Use properties of operations to complete the equivalent expression. 5(y+9)=___y+__

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

2 years ago

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bath walked 10 7/8 miles one week she walk 2 1/4 fewer miles the following week about how many miles did she walk the second wee

bagirrra123 [75]

Answer:

8 and 5/8

Step-by-step explanation:

The question is just subtraction of fractions. First, you subtract the whole numbers. 10-2=8. Then you subtract the fractions. To do this, you have to make them equivalent. Just multiply the 1/4 by 2 and you get 2/8. Now, 7/8 - 2/8 = 5/8. Your final answer is 8 and 5/8

7 0

2 years ago

(ab^2 x -b^4a^3)^2<br><br> What is the answers

Umnica [9.8K]

Answer:

$\left(ab^2x-b^4a^3\right)^2:\quad a^2b^4x^2-2a^4b^6x+a^6b^8$

Step-by-step explanation:

Given the expression

$\left(ab^2\:x\:-b^4a^3\right)^2$

solving the expression

$\left(ab^2\:x\:-b^4a^3\right)^2$

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2$

$a=ab^2x,\:\:b=b^4a^3$

so the expression becomes

$=\left(ab^2x\right)^2-2ab^2xb^4a^3+\left(b^4a^3\right)^2$

$=a^2b^4x^2-2a^4b^6x+a^6b^8$

Thus,

$\left(ab^2x-b^4a^3\right)^2:\quad a^2b^4x^2-2a^4b^6x+a^6b^8$

3 0

2 years ago

One of Newton’s laws of motion states that objects in motion tend to stay in motion. What is the reason that this law may not al

Nastasia [14]

The answer is D.

The full specification of Newton's First Law is (from Wikipedia)

In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

On earth we're generally in slightly a non-inertial frame, with rotation and revolution around the sun. It's also impossible to turn of gravity, so objects are being acted upon by an outside force. Typically there's also the outside force of friction, which makes things tend to stop.

4 0

2 years ago

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Find the slope of a line parallel to y=(2/5)x + (4/5)

Tcecarenko [31]

Answer:

So if a line was parallel it would have same slope. You can search up what slope-intercept form means. But if you have an equation like this:

y = mx+b

The slope will be m. Your question is written in the form. 2/5 = m.

The slope is 2/5

The y-intercept is 4/5

6 0

2 years ago

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Use properties of operations to complete the equivalent expression. 5(y+9)=​___y+​___ 5(y+9)=nothingy+nothing

Use properties of operations to complete the equivalent expression. 5(y+9)=_y+_ 5(y+9)=nothingy+nothing