Please help me answer the question in the picture

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Virty [35]

Answer:

$33 for 11 packs of paper

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

2 years ago

Read 2 more answers

Consider the line shown on the graph. Enter the

Semenov [28]

<h2>Solution -</h2>

From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.

So, slope of the line (m) passing through the points (a, b) and (c, d) is

m = d - b/ c - a

<h3>So, on substituting the values, we get </h3>

m = 4 - 3 / 1 - 0 = 1/1 = 1

Also, line makes an intercept of 3 units in positive direction of y - axis.

So, c = 3

<h3>So, Equation of line is given by</h3>

y = mx + c

y = 1 × x + 3

<h3>Alternative Method :-</h3>

We know, Equation of line passing through the points (a,b) and (c, d) is given by

y - b = d - b / c - a (x - a)

a = 0

b = 3

c = 1

d = 4

<h3>So, on substituting these values in above result, we get :-</h3>

y - 3 = 4 - 3 /1 - 0 ( x - 0 )

y - 3 = 1/1 ( x - 0 )

y - 3 = x

<h3>Different forms of equations of a straight line :-</h3>

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

<h3>2. Point-slope form equation of line</h3>

Equation of line passing through the point (a, b) having slope m isy - b = m(x - a)

<h3>3. Slope-intercept form equation of line</h3>

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

<h3>4. Intercept Form of Line</h3>

Equation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.

<h3>5. Normal form of Line</h3>

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.

<h2 />

8 0

2 years ago

The towns of Franklin and Chester post their populations on signs just outside of their towns. The signs are

Andre45 [30]

Answer:

year 13

Step-by-step explanation:

franklin's population is growing by 1000 people per year(5% of 20000 is 1000) and Chester is growing by 500 per year so at year 13 franklin will be at 32000 while Chester is at 31500

4 0

3 years ago

What is the area of a trapezoid? 47,45,65

Masteriza [31]

Area = 2,520m^2
(47+65)/2 = 56
56x45 = 2,520

8 0

3 years ago