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2 years ago

What is the equation in point slope form of the line that passes through the point

1 answer:

6 0

Since you already have the slope, you just have to plug in the points in the equation $y- y_{1} =m(x- x_{1})$

Just plug in the number in for y1 and x1 and you'll get:
$y+2 =3(x-1)$

Which is C!

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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

6 0

2 years ago

Read 2 more answers

Find the slope-intercept form of the equation of the line passing through the points.

LekaFEV [45]

Plog in to y=ax+b and u will find a b

5 0

2 years ago

BRAINLIEST ANSWERS ONLY.

mars1129 [50]

Answer:

Heyy

Step-by-step explanation:

△ABC is a right angled triangle and right angle at B

sinA=

, cosA=

⟹sinA+cosA=

BC+AB

[We know that sum of two sides of a triangle is greater than the third side]

⟹sinA+cosA>

Hence, sinA+cosA>1

4 0

1 year ago

H=2.9L+78.1<br> About how tall would the male have been if the length of the humerus measured 39 cm?

dalvyx [7]

Answer:H=191.2

Step-by-step explanation:

H=2.9(39)+78.1

H=113.1+78.1

H=191.2 cm

3 0

3 years ago

Which is the definition of a line segment?

maxonik [38]

Hi there!

A line segment, hence its name, is basically a part of a line. It has two endpoints and does not continue forever in any directions.

Hope this helps!

8 0

3 years ago

Read 2 more answers