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3 years ago

Which of the following exponential functions goes thru points (1,6) and (2,12)

Mathematics

1 answer:

Alexandra [31]3 years ago

7 0

Answer:

Noting that e^b = 6/a

Step-by-step explanation:

Use the general expo function y = ae^(bx).

Subbing 6 for y and 1 for x, we get 6 = ae^(b), or e^b = 6/a.

Subbing 12 for y and 2 for x, we get 12 = ae^(2b), or 12/a = (e^b)²

Now let's find the value of the coefficient a. Noting that e^b = 6/a, rewrite

12/a = (e^b)² as 12/a = (6/a)².

Dividing both sides by 6/a, we get 2 = 6/a, or a = 3.

Again Noting that e^b = 6/a, e^b = 6/3, or e^b = 2.

Taking the natural log of both sides, we get b = ln 2.

Then our y = ae^(bx) becomes:

y = 3e^(ln 2·x), or y = 3·2^x

Note: next time, please share the answer choices. Thank you.

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When an amount of heat Q (in kcal) is added to a unit mass (kg) of a

lisov135 [29]

Answer:

The change in temperature per minute for the sample, dT/dt is 71. $\overline {6}$ °C/min

Step-by-step explanation:

The given parameters of the question are;

The specific heat capacity for glass, dQ/dT = 0.18 (kcal/°C)

The heat transfer rate for 1 kg of glass at 20.0 °C, dQ/dt = 12.9 kcal/min

Given that both dQ/dT and dQ/dt are known, we have;

$\dfrac{dQ}{dT} = 0.18 \, (kcal/ ^{\circ} C)$

$\dfrac{dQ}{dt} = 12.9 \, (kcal/ min)$

Therefore, we get;

$\dfrac{\dfrac{dQ}{dt} }{\dfrac{dQ}{dT} } = {\dfrac{dQ}{dt} } \times \dfrac{dT}{dQ} = \dfrac{dT}{dt}$

$\dfrac{dT}{dt} = \dfrac{\dfrac{dQ}{dt} }{\dfrac{dQ}{dT} } = \dfrac{12.9 \, kcal / min }{0.18 \, kcal/ ^{\circ} C } = 71.\overline 6 \, ^{\circ } C/min$

For the sample, we have the change in temperature per minute, dT/dt, presented as follows;

$\dfrac{dT}{dt} = 71.\overline 6 \, ^{\circ } C/min$

8 0

2 years ago

What numbers can I divide that will give me a quotient that’s is greater than 20 but less than 25.

cluponka [151]

Answer:

42 divided by 2

Step-by-step explanation:

That will give you 21.

8 0

3 years ago

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A cone has a volume of 24 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

ivann1987 [24]

Answer:

8 cubic inches

Step-by-step explanation: I just know

6 0

3 years ago

Find the domain of f/g

san4es73 [151]

Answer:

C. All real numbers except 3/4

Step-by-step explanation:

We are given

$f(x)=3x^2+x^4+2$

$g(x)=4x-3$

Firstly, we will find f/g

$\frac{f}{g}=\frac{3x^2+x^4+2}{4x-3}$

Domain:

We know that domain is all possible values of x for which any function is defined

so, we know that denominator of any function can not be zero

so, firstly we set denominator =0

and then we can solve for x

$4x-3=0$

Add both sides by 3

$4x-3+3=0+3$

$4x=3$

$x=\frac{3}{4}$

so, this function is defined for all values of x except at

$x=\frac{3}{4}$

Domain will be

All real numbers except 3/4

5 0

3 years ago

The product of 576 and 684 is irrational or rational

umka2103 [35]

Answer: rational

Step-by-step explanation:

Definitely rational because 576 and 684 are both natural numbers

6 0

3 years ago

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