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2 years ago

The relation {(-1, 4), (2, 7), (3, 7)} is a function.

1 answer:

4 0

It is a function because the X does not repeat. If the X repeat then it is not function for example.
(2,4), (5,6), (2,8) if it repeat like this then it is not function

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An 8-oz bottle of ketchup costs $1.39. If the unit rate stays the same, how much should a 14-oz bottle cost? $0.79 $2.43 $2.78 $

Thepotemich [5.8K]

To find the unit rate you do

$1.39/8 oz.=.17

Then, you multiply the unit rate by the ounces

.17 * 14 oz. = $2.43

6 0

3 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

6 0

1 year ago

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Hi there! please please help:)) have a good day

Elina [12.6K]

Answer:

Step-by-step explanation:

sorry if wrong dont report

3 0

2 years ago

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4. Mr. Downey used the function f(x) = -3x2 + 12x to model the flight of a glider. In Mr. Downey's

tankabanditka [31]

Answer: 120 seconds

Step-by-step explanation: In order to find the maximum value of a function, you can take the derivative of the function and equalize the result to 0.

f'(x)=(-3x^2 + 12x)'=-6x+12=0

x=2

When x is 2, the function will reach its maximum value.

f(2)=-3(2)^2 + 12.2 = -12 + 24 = 12

The maximum value (f(x)) is equal to 12 and the time passed is 2 minutes which is equal to 120 seconds.

6 0

2 years ago

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Which series of transformations takes the graph of f(x)=3x−8 to the graph of g(x)=−3x+12 ?

kumpel [21]

<span> reflect the graph about the x-axis and translate 4 units down </span>

4 0

2 years ago

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