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velikii [3]
3 years ago
10

A scientist measure change in the temperature of chemical solution at the start of the experiment , the solutions is at temperat

ure of -14.96C. The temperature decreases 2.9C each hour
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
4 0

Answer:

The temperature of the chemical solution after t hours is -14.96-2.9t\;^{\circ}C

Step-by-step explanation:

Given that the initial temperature of the chemical solution, T_0= -14.96^{\circ}C.

The rate of decreasing temperature, R = 2.9^{\circ}C/ hour

So, after t hours, the temperature of the chemical solution will decrease by Rt=2.9t^{\circ}C.

So, the temperature of the chemical solution after t hours,

T=T_0-Rt \\\\\Rightarrow T = -14.96-2.9t\;^{\circ}C

Hence, the temperature of the chemical solution after t hours is -14.96-2.9t^{\circ}C.

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What is the domain of f?
Alona [7]

Answer:

C

Step-by-step explanation:

The domain is the set of x-values used by the graph.

7 0
3 years ago
1/3 cup of flour is used to make 5 dinner rolls.
RoseWind [281]

we know that

\frac{1}{3} cup of flour is used to make 5 dinner rolls.

Part a) How much flour is needed to make one dinner roll?

by using proportion

\frac{\frac{1}{3}}{5}  =\frac{x}{1} \\ \\ x=\frac{\frac{1}{3}}{5}\\ \\ x=\frac{1}{15}

therefore

the answer Part a) is

To make one dinner roll is needed \frac{1}{15} cup of flour

Part b) How many cups of flour are needed to make 3 dozen dinner rolls?

Multiply the value obtained in part a) by 36

so

\frac{1}{15} *36=\frac{36}{15} \\ \\ =\frac{12}{5}

\frac{12}{5} =2\frac{2}{5}

therefore

the answer Part b) is

To make 3 dozen dinner rolls are needed 2\frac{2}{5} cup of flour

Part c) How many rolls can you make with 5 2/3 cups of flour?

5\frac{2}{3} =\frac{17}{3}

by using proportion

\frac{\frac{1}{3}}{5}  =\frac{\frac{17}{3}}{x} \\ \\ \frac{x}{3} =\frac{85}{3} \\ \\ x=85

therefore

the answer part c) is

85 rolls

6 0
3 years ago
Read 2 more answers
The South Coast Air Basin (Los Angeles, Orange, and San Bernardino counties) does not meet the air quality standards for carbon
Archy [21]

Answer:

0.2225 gr/mile

Step-by-step explanation:

Let's work out first the amount of CO sent out in 1990.

The population we estimated in 12.5 million people with a total of driven miles per year of about  

12.5 million*8,700 = 108,750 million miles.

With an CO emission factor of 0.9 g per mile, we would have a total of CO emitted rounding 0.9*180,750 = 97,875 million grams

Now, we must estimate the population for 2020.

Since we are assuming an exponential growth, the population in year t is given by a function

\bf P(t)= Ce^{kt}

where C and k are constants to be determined.

We can take 1980 as year 0. This way calculations are lighter. 1990 is year 10 and 2020 is year 20.

So P(0) = 10.3 and C=10.3

So far we have

\bf P(t)= 10.3e^{kt}

Given that P(10)=12.5

\bf 10.3e^{k*10}=12.5\rightarrow e^{10k}=\frac{12.5}{10.3}=1.21359\rightarrow \\10k=log(1.21359)\rightarrow k=0.01936

And the function that models the population growth is

\bf P(t)= 10.3e^{0.01936t}

We need P(20)

\bf P(20)= 10.3e^{0.01936*20}=10.3e^{0.38717}=15.17\;million

If the miles driven per person per year remains constant at 8700 mi/yr.person, then we have a total miles driven of

15.17*8,700=131,979 million miles, so the CO emitted would be 0.9*131,979=118,781.1 million grams.

The 30% of the CO sent out in 1990 is 0.3*97,875=29,362.5 million grams.

We must reduce 118,781.1 down to 29,362.5

Hence the new CO emission factor would be

29,362.5/131,979 = 0.2225 gr/mile

6 0
3 years ago
Which of these equations are in slope-intercept form?
maxonik [38]

Answer:

y = mx + b

Step-by-step explanation:

6 0
3 years ago
Solve irrational equation pls
rusak2 [61]
\hbox{Domain:}\\
x^2+x-2\geq0 \wedge x^2-4x+3\geq0 \wedge x^2-1\geq0\\
x^2-x+2x-2\geq0 \wedge x^2-x-3x+3\geq0 \wedge x^2\geq1\\
x(x-1)+2(x-1)\geq 0 \wedge x(x-1)-3(x-1)\geq0 \wedge (x\geq 1 \vee x\leq-1)\\
(x+2)(x-1)\geq0 \wedge (x-3)(x-1)\geq0\wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle1,\infty) \wedge x\in(-\infty,1\rangle \cup\langle3,\infty) \wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle3,\infty)



\sqrt{x^2+x-2}+\sqrt{x^2-4x+3}=\sqrt{x^2-1}\\
x^2-1=x^2+x-2+2\sqrt{(x^2+x-2)(x^2-4x+3)}+x^2-4x+3\\
2\sqrt{(x^2+x-2)(x^2-4x+3)}=-x^2+3x-2\\
\sqrt{(x^2+x-2)(x^2-4x+3)}=\dfrac{-x^2+3x-2}{2}\\
(x^2+x-2)(x^2-4x+3)=\left(\dfrac{-x^2+3x-2}{2}\right)^2\\
(x+2)(x-1)(x-3)(x-1)=\left(\dfrac{-x^2+x+2x-2}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-x(x-1)+2(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-(x-2)(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\dfrac{(x-2)^2(x-1)^2}{4}\\
4(x+2)(x-3)(x-1)^2=(x-2)^2(x-1)^2\\

4(x+2)(x-3)(x-1)^2-(x-2)^2(x-1)^2=0\\
(x-1)^2(4(x+2)(x-3)-(x-2)^2)=0\\
(x-1)^2(4(x^2-3x+2x-6)-(x^2-4x+4))=0\\
(x-1)^2(4x^2-4x-24-x^2+4x-4)=0\\
(x-1)^2(3x^2-28)=0\\
x-1=0 \vee 3x^2-28=0\\
x=1 \vee 3x^2=28\\
x=1 \vee x^2=\dfrac{28}{3}\\
x=1 \vee x=\sqrt{\dfrac{28}{3}} \vee x=-\sqrt{\dfrac{28}{3}}\\

There's one more condition I forgot about
-(x-2)(x-1)\geq0\\
x\in\langle1,2\rangle\\

Finally
x\in(-\infty,-2\rangle\cup\langle3,\infty) \wedge x\in\langle1,2\rangle \wedge x=\{1,\sqrt{\dfrac{28}{3}}, -\sqrt{\dfrac{28}{3}}\}\\
\boxed{\boxed{x=1}}
3 0
3 years ago
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