A circuit containing an electromotive force (a battery), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ω). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives

RI+(Q/C)=E(t).

Since the current is I=dQ/dt, we have

R(dQ/dt)+(1/C)Q=E(t).


Suppose the resistance is 20Ω, the capacitance is 0.1F, a battery gives a constant voltage of E(t)=60V, and the initial charge is Q(0)=0C.
Find the charge and the current at time t.
Q(t)= ,
I(t)= .

Answer:

a=11

Step-by-step explanation:

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(A) Let's find first the derivative of the function f(x), as follows:

To find the slope of the line tangent to f(x), we just input x = 5 on the f'(x) to solve f'(5), which is:

Hence, the slope of the tangent line is m = -20.

(B) The instantaneous rate of change is also the slope of the tangent line of the given function f(x). This means that it has the same value as part (A), which is f'(5) = -20.

(C) For the equation of the tangent line, let's look first at the tangent point. We can get this by substituting x = 5 on the equation f(x) and calculate:

Our tangent point is (5, -48). We then use the slope-intercept equation y = mx + b to generate the equation of the tangent line.

We already solved m which is equal to -20. The values of x and y are equal to the tangent point. What's left is to compute the value of b. We substitute the values of m, x, and y on y = mx + b to solve b, as follows:

Hence, the equation of the tangent line can now be written as:

Answers:

(A) m = -20

(B) f(5) = -20

(C) y = -20x + 58

Answer:

2nd one

Step-by-step explanation:

Just the 2nd one

Answer:

Step-by-step explanation:

Answer:

Plane

Step-by-step explanation:

Answer:

abscissa and ordinate

Step-by-step explanation:

The first number of an ordered pair will represent the x-axis value.

What this is called is the abscissa

The second number of an ordered pair will represent the y-axis value

What this is called is the ordinate

Answer: X coordinate

Step-by-step explanation: You have a graph an on the left is the X coordinate and on the right is called the Y coordinate.

Answer:

x * 3 + 13 ≤ 7

Step-by-step explanation:

three times a number

x * 3

13 more than that

x * 3 + 13

less than or equal to 7

x * 3 + 13 ≤ 7

Please mark as brainliest

Answer:

4.75/ 19/4

Step-by-step explanation:

a=1/4; b=6

12a+(b-a-4)=?

12(1/4)+(6-1/4-4)=?

3+1.75 or 7/4=?

=4.75 or 19/4

I'm not very sure but I tried lol

Supply of smartphone will decrease causing an increase in market price.

Majorities of the smartphone manufactures make their phones in china because china charges the least amount for the companies to make phones in Chinese factories.

If several major suppliers of smartphones go out of business this news hits there can be several possibilities. Optimistic smartphone companies will see this as an opportunity to enter the smartphone market and on the other hand a new organisation may not take the risk of entering into smartphone businesses because of the fear of going out of the business.

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The Given Series 1000+200+40+8+8/5 is Convergent.

If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on increasing or dropping as the terms of the series tend to infinity, it is said to be divergent.

Given:

The series is given as 1000+200+40+8+8/5

The common ratio is

200/1000

= 1/5

Then,40/200

= 1/5

= 0.2

Now, As the common ratio is < 1 so the series is convergent.

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Answer:

You have to translate these sentences into expressions.  I am not going to solve all of these because if I explain one/two problems to you, you'll get the hang of it.  Seven more than three times a number: 7+3x; Five times a number decreased by six: 5x-6

Step-by-step explanation:

Why?  We don't know what number that is, so we can put any variable like (x, y, z, a, b, etc.). Three times a number is simply that number times 3.  In this case we would input: 3*x, or 3x.  7 more than that number is 3x+7.  Five times a number decreased by six: 5x-6 .  Remember: it is simply 5*x which simplifies to 5x.  Decreased is take away, so take away 6, and get 5x-6

Key words: Quotient: the result after dividing two/or more numbers; Product: the result after multiplying two/ or more numbers; Decreased: take away (Example: x decreased by 7=x-7)

I hope you understand!! It is very simple after you start to get the hang of it!!

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

Perimeter of rectangle B = 29cm

Step-by-step explanation:

Area of A = 4x x 2.5

Area of B = (2x - 3) x 7

The area of A and B are equal so

4x x 2.5 = (2x - 3) x 7

10x = 14x - 21

-4x = -21

4x = 21

x = 5.25

Work out the perimeter of B:

2x - 3

= (2 x 5.25) - 3

= 7.5

7.5 x 2 = 15

15 + (7 x 2) = 29

Therefore, the perimeter of rectangle B = 29cm

The area of Rectangle is length times of width. Perimeter of rectangle A is 47cm

The area of Rectangle is length times of width.

Area of rectangle A is 4x x 2.5

Area of B = (2x - 3) x 7

The area of A and B are equal so

4x x 2.5 = (2x - 3) x 7

10x = 14x - 21

Take common variables on one side

10x-14x=-21

-4x = -21

Multiply minus on both sides

4x = 21

Divide both sides by 4

x = 5.25

So 4x=4(5.25)=21

2x-3=2(5.25)-3=7.5

Let us find the perimeter of a rectangle with length 21 and width 2.5

2(21+2.5)

2(23.5)=47

The perimeter of rectangle A is 47

Hence the perimeter of rectangle A = 47cm

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(a) If q < 1, the limit of an is 0 as n approaches infinity.

(b) If q > 1, the limit of an is infinity as n approaches infinity.

(a) If q < 1, then lim an = 0 as n approaches infinity.

When the limit of the absolute value of the ratio of consecutive terms, |an+1/an|, approaches a value q less than 1 as n tends to infinity, it implies that the terms an+1 are significantly smaller than the terms an. In other words, the sequence an converges to zero.

As n becomes very large, the term an+1 becomes increasingly insignificant compared to an. Thus, the sequence approaches zero in the limit.

(b) If q > 1, then lim an = ∞ (infinity) as n approaches infinity.

When the limit of |an+1/an| approaches a value q greater than 1 as n tends to infinity, it means that the terms an+1 grow significantly larger than the terms an. The sequence an diverges and tends towards infinity.

As n becomes very large, the ratio |an+1/an| approaches q, indicating that the terms an+1 grow at a faster rate than an. Consequently, the sequence an grows indefinitely, reaching infinitely large values as n tends to infinity. Thus, the limit of an is infinity.

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Answer:

290

Step-by-step explanation:

Let the number of time the standard version was downloaded be "x", then the number of times the high-quality version was downloaded will be "4x".

The total MB downloaded for standard will be 2.1x, and the total MB downloaded for high-quality will be (4x*4.1)=16.4x.

So we have

\(2.1x+16.4x=5365\\18.5x=5365\\x=290\)

So there were 290 downloads of the standard version.

Answer: 181 square inches

Step-by-step explanation:

Answer:

25.

The answer is 25

10÷2=5

10÷5=2

so 25

:)

Hope dis helps

Learning with nat~

Answer:

its is 15.7

Step-by-step explanation:

Answer:

it may be A log x ........

The order of the divers, from least to greatest, based on the amount of oxygen left in their tanks is Dante, Sofia, and Alexi.

The three divers, Alexi, Dante, and Sofia, went scuba diving for a few hours and the table shows how much oxygen they had left in their oxygen tanks. In order to determine the order from least to greatest, based on the amount of oxygen left in their tanks, it is necessary to compare the values. Dante had 7.5 liters left in his tank, Sofia had even and five eighth liters left, and Alexi had seventy one ninth liters left. Therefore, the order from least to greatest is Dante, Sofia, and Alexi. The least amount of oxygen left in the tank was 7.5 liters, which belonged to Dante, and the greatest amount of oxygen left in the tank was seventy one ninth liters, which belonged to Alexi. The amount of oxygen left in Sofia's tank fell in between the two, at even and five eighth liters.

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Answer:

Step-by-step explanation: company A $55.50 and 16 cent per mile

company B $45.50 and 10 cent per mile

company A $55.50+16=$55.66

Company B $45.50+10=$45.60

Company A charges $10 and 6cent  more then company B

company B  charges $45.50

Comapny A charges $55.50 + 16 cent

Company B charges $45.50+10

Answer: ? what is the question

Step-by-step explanation:

the answer is 6 uniforms. 57/9.5=6

We can expect that about 45.86% of high-risk drivers will be involved in an accident during the first 80 days of the calendar year.

Let X be the number of days between the beginning of the calendar year and the moment a high-risk driver is involved in an accident. We know that X follows an exponential distribution.

Let λ be the rate parameter of the exponential distribution, which represents the average number of accidents per unit of time. We want to find the probability that a high-risk driver is involved in an accident during the first 80 days of the year, given that the probability of an accident in the first 50 days is 0.3.

We can use the cumulative distribution function (CDF) of the exponential distribution to find this probability:

P(X ≤ 80) = 1 - e^(-λ*80)

To solve for λ, we can use the fact that the probability of an accident in the first 50 days is 0.3:

P(X ≤ 50) = 1 - e^(-λ*50) = 0.3

e^(-λ*50) = 0.7

-λ*50 = ln(0.7)

λ = -ln(0.7)/50

λ ≈ 0.0296

Now we can substitute λ into the expression for P(X ≤ 80):

P(X ≤ 80) = 1 - e^(-0.0296*80)

P(X ≤ 80) ≈ 0.4586

Therefore, we can expect that about 45.86% of high-risk drivers will be involved in an accident during the first 80 days of the calendar year.

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Answer:

f(2) = -10

f(4) = -6

f(-3) = 15

Step-by-step explanation:

f(x) = x^2 - 4x - 6

To find f(2), substitute 2 in place of the x in x^2 and -4x.

f(2) = 2^2 - 4(2) - 6

= 4 - 8 - 6

= -4 - 6

= -10

f(2) = -10

f(4) = 4^2 - 4(4) - 6

= 16 - 16 - 6

= 0 - 6

= -6

f(4) = -6

f(-3) = (-3)^2-4(-3)-6

= 9 + 12 - 6

= 21 - 6

= 15

f(-3) = 15

The length of AD is approximately 9.2 units.

A triangle is a geometric figure that is formed by three line segments joining three non-collinear points in a plane. It is a three-sided polygon and the most basic two-dimensional shape. A triangle has three interior angles and three vertices. The sum of the interior angles of a triangle is always 180 degrees, and each angle is measured in degrees. Triangles can be classified based on the length of their sides and the measures of their angles. There are several types of triangles such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are used in various fields such as engineering, architecture, mathematics, and physics, and they are an essential part of many geometric calculations and constructions.

To solve this problem, we can use the angle bisector theorem which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides.

Let AD = x. Then we can set up the following proportion:

AC/CD = AB/BD

Substituting the given values, we get:

24/x = 15/(18 - x)

Simplifying this equation, we get:

360 - 15x = 24x

39x = 360

x = 9.23 (rounded to the nearest tenth)

Therefore, the length of AD is approximately 9.2 units.

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Answer:

price = $175

percentage off the price = 20%

20% of 175 = 20/100 x 175 = 35

the price off the main price = 35

therefore the price of the boots is 175 -35 = 140

the price is $140

Marcia states that some numbers have an odd number of factors so Marcia is correct

Factors

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers  are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors multiplication and division.

Odd Number and Even Number

Odd numbers are those numbers that cannot be divided into two equal parts, whereas even numbers are those numbers that can be divided into two equal parts. Examples of odd numbers are 3, 5, 7, 9, 11, 13, 15 Examples of even numbers are 2, 4, 6, 8, 10, 12, 14

Rob states that all numbers have an even number of factors.

Marcia states that some numbers have an odd number of factors.

Consider the number 36. It is given that,

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

The repeated factor is counted only once. So, the factors of 36 are given by 1, 2, 3, 4, 6, 9, 12, 18, and 36.

This tells us that 36 has 9 factors and has an odd number of factor. Then Marcia is correct

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whole numbers and coefficients that can be constants or variables. The exponents in a polynomial must be non-negative integers (whole numbers).

The polynomial terms can be added or subtracted, but the exponents of the variables must still be whole numbers.

For example, the following are polynomials:

1. 3x^2 + 5x - 2

2. 2y^3 + 4y^2 - 7y + 1

3. x^4 + 2x^3 - x^2 + 3x - 1

In these examples, the exponents are all whole numbers (2, 3, and 4), and the coefficients (the numbers multiplied by the variables) can be constants or variables themselves.

However, expressions like 2x^(1/2) or 3x^(-2) are not considered polynomials because the exponents in these cases are not whole numbers.

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Ka and Kb are both acid-base equilibrium constants, but they apply to different types of reactions. Ka (acid dissociation constant) is used to describe the dissociation of an acid in water, while Kb (base dissociation constant) is used to describe the dissociation of a base in water.

Specifically, Ka is a measure of the strength of an acid in terms of how easily it donates a proton (H+) to a solvent like water. A higher Ka value indicates a stronger acid, while a lower Ka value indicates a weaker acid. Kb, on the other hand, is a measure of the strength of a base in terms of how easily it accepts a proton (H+) from a solvent like water. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base. There is a mathematical relationship between Ka and Kb for conjugate acid-base pairs, which are molecules or ions that differ by the presence or absence of a single proton. The relationship is expressed by the equation: Ka x Kb = Kw, where Kw is the ion product constant for water, which is 1.0 x 10⁻¹⁴ at 25°C. This relationship shows that the stronger the acid, the weaker its conjugate base, and vice versa.

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