K=5/9(f-32)+273.15 solve the formula for f
ok i know the answer is f=32+9/5(k-273.15) but how? i need to show my work and i dont know how to get to the answer can u write out how step by step thx!

5463

Simplify ————

20

Equation at the end of step 1 :

5 5463

k - ((— • (f - 32)) + ————) = 0

9 20

Step 2 :

5

Simplify —

9

Equation at the end of step 2 :

5 5463

k - ((— • (f - 32)) + ————) = 0

9 20

Step 3 :

Equation at the end of step 3 :

5 • (f - 32) 5463

k - (———————————— + ————) = 0

9 20

Step 4 :

Calculating the Least Common Multiple :

4.1 Find the Least Common Multiple

The left denominator is : 9

The right denominator is : 20

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

3202

2022

5011

Product of all

Prime Factors 920180

Least Common Multiple:

180

Calculating Multipliers :

4.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 20

Right_M = L.C.M / R_Deno = 9

Making Equivalent Fractions :

4.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 5 • (f-32) • 20

—————————————————— = ———————————————

L.C.M 180

R. Mult. • R. Num. 5463 • 9

—————————————————— = ————————

L.C.M 180

Adding fractions that have a common denominator :

4.4 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5 • (f-32) • 20 + 5463 • 9 100f + 45967

—————————————————————————— = ————————————

180 180

Equation at the end of step 4 :

(100f + 45967)

k - —————————————— = 0

180

Step 5 :

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 180 as the denominator :

k k • 180

k = — = ———————

1 180

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

k • 180 - ((100f+45967)) 180k - 100f - 45967

———————————————————————— = ———————————————————

180 180

Equation at the end of step 5 :

180k - 100f - 45967

——————————————————— = 0

180

Step 6 :

When a fraction equals zero :

6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

180k-100f-45967

——————————————— • 180 = 0 • 180

180

Now, on the left hand side, the 180 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

180k-100f-45967 = 0

Equation of a Straight Line

6.2 Solve 180k-100f-45967 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 180k-100f-45967 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when k = 0 the value of f is 45967/-100 so this line "cuts" the f axis at f=-459.67000

f-intercept = 45967/-100 = -459.67000

Calculate the X-Intercept :

When f = 0 the value of k is 45967/180 Our line therefore "cuts" the k axis at k=255.37222

k-intercept = 45967/180 = 255.37222

Calculate the Slope :

Slope is defined as the change in f divided by the change in k. We note that for k=0, the value of f is -459.670 and for k=2.000, the value of f is -456.070. So, for a change of 2.000 in k (The change in k is sometimes referred to as "RUN") we get a change of -456.070 - (-459.670) = 3.600 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 3.600/2.000 = 1.800

Geometric figure: Straight Line

Slope = 3.600/2.000 = 1.800

k-intercept = 45967/180 = 255.37222

f-intercept = 45967/-100 = -459.67000

a

Step-by-step explanation: