An app developer projects that he will earn $20.00 for every 8 apps downloaded. Write an equation to represent the proportional relationship between the number of apps and the total earnings.

Answer:

253 units

Step-by-step explanation:

-253 is 253 units behind 0.

Answer:

a) True. The differential equation is [tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex], where [tex]T[/tex] is measured in Celsius.

b) The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.

Step-by-step explanation:

a) The object is heated up by convection and radiation, from First Law of Thermodynamics we get that energy interactions on the object are represented by:

[tex]-\dot Q_{out} + \dot W_{in} = \frac{dU_{sys}}{dt}[/tex] (Eq. 1)

Where:

[tex]\dot Q_{in}[/tex] - Heat transfer rate to the object, measured in watts.

[tex]\dot W_{in}[/tex] - Electric power given by the microwave owen, measured in watts.

[tex]U_{sys}[/tex] - Internal energy of the object, measured in watts.

Then, we expand the expression by means of definition from Heat Transfer and Thermodynamics:

[tex]-h_{c}\cdot A_{s}\cdot (T-T_{\infty})+\dot W_{in} = m\cdot c\cdot \frac{dT}{dt}[/tex]

Where:

[tex]h_{c}[/tex] - Heat transfer coefficient, measured in watts per square meter-Celsius.

[tex]A_{s}[/tex] - Surface area of the object, measured in square meters.

[tex]T[/tex] - Temperature of the object, measured in Celsius.

[tex]T_{\infty}[/tex] - Internal temperature of the microwave oven, measured in Celsius.

[tex]m[/tex] - Mass of the object, measured in kilograms.

[tex]c[/tex] - Specific heat of the object, measured in joules per kilogram-Celsius.

After some algebraic handling, we get this non-homogeneous first order differential equation:

[tex]\frac{dT}{dt} = -\frac{h_{c}\cdot A_{s}}{m\cdot c} \cdot (T-T_{\infty}) + \frac{\dot W_{in}}{m\cdot c}[/tex]

[tex]\frac{dT}{dt}+\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T =\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T_{\infty}+\frac{\dot W_{in}}{m\cdot c}[/tex] (Ec. 2)

If we know that [tex]h_{c} = 40\,\frac{W}{m^{2}\cdot ^{\circ}C}[/tex], [tex]A_{s} = 0.01\,m^{2}[/tex], [tex]m = 1\,kg[/tex], [tex]c = 1000\,\frac{J}{kg\cdot ^{\circ}C}[/tex], [tex]T_{\infty} = 25\,^{\circ}C[/tex] and [tex]\dot W_{in} = 50\,W[/tex], the differential equation is:

[tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex]

b) The solution of this differential equation is:

[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+ \frac{0.06}{0.0004}\cdot (1-e^{-0.0004\cdot t})[/tex]

Where [tex]T_{o}[/tex] is the initial temperature of the object, measured in Celsius.

[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+150\cdot (1-e^{-0.0004\cdot t})[/tex]

[tex]T(t) = 150+(T_{o}-150)\cdot e^{-0.0004\cdot t}[/tex]

Where [tex]t[/tex] is the time, measured in seconds.

If we know that [tex]T_{o} = 25\,^{\circ}C[/tex], then:

[tex]T(t) = 150-125\cdot e^{-0.0004\cdot t}[/tex] (Ec. 3)

For [tex]t = 200\,s[/tex], we get that temperature of the object is:

[tex]T(200) = 150-125\cdot e^{-0.0004\times 200}[/tex]

[tex]T(200) \approx 34.611\,^{\circ}C[/tex]

The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.

Answer:

2/9

Step-by-step explanation:

Any fraction in the form 0.n repeated is in the form n/9

Answer:

3

Step-by-step explanation

3 x 2.50 = 7.50

7.50 x 0.06 = 0.45

7.50 + 0.45 = 7.95

So, she would be able to buy 3 sodas and it would cost $7.95

Answer:

2 miles.

Step-by-step explanation: Hopefully this helped!

Answer:

1/6 more

Step-by-step explanation:

find the common denominator which gives you 4/6, rest is self explanatory, 5/6 is 1/6 more than 4/6

Answer:

0.008 3 with bar

Step-by-step explanation:

the line under 8 is supposed to be over 8

i know im late sorry

Answer:

0.0008 ModifyingAbove 3 with bar

Step-by-step explanation:

Answer:

41.4$

Step-by-step explanation:

10% of 230 is 23$

23/5=4.6

4.6$=2%

18.4$=8%

23+18.4$

41.4$

Answer:

41.4

Step-by-step explanation:

Hope this helped

Answer:

1 minute

Step-by-step explanation:

141/47=3. then 3*20=60 which is equal to one minute

Answer:

$7.38

Step-by-step explanation:

multiply 49.20 by 15 percent.

Answer:

Add 16.20+ 40+8

Step-by-step explanation: 16+20+40+8= 84

Answer:

Two objects are similar if they have the same shape,or one has the same shape as the mirror image of the other.

Hope that helped :3

Answer:

the answer would be 12 minutes

Step-by-step explanation:

Answer:

[tex]\frac{1}{125}[/tex]

Step-by-step explanation:

whenever you see a negative exponenet, you should always write the reciprocal of it

[tex]5^{-3}[/tex] becomes  [tex]\frac{1}{5^{3} }[/tex]

solve the denominator

[tex]5^{3}[/tex] = 125

therefore, your answer is [tex]\frac{1}{125}[/tex]

hope this helps!! :)

Answer:

When you spend $45 or more, you get 3 free songs.

You already spent $15.

Then, if we define m as the amount that you need to spend in order to get the 3 free songs, the minimum value of m will be such that you spend exactly $45 in total.

$15 + m = $45.

But if you spend more than $45 you also get the songs, so the inequality that represents this situation is:

$15 + m ≥ $45.

2)Solving the equation for m we have:

m ≥ $45 - $15 = $30

m ≥ $30.

So the minimum amount that you can spend in order to get the songs is when the equality is true, this means that:

m = $30 is the minimum that you must spend if you want the 3 free songs.

Answer:

a. -29

b. 16

c. -6

d. 23

e. ?

f. x = -5

g. x = -24

h. x = 4

i. -29

j. 16 i think

Step-by-step explanation:

Step-by-step explanation:

2x(x-6)=10

use foil method so 2x times x-6 magiging 2x²-12x

tas yung +10 itratranspose mo magiging -10 kasi kapag nagtratranspose ang positive magiging negative and vice versa, so ang sagot ay

2x²-12x-10=0

a=2

b=-12

c=-10

Answer:

f-1(x)=2x/x-1

Step-by-step explanation:

Answer:

5n+23

Step-by-step explanation:

five times a number is 5n and 23 is +3

Answer:

|(15,055) is the number of pages in a book with

15,055 words.

Step-by-step explanation:

becuz the no of pages is a function to the words ..

Answer:

A)

[tex]-39.6[/tex]

B)

[tex]4.5\text{ minutes}[/tex]

Step-by-step explanation:

We know that the scuba diver is exploring a reef 39.6 meters below the sea level.

Remember that sea level is always 0 meters in elevation.

We also know that the diver ascended to the surface at a rate of 8.8 meters per minute.

Part A)

Since sea level is the 0th meter, anything below this will be negative.

So, since the diver is 39.6 meters below sea level, we can express this as:

[tex]-39.6[/tex]

Part B)

We know that the diver ascends at a rate of 8.8 meters per minute.

The diver is currently at 39.6 meters.

Remember that the surface is the sea level. So, we want to find after how many minutes m does the diver reach the 0th meter.

So, we can write the following equation and solve for m:

[tex]-39.6+8.8m=0[/tex]

The -39.6 represents the diver's current altitude.

The 8.8m represents the diver's rate of ascending 8.8 meters per minute m. Notice that 8.8m is positive because we're ascending.

And the 0 represents the 0th meter or sea level or the surface.

So, solve for m. Add 39.6 to both sides:

[tex]8.8m=39.6[/tex]

Divide both sides by 8.8. So:

[tex]m=4.5[/tex]

So, it will take the diver 4 and a half minutes to reach the surface.

And we're done!

Answer:

3 1/5

Step-by-step explanation:

24/5 ÷ 3/2

24/5 x 2/3

48/15

16/5

3 1/5

Answer:

-12r2-9r-6

Step-by-step explanation:

-distribute the subtraction symbol  to the second group of numbers

-(9r2+7r+2) = (-9r2-7r-2)

-then combine each term together (-3r2-2r-4)+(-9r2-7r-2)

= -12r2-9r-6

HOPE THIS HELPS!!

Answer:

A person pushing a swing will make the swing rotate about its pivot.

A worker applies a force to a spanner to rotate a nut.

A person removes a bottle's cork by pushing down the bottle opener's lever.

A force is applied to a door knob and the door swings open about its hinge.

Answer:

96%

Step-by-step explanation:

20/ 0.80 = 25 (total number of questions)

24/25 = .96 x 100 = 96%

Answer:

1) variables

2)26

3)8x+2y+2

4)38

Answer:

240

Step-by-step explanation:

20 x 12 = 240

Answer:

Step-by-step explanation:

2.6 ÷ 2 = 1.3