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3 years ago

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The formula C − 5 sF 2 32d, where F > 2459.67, 9 expresses the Celsius temperature C as a function of the Fahrenheit temperat

ure F. Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

1 answer:

denpristay [2]3 years ago

3 0

Answer:

a) The inverse of the function is $F=\frac{9}{5}C+32$

b) The domain of the inverse function is C>1348.70.

Step-by-step explanation:

Given : The formula $C=\frac{5}{9}(F-32)$ , where $F>2459.67$ express the Celsius temperature C as a function of the Fahrenheit temperature F.

To find : a) A formula for the inverse function and interpret it.

b) What is the domain of the inverse function?

Solution :

a) The formula $C=\frac{5}{9}(F-32)$

The inverse function of the given formula is the value of F.

Taking F to one side and rest term to other side,

$\frac{9}{5}C=(F-32)$

$\frac{9}{5}C+32=F$

Therefore, The inverse of the function is $F=\frac{9}{5}C+32$

i.e. Fahrenheit temperature F as a function of the Celsius temperature C.

b) The domain of the inverse function.

We have given, $F>2459.67$

Substituting in the formula,

$C=\frac{5}{9}(F-32)$

$C=\frac{5}{9}(2459.67-32)$

$C=\frac{5}{9}(2427.67)$

$C=1348.70$

The domain of the inverse function is C>1348.70.

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Two numbers, 3 and a, have a geometric mean of 9. Find the value of a.

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So, if the geometric mean of 3 and a is 9 =>

9 = √(3a)

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=> a = 9^2 / 3

a = 81 / 3

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Answer: the value of a is 27.

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3 years ago

5a + 3b + c= 40<br> a-3b+2c= -10<br> 14a-2b+3c= 50

aalyn [17]

Answer:

a= 40-3b-c/5

a=-10+3b-2c

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Step-by-step explanation:

5a+3b+c-(3b+c)=40-(3b+c)

5a=40-3b-c

5a/5=40/5-3b/5-c/5

a= 40-3b-c/5

a-3b+2c-(3b+2c)=-10-(-3b+2c)

a=-10+3b-2c

14a-2b+3c-(-2b+3c)=50-(-2b+3c)

14a=50+2b-3c

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3 years ago

liubo4ka [24]

Answer:

The correct option is B.

Step-by-step explanation:

The amount of money, in dollars, in a savings account after x years is given by $M(x) = 10000(1.03)^{x}$

This above equation represents that $10000 becomes M(x) after x years at a rate of interest 3% compounded in each year.

Therefore, the value in the expression 1.03 represents that there is a 3 percent increase in the savings account each year.

So, the correct option is B. (Answer)

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4 years ago

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

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$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
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By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

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3 years ago

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pickupchik [31]

Answer:

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If you divide 2 by 3, you will end up with 0.6.

Now, you can compare the two numbers 0.6 and 0.67.

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