Pls solve the following problem:?

Question

1. The temperature of an object in Celsius and Fahrenheit scales are related by a linear function.Water boils at 100 degrees celsius or 212 degrees fahrenheit, and freezes at 0 degree celsius or 32 degrees fahrenheit.
a. Write the function expressing F in terms of C.
b.Transform the function so that C is expressed in terms of F..
c. Normal body temperature is 98.6 degrees fahrenheit.What celsius temperature is this?
d. If the weather is forecast at 40 degrees celsius today,will it be cold, hot or just warm? Explain...
e. Sketch the graph of F as a function of C.
pls with complete solution and explain the answer........

Answer 1

a)
The points are in the form (F, C)
We have two:
(212, 100)
(32, 0)

First find the slope:
m = (100 - 0) / (212 - 32) = 100 / 180 = 5/9

Now find the line using point-slope form:
C - 0 = (5/9)(F - 32)
C = (5/9)(F - 32)

b)
(5/9)(F - 32) = C
F - 32 = (9/5)C
F = (9/5)C + 32

c)
Plug in 98.6 for F and solve.
C = (5/9)(F - 32)
C = (5/9)(98.6 - 32)
C = (5/9)(66.6) = 37

d)
Plug in 40 for C and solve.
F = (9/5)C + 32
F = (9/5)(40) + 32
F = 72 + 32 = 104

e)
Graph C = (5/9)(F - 32).
Put F on the x-axis and C on the y-axis.
Plot points (32, 0) and (212, 100) and connect the dots.

Answer 2

you have

F=aC+b where a and b are the coefficients
if C=0 F=32 so the coefficient b is 32
F=212 when C=100 so 212=a*100+32and 180 =100a a=1.8

so answer a) F =1.8 C +32

b) from a) you have F -32 = 1.8C and C=(F-32)/1.8

c) C= (98.6-32)1.8 =37

d)if C=40 then F= 1.8*40+32= 104 pretty warm

e) the graph is a line passing by 32 on the ordinate axis and the point with abcissa 100 and ordinate 212

Answer 3

1)
The fact that they are related linearly suggests that
F = a*C+b,
where a and b are constants.

Plugging in some constant values for F and C that you know,
212 = a*100 +b,
and
32 = a*0 + b
32 = b

Then 212 = 100*a +32, and reduce.
180 = 100*a
9/5 = a
Therefore,
F = (9/5)*C + 32

2) Just flip it around,
F - 32 = (9/5)*C
C = (5/9)(F-32)

3)
C = (5/9)*(98.6-32)
C = (5/9)*(66.6)

4)Convert into degrees Fahrenheit from your previous equation, and it's plain to see that it'll be quite hot.

5) Should be a straight line with a positive slope.

Answer 4

Convert fahrenheit to celsius formula

F = 9/5C + 32

The reciprocal of 9/5 is 5/9. Multiply both sides of the equation by 5/9

5/9F = 5/9(9/5)C + 32

5/9F = C + 32

Transpose 32

5/9F - 32 = C + 32 - 32

5/9F - 32 = C . . .←..This is the Celsius Formula

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C = 5/9(F - 32)

C = 5/9(98.6 - 32)

C = 5/9(66.6)

C = 333 / 9

C = 37°

37° Celsius equals 98.6° Fahrenheit

- - - - - - -s-

Answer 5

C=5/9(F-32)

i think the rest is easy and u can do it urself