Evaluate 5^-4. Write your answer as a fraction in simplest form

Answer:

76.09 pounds

Step-by-step explanation:

From the information given:

[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]

[tex]R_{in} =3 \ lb/min[/tex]

At a slower of 4 gal/min, the solution gets pumped out;

So,

[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]

[tex]R_{out} = \dfrac{2A}{50+t }[/tex]

The differential of the equation is:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]

For the linear differential equation, the integrating factor is determined as:

[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]

[tex]= (50+t)^2[/tex]

Multiplying [tex](50+t)^2[/tex] with the above integration factor;

[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]

[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]

[tex](50+t)^2 A = (50 +t)^3 + c[/tex]

[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]

By using the given condition:

A(0) = 40

40 = 50 + c (50)⁻²

10 = c(50)⁻²

OR

c = -10 × 2500

c = -25000

A = (50 + t) - 25000(50 + t)⁻²

The number of pounds of salt in the tank after 30 min is:

A(30) = (50+30) - 25000(50 + 30)⁻²

[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]

[tex]A(30) = 76.09 \ pounds[/tex]

Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.

Answer:

more context please:)

Step-by-step explanation:

Answer:

3 + x + 3

Step-by-step explanation:

Hope it helps!

Answer:

Mabey 102 try that.

Step-by-step explanation:

Hope this helps!

Answer:

Graph A <==

Step-by-step explanation:

$ 50 for 5 hours......50/5 = 10...thats $ 10 per hr

so the equation would be : y = 10x...with x being the number of hrs and y being the total cost.

So ur x axis will be the hours and your y axis will be the total cost.

so ur answer is :the title of the graph is cycle renting. the x axis (the horizontal axis)...since it is the hours, will be labeled 0,1,2,3,4,5,6

the y axis (the vertical axis)...since it is the total cost, will be labeled  

0,10,20,30,40,50,60. points are plotted on (1,10),(2,20), and (3,30)

Answer:

Step-by-step explanation:

Figure (1)

x° = 107° [Vertically opposite angles]

Since, vertical angles are equal in measure.

Figure (2)

x + 71° = 90° [Given, complementary angles]

x = 90° - 71°

x = 19°

Figure (3)

x + 21° = 180° [Given as supplementary angles]

x = 180° - 21°

x = 159°

Figure (4)

x = 129° [Vertical angles]

Figure (5)

x° = 90° [Given]

z° + 34° = 90°

z° = 90° - 34°

z° = 56°

Since, x° + y° + z° = 180° [Linear angles]

90° + y° + 56° = 180°

y° + 146° = 180°

y° = 180° - 146°

y° = 34°

Answer:

i thinking a or d

Step-by-step explanation:

The absolute value equation is |x+15|=25. Therefore, option B is the correct answer.

To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.

Given that, on average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes.

Let x represent the maximum and minimum time.

So, the absolute value equation is |x+15|=25

Therefore, option B is the correct answer.

To learn more about a absolute value equation visit:

https://brainly.com/question/2166748.

#SPJ2

Answer:

x-3*2

Step-by-step explanation:

A Cause I'm big brain and we learned that

Answer:

[tex]x = 18[/tex]

Step-by-step explanation:

Given

[tex]\frac{x}{6} - 7 = -4[/tex]

Required

Solve for x

[tex]\frac{x}{6} - 7 = -4[/tex]

Add 7 to both sides

[tex]\frac{x}{6} - 7+7 = -4+7[/tex]

[tex]\frac{x}{6} = -4+7[/tex]

[tex]\frac{x}{6} = 3[/tex]

Multiply through by 6

[tex]6 * \frac{x}{6} = 3 * 6[/tex]

[tex]x = 3 * 6[/tex]

[tex]x = 18[/tex]

Answer:

1 2 3 6 7 11 22 26 33 66

Step-by-step explanation:

I did the math

I am a College Major at UOF in Florida

Mark me Brainliest!!!!

Hey there!

“What are the factors of 66?”

1 * 66 = 66

2 * 33 = 66

3 * 22 = 66

6 * 11 = 66

Answer

66 factors are…. 1, 2, 3, 6, 11, 22, 33, and 66.

• 1, 2, 3, 6, 11, 22, 33, & 66

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

The team building event will cost $24 for 4 attendees.

Step-by-step explanation:

Given,

Cost charged corporate team building = $6 for every attendee

Number of attendees = 4

We will multiply the amount of one ticket with number of attendees in order to find the total cost.

Cost charged for 4 attendees = 6*4

Cost charged for 4 attendees = $24

Answer:

T is correct (the fourth answer)

Step-by-step explanation:

Step-by-step explanation:

I believe it's graph T..

Answer:

U

Step-by-step explanation:

Answer:

V

Step-by-step explanation:

Sum of angles in a triangle = 180°

66c + 40c +74c = 180°

106c + 74c =180

180c = 180

c=1

Side v is the largest

Answer:

10(10)-3(10)-2/4+5=149/2 (decimal 74.5)

Answer:

B. -8+10

Step-by-step explanation: keep the -8 change - sign to +sign then change -10 to 10 .

Hope it helps :)

Answer:

12 small, 18 large

Step-by-step explanation:

x - small

y - large

z- medium

4z=2x=3y then she orders 24

24/4=6 times more than usually, so we should *6 for every x and z

24z=6*2x=6*3y

12 - x - small tshirt

18 - y - large

Answer:

How many variables?

Step-by-step explanation:

Answer:

y = 7   x = 9

Step-by-step explanation:

2y-x=8

2(2y-x=8)

4y-2x=16

-(y-2x= -5)

3y +0x= 21

3y=21

y=7

2(7)-x=8

14-x=8

9=x

Answer:

x=3 in equation ;5x=15 and in equation C.

Answer:

The total of all the boxes would be $5.00.

Answer: 7.2ft not sure if ur rounding answers. If nearest whole number than 7ft.

Step-by-step explanation:

Use Pythagorean theorem.

4^2 + 6^2 = c^2

16 + 36 = 52 = c^2

C = 7.2ft

Answer:

y=x+4

Step-by-step explanation:

Slope intercept is y= mx+b

The slope is rise/run or change in y/change in x. Here the slope is 1 since when y goes up1, x goes to the right 1 (1/1=1).

The y intercept is 4 since it hits the y axis at 4.

so it would be y= 1x+4 which is y=x+4

Answer: 8

Step-by-step explanation:

I think the answer is 8

Answer:

Step-by-step explanation:

4x4x4x4x4=4^5=1024

Answer:

[tex]16x < - 64 \\ x < - \frac{64}{16} \\ x < - 4[/tex]

hope this helps.

Answer:

B

Step-by-step explanation:

∠ACE and ∠ECB form a straight angle whose sum = 180°, hence

2x + 2 + 5x + 3 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25 → C

Answer:

The answer is 1/6

Step-by-step explanation:

This is the answer because it is.

Answer:

3

Step-by-step explanation:

Answer:

The triangles are congruent

Step-by-step explanation:

Given

[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]

Required

Determine if PQR = XYZ

To do this, we make use of distance formula.

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For PQ:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]

So:

[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]

[tex]PQ = \sqrt{64+121}[/tex]

[tex]PQ = \sqrt{185}[/tex]

For XY:

[tex](x_1,y_1) = (-2,-1)[/tex]

[tex](x_2,y_2) = (9,7)[/tex]

So:

[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]

[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]

[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]

[tex]XY = \sqrt{121+64}[/tex]

[tex]XY = \sqrt{185}[/tex]

For QR:

[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]

[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]

[tex]QR = \sqrt{(3)^2 + 25}[/tex]

[tex]QR = \sqrt{9 + 25}[/tex]

[tex]QR = \sqrt{34}[/tex]

For YZ:

[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]

[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]

[tex]YZ = \sqrt{36+25}[/tex]

[tex]YZ = \sqrt{61}[/tex]

For PR:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]

[tex]PR = \sqrt{25+36}[/tex]

[tex]PR = \sqrt{61}[/tex]

For XZ:

[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]

[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]

[tex]XZ = \sqrt{5^2+3^2}[/tex]

[tex]XZ = \sqrt{34}[/tex]

From the calculations above:

[tex]PQ = XY = \sqrt{185[/tex]

[tex]QR = XZ = \sqrt{34[/tex]

[tex]PR = YZ = \sqrt{61[/tex]

Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)