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3 years ago

6

Kyle has 1 3 of a gallon of apple juice. If he divides the apple juice into 5 equal servings, how much apple juice will he have

in each serving?

1 answer:

valkas [14]3 years ago

3 0

He would be serving 2.5 gallons each.

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Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of

maria [59]

Answer:

305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

<h3>Cooling Model</h3>

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

a = 1200 -80 = 1120

b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

Note that units of time are hours.

<h3>Application</h3>

We want y when t=4.

y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

<em>Additional comment</em>

The differential equation will have a solution of the form ...

$T-T_R=(T_0-T_R)e^{kt}$

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

5 0

2 years ago

If angle ABC is one degree less than three times angle ABD and angle DBC=47 find each measure

Contact [7]

It has not been indicated whether the figure in the questions is a triangle or a quadrilateral. Irrespective of the shape, this can be solved. The two possible shapes and angles have been indicated in the attached image.

Now, from the information given we can infer that there is a line BD that cuts angle ABC in two parts: angle ABD and angle DBC

⇒ Angle ABC = Angle ABD + Angle DBC

Also, we know that angle ABC is 1 degree less than 3 times the angle ABD, and that angle DBC is 47 degree

Let angle ABD be x

⇒ Angle ABC = 3x-1

Also, Angle ABC = Angle ABD + Angle DBC

Substituting the values in the above equations

⇒ 3x-1 = x+47

⇒ 2x = 48

⇒ x = 24

So angle ABD = 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree

8 0

3 years ago

Write a quadratic function that has been translated 1<br> units to the right and 3 units down.

vodka [1.7K]

Step-by-step explanation:

Hi,

f(x) = (x - 1) - 3

The -1 is the 1 unit to the right (even though it's being subtracted, it's going to the right because it's embedded with the x)

And the -3 is not embedded with the x, meaning the function will move 3 units down.

I hope this helps :)

6 0

3 years ago

Describe the process of rewriting the expression Please Help

Mazyrski [523]

Answer:

$x^{\frac{21}{4} }$

Step-by-step explanation:

Given expression is:

$(\sqrt[8]{x^7} )^{6}$

First we will use the rule:

$\sqrt[n]{x} = x^{\frac{1}{n} }$

So for the given expression:

$\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }$

We will use tha property of multiplication on powers:

$=x^{7*\frac{1}{8} }$

$= x^{\frac{7}{8} }$

Applying the outer exponent now

$(x^{\frac{7}{8} })^6$

$= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }$

8 0

3 years ago

Identify which table shows a direct variation.

DochEvi [55]

Only Table 2 shows direct variation. Every y value is 7 times the associated x value.

8 0

3 years ago