Question 21 (Essay Worth 8 points)
[2.08] The formula for degrees Celsius is: C = 9 over 5 (F − 32), where F stands for degrees Fahrenheit.
Part 1: Solve the formula for F. Show all steps.
Part 2: Determine how many degrees Fahrenheit 2 degrees Celsius is.
I am reminded of a recent post entitled
9th Grade speeling
Here: multiply both sides by 5/9
5/9 C=F-32
add 32 to both sides.
A curious question: At what temperature is F and C exactly the same? I leave that to you to explore.
[6.02] Use the Substitution Method to solve the following system of equations.
2x + y = 3
-3x + 4y = 1
(1, 1)
(-1, -1)
(1, -1)
(-1, 1)
POOPOPPPOPOPOPOPOPOPOP
Part 1: To solve the formula C = 9/5 (F - 32) for F, we need to isolate F on one side of the equation.
Starting with the formula C = 9/5 (F - 32), let's first get rid of the fraction by multiplying both sides of the equation by the reciprocal of 9/5, which is 5/9. This gives us:
C * (5/9) = (9/5) * (F - 32)
Now we can simplify the equation:
(5/9)C = (9/5)F - (9/5)32
Next, let's simplify the equation further by distributing (9/5) to F and 32:
(5/9)C = (9/5)F - (288/5)
Now we want to isolate F, so let's move the term (-288/5) to the other side of the equation:
(5/9)C + (288/5) = (9/5)F
To further simplify the equation, we can find a common denominator for the fractions:
(25/45)C + (288/45) = (81/45)F
Now we can combine the fractions:
(25C + 288) / 45 = (81F) / 45
Finally, to isolate F, we divide both sides of the equation by (81/45):
[(25C + 288) / 45] * (45/81) = F
Simplifying the equation:
F = (25C + 288) / 81
Therefore, the solution to part 1 is F = (25C + 288) / 81.
Part 2: To determine how many degrees Fahrenheit 2 degrees Celsius is, we can use the formula we obtained in part 1.
Plugging in C = 2 into the formula for F:
F = (25(2) + 288) / 81
Simplifying the equation:
F = (50 + 288) / 81
Performing the addition and division:
F = 338 / 81
This gives us a decimal value for F. To find the exact value, we can divide 338 by 81:
F ≈ 4.1728
Therefore, 2 degrees Celsius is approximately 4.1728 degrees Fahrenheit.