What is the value of x in the equation 2(x−3) 9=3(x 1) x? x = −3 x = −1 x = 0 x = 3

Answer:

The current of the circuit at t = 0 is equal to 0.

If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:

[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:

[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Slope Fields

Integration

Integration Rule [Reverse Power Rule]:

[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:

[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:

[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Method: U-Substitution

Electricity

Ohm's Law: V = IR

Circuits

Step-by-step explanation:

*Note:

In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.

Step 1: Define

Identify given.

[tex]\displaystyle L \frac{dI}{dt} + RI = V[/tex]

[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.

Step 2: Find Current Expression Pt. 1

Step 3: Find Current Expression Pt. 2

Identify variables for u-substitution.

Step 4: Find Current Expression Pt. 3

Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.

Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.

Step 5: Solve

If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:

[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}[/tex]

If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:

[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}[/tex]

∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.

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Topic: AP Physics C - EMAG

Unit: Induction

Answer:

33.51 units³

Step-by-step explanation:

Volume of a sphere is given by the formula :

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

Because we have the radius we can plug it into the equation to give us :

V  = (4/3)×π×(2)³

V = 4/3×8π

V ≈ 33.51

Units will be units³ since no measurement is given but it to the power of 3 since it is volume.

Answer:

C

Step-by-step explanation:

Answer:

11

Step-by-step explanation: Uh- if X=3 then it would be 2(3) +5. 2x3 is 6, and 6+5 is 11.

Answer:

11

Step-by-step explanation:

2(3) + 5

simplify

6 + 5 = 11

hope this helps

Answer:

y = 5x

Step-by-step explanation:

Hey there!

To start with the hypotenuse of a triangle is the longest side of it

and to get an equation of a line you would use

y = mx + b

where m is the slope

and b is the y-intercept

to get the slope you would do rise over run

rise/run

take 2 points and see how much it rises and runs to the next point

you would then get 5

then we figure out the y-intercept where the line intercepts the y-axis

in this case 0

In conclusion the answer is y = 5x + 0

we can also remove the 0 because it is unnecessary

y = 5x

Answer:

(B) and (D)

Step-by-step explanation:

it's B and D because they are the only two points with constant rate

Answer:c

Step-by-step explanation:

Answer:

18.32 gm

Step-by-step explanation:

= 35 ( 1-.0525)^12 = 18.32 gm remain

Answer:

8/9

Step-by-step explanation:

4/9 ÷ 1/2 =  dividing by 1/2 is the same as multiplying by its reciprocal 2/1

4/9 × 2/1 = (4×2)/(9×1) multiply numerators (top numbers) and multiply denominators (bottom numbers)

Answer:

The Answer is 96 units squared

Step-by-step explanation:

First, you find the area of all the sides:

Triangle 1: 6

Triangle 2: 6

Rectangle 1: 21

Rectangle 2: 28

Rectangle 3: 35

Then you add all of the numbers together.

6+6+21+28+35 = 96 units squared

I hope this helps :)

Answer:

EASYYY   90°

Step-by-step explanation:

30 + 60 = 90

180-90=90

also

thats a right angle which is always 90°

ALSO

the angle opposite another angle is always the same measurement.

Using proportions, it is found that Yes, there could be 5 kids, with 3 boys and 2 girls.

A proportion is a fraction of a total amount.

In this problem, supposing a total of 5 kids:

Hence, Yes, there could be 5 kids, with 3 boys and 2 girls.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

B

Step-by-step explanation:

Answer:

those are corrisponding angles which means they equal each other making <H and <G both 57 degrees

Answer:

Step-by-step explanation:

1. The sequence is not arithmetic.

2. d=-30

Answer:

d/dx = -2/x^3

Step-by-step explanation:

1/x^2 + 1

We can solve for the derivative using the power rule

d/dx = -2/x^3 + 0

d/dx = -2/x^3

Answer:

  90√2 feet

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle with sides 90 feet. The length of the hypotenuse is the distance from home plate to 2nd base. The Pythagorean theorem tells you that distance (c) is ...

  c² = a² +b²

  c² = (90 ft)² +(90 ft)² = 8100 ft² +8100 ft²

  c² = 16200 ft²

  c = √16200 ft = 90√2 ft

The distance between home plate and second base is 90√2 feet.

Answer:

A baseball field is in the shape of a square. The distance between each pair of bases along the edge of the square is 90 feet. What is the distance between home plate and second base?

(90) StartRoot 2 EndRoot feet

Step-by-step explanation:

Answer:

2/10

Step-by-step explanation:

Since the denominator is 10, we must find what the numerator is so that the fraction can be equal to 1/5. Since 10 is twice of 5, we multiply 2 by 2 as well. With that, we get a final answer of 2/10.

Answer:

ACD and DCB are supplementary and others are correctly chosen ...

Answer:

First choose a common denominator, here i picked 11 then we think of 3 diffrent numbers so that their sum is 11 such as 2+4+5=11 so a possible equasion would be

Step-by-step explanation:

Answer: (2,-5)  X:2. Y:-5

Move accross 2 units to the right and then 5 units down from 2

Answer:

The answer would be 64,000.

Step-by-step explanation:

To find the area of one concrete block you will multiple length x width x height. Using the measurements provided, one block will equal 40. You will then multiple this by 1,600 to equal 64,000.

Answer:

25% profit

Step-by-step explanation:

Statement

An article is bought and sold at a profit of one fourth of selling price.

⇒ Buying price = x

⇒ Selling price = Buying price (1 + 1/4) = 5x/4

Profit %

Answer:

58cm

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

16 +16=32

13+13=26

32+26=58

Hope it Helps

Answer:

1296mm^2

Step-by-step explanation:

Surface Area of the Rectangular Prism to the left on top of the box:

Area of square = lw, 9mm * 9mm = 81mm, then multiply by 2 because 2 of the squares are a part of the surface, giving 162mm^2

Area of a rectangle =lw, 9mm * 9mm = 81mm, then multiply by 2 again, because 2 rectangles are a part of the surface, giving 162mm^2

So, the total surface area of the rectangular prism to the left on top, is 324mm^2

Surface Area of the Triangular Prism:

Area of a triangle: 1/2bh, and our base length would be 12, because we have to subtract 9 from 21 since the base length of the triangle isn't stated. Anyways, A = 1/2bh, so A = 1/2(12)(9) = 54mm^2, but multiply by two, so we get 108mm^2.

Area of the rectangle: lw, so 15mm * 9mm = 135mm^2

So, the total surface area of the triangular prism is 243mm^2

Surface Area of the Rectangular Prism at the bottom:

Area of the long rectangles in front = lw, 21mm * 9mm = 189mm^2, multiply by 2, 378mm^2

Area of the rectangles to the side = lw, 9mm * 9mm = 81mm^2, multiply by 2, 162mm^2

Area of the rectangle at the very bottom = lw, 21mm * 9mm = 189mm^2

So, the total surface area of the rectangular prism at the bottom is 729mm^2

Add all the total surface areas of each shape to get the total surface area of the figure:

324mm^2 + 243mm^2 + 729mm^2 = 1296mm^2

The surface area of the figure above is 1296mm^2

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{2} \\\\\\ \cfrac{k-3}{4}=2\implies k-3=8\implies k=11[/tex]

So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!

So let us assume the unknown positive integers as a and (a + 1).

★ Product of both integers :-

★ Solving the equation :-

[tex]: \longrightarrow \: \sf{a \: (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a \times (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: - \: 156 = 0} \\ \\: \longrightarrow \: \sf{a {}^{2} \: - \: 12a + 13a\: - \: 156 = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{(a \: - \: 12) (a\: + \: 13) = 0} \\ \\ : \longrightarrow \: \red{\bf{a \: = \: 12 }}[/tex]

Therefore,

★ Second positive integer :-