the angles of 30º - 60º - 90º always has side lengths in this proportion:
x, , 2x
We can line this up with the given sides. If x is 6, then 2x would be 12.
x : : 2x = 6 :
: 12
Angle B is across from 6, the shortest side. That also means that it corresponds to x, or the smallest angle in the proportion, 30º.
m < B = 30º
Solving for < A:
Method 1) Sum of Angles in a Triangle
Since we already know that one angle is right and therefore 90º and m < B is 30º, we can subtract these from the total sum of angle measures in a triangle to get the last angle, < A.
180º - 90º - 30º = 60º
m < A = 60º
Method 2) Using the second part of the proportion
Since m < A is across from the second largest side, we know that it is equal to (
in this question) or 60º in the angle proportion.
This means that m < A = 60º
Let me know if you have any questions!