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const2013 [10]
3 years ago
9

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Cels

ius. Based on the equation, which of the following must be true?
l. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature
increase of 5/9 degree Celsius.
ll. A temperature increase of 1 degree Celsius is equivalent to a temperature
increase of 1.8 degrees Fahrenheit.
lll. A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature
increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

If u put a wrong answer ill report u
Mathematics
1 answer:
Maru [420]3 years ago
8 0

If you think of the equation as an equation for a line.


y=mx+b

y

=

m

x

+

b


where


C=5/9(F−32)

C

=

5

/

9

(

F

−

32

)


or


C=5/9F−5/9(32)

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Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a
NARA [144]

x^3y^2+\sin(x\ln y)+e^{xy}=0

Differentiate both sides, treating y as a function of x. Let's take it one term at a time.

Power, product and chain rules:

\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}

=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}

=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}

Product and chain rules:

\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}

=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)

=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)

=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}

Product and chain rules:

\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}

=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)

=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)

=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0

Isolate the derivative, and solve for it:

\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by y to get rid of that fraction in the denominator.

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}

3 0
3 years ago
35POINTS PLZ HELP FAST
meriva

Answer:

Step-by-step explanation:

16.76FT^3

3 0
3 years ago
Two numbers have a sum of -15 and a<br> product of -100. What are the numbers?
Bumek [7]

Answer:

the numbers are -20 and 5

Step-by-step explanation:

4 0
2 years ago
Fill in the blank for Remainder Therom<br><br><br> x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x+?)
icang [17]
Not sure about remainder theorem but I'm sure that the last terms should all multiply tho the last term


see the expanded form is -45

so the last terms of each binomial should multiply to -45

3 times -5 times ?=-45
-15 times ?=-45
divide by -15
?=3

the question mark is 3
5 0
3 years ago
Read 2 more answers
What is the value of the 5 in the number 2.005?<br> 0.5<br> 0.005<br> 0.05<br> 5
tino4ka555 [31]
The correct answer is 0.005
7 0
3 years ago
Read 2 more answers
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