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2 years ago

9

Consider the following equation. x+4/x-6 +3/2x+5=7. What are the constraints on x?

1 answer:

TiliK225 [7]2 years ago

6 0

X cannot be 6 or -2/5 because if they were the denominator would be zero

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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

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1 year ago

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Volume of a cube is 1728 cm3.Find its surface area

Leno4ka [110]

Answer:

<h2>a=V⅓=1728⅓≈12</h2><h2 />

Step-by-step explanation:

<h2>Using the formula</h2><h2>V=a3</h2>

<h2>it is right answer </h2><h3>hope it will help you </h3>

8 0

2 years ago

Use the following diagram to answer question 4 and 5

baherus [9]

Answer:

3x-13+2x+4=116( the sum of two interior angle is epual to the sum of exterior angle )

5x =116-9

5x=107

x=21.4 degree

then

angle a= 3*21.4-13

a=51.2degree

angle b=2*21.4+2

b =44.8degree

Step-by-step explanation:

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A scuba diver ascends 5 3/4 feet to the top of a boat platform. The diver then descends 20 1/8 feet by jumping off the boat. Wri

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-15 5/8 feet
5 6/8- 20 1/8

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sladkih [1.3K]

Answer:

-6 is the answer

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