Solve the initial value problem given by the differential equation: C1​C2​R2​(Rc​+R1​)dt2d2qc2​​​+[(Rc​+R1​)(C1​+C2​)​+R2​C2​]dtdqc2​​​+qc2​​=C2​E​ and the initial conditions: qc2​​(0)dtdqc2​​​(0)​=0=0​ Hereafter we will use the following values of the resistors, capacitances, and voltage: C1=10μFC2=100μFR1=100ΩR2=100ΩRc=1kΩE=5 V​

Answer:

3a+10

Step-by-step explanation:

3a+6+4

3a=10

5a-2a=3a+6+4

3a=10

Answer:

the answers are in the picture

Step-by-step explanation:

The probability distribution of the number of hours per day people are able to relax is constructed, and probabilities of relaxing more than 4 hours, between 2 to 6 hours, and not relaxing at all are 0.283, 0.767 and 0.068 respectively. The mean and standard deviation are 3.326 hours and 1.950 hours (approx.) respectively.

The probability distribution of X is:

X Frequency Probability

0 114                    0.068

1 156                    0.093

2 336                    0.201

3 251                     0.150

4 316                      0.189

5 231                     0.138

6 149                    0.089

7 33                    0.020

8 60                    0.036

      1676                     1.000

The probability that a person relaxes more than 4 hours per day is:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 0.138 + 0.089 + 0.020 + 0.036

= 0.283

The probability that a person relaxes from 2 to 6 hours per day is:

P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.201 + 0.150 + 0.189 + 0.138 + 0.089

= 0.767

The probability that a person does not relax at all is:

P(X = 0) = 0.068

The mean Mx is:

Mx = Σ(X * P(X))

= 00.068 + 10.093 + 20.201 + 30.150 + 40.189 + 50.138 + 60.089 + 70.020 + 8*0.036

= 3.326 hours

The standard deviation Ox is:

Ox = sqrt[Σ(X^2 * P(X)) - Mx^2]

= sqrt[(0^20.068)+(1^20.093)+(2^20.201)+(3^20.150)+(4^20.189)+(5^20.138)+(6^20.089)+(7^20.020)+(8^2*0.036) - 3.326^2]

= 1.950 hours (approx.)

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Answer: Parallel

Step-by-step explanation:

if two secanys of a circle are made them they cut off congruent arcs

Answer:

The first digit would go in the tens place.

Step-by-step explanation:

First we estimate the approximate numbers. For 6130 we estimate 6000 and for 153 we estimate almost 150.

So dividing 6000 by 150 would give 40 .

The four would go in the ten's place .

Now check by dividing

         40.1     So the answer is correct. The quotient is 40.12.

\(153\sqrt{6139}\)

      612

           190

           153

             37

The first digit would go in the tens place.

The answer is justified. We can easily decide where to place the first digit.

Step-by-step explanation:

explain how you can decide where to place the first diget in the quotiont for 6,139÷135

Reduced sample size is a result of a fall in predicted rate, an increase in the tolerated rate, and a rise in the allowable risk of estimating control risk too low.

Given that,

We have to find what impact does a larger acceptable risk of estimating control risk too low have on sample size in characteristics sampling.

The term "risk of over-reliance" refers to the "risk of estimating control risk too low" in characteristics sampling, and it relates with the so-called 

Reduced sample size is a result of a fall in predicted rate, an increase in the tolerated rate, and a rise in the allowable risk of estimating control risk too low.

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The second-order homogeneous ordinary differential equation that corresponds to the given solution y = C₁ + C₂e^t is y'' + (a + 1)y' = 0.

A second-order homogeneous ordinary differential equation (ODE) is of the form:

y'' + ay' + by = 0,

where y'' represents the second derivative of y with respect to the independent variable, a and b are constants, and y is the dependent variable.

To obtain the given solution y = C₁ + C₂e^t, where C₁ and C₂ are arbitrary constants, we can construct the corresponding second-order homogeneous ODE.

Since y = C₁ + C₂e^t, taking the first and second derivatives of y, we have:

y' = 0 + C₂e^t = C₂e^t,

y'' = 0 + C₂e^t = C₂e^t.

Substituting these derivatives into the general form of the second-order homogeneous ODE, we get:

C₂e^t + a(C₂e^t) + b(C₁ + C₂e^t) = 0.

Simplifying this equation, we have:

C₂e^t + aC₂e^t + bC₁ + bC₂e^t = 0.

We can collect the terms with the same exponential factors:

(1 + a + bC₂)e^t + bC₁ = 0.

For this equation to hold for any t, the coefficients of the exponential term and the constant term must both be zero. Therefore, we have:

1 + a + bC₂ = 0,

bC₁ = 0.

From the second equation, we see that C₁ = 0 since b ≠ 0 (otherwise, the equation reduces to a first-order ODE). Substituting C₁ = 0 into the first equation, we get:

1 + a = 0.

Hence, the second-order homogeneous ODE that results in the given solution y = C₁ + C₂e^t is:

y'' + (a + 1)y' = 0.

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The inequality that describes this graph of the number line is x ≥ 4

From the question, we have the following properties:

The property 3 above implies that the domain of the number line is the set of all real numbers.

The property 4 above implies that the inequality of the number line is a greater than or equal to inequality, and the value starts from 4

This is represented by the following inequality

x ≥ 4

Hence, the inequality that describes this graph of the number line is x ≥ 4

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The number of elements common to sets S and T, where S is the set of the 2005 smallest positive multiples of 4 and T is the set of the 2005 smallest positive multiples of 6, can be determined by finding the least common multiple (LCM) of 4 and 6 and dividing it by 4.

The multiples of 4 can be written as {4, 8, 12, 16, ...}, while the multiples of 6 can be written as {6, 12, 18, 24, ...}. To find the common elements, we need to determine the numbers that are divisible by both 4 and 6.

The LCM of 4 and 6 is 12. To find the number of elements common to sets S and T, we divide the LCM (12) by 4 since the sets consist of the smallest positive multiples. This gives us 12/4 = 3.

Therefore, there are 3 elements that are common to both sets S and T.

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To dilate triangle ABC using center P and a scale factor of 32, we can apply the following steps. Firstly, locate the center of dilation, P, which will be the reference point for the dilation. Then, for each vertex of the original triangle, draw a line segment from the vertex to point P. Finally, multiply the length of each line segment by the scale factor of 32 to determine the corresponding points on the dilated triangle.

In summary, to dilate triangle ABC with center P and a scale factor of 32, we locate the center of dilation, draw line segments from each vertex to point P, and multiply the length of each line segment by the scale factor of 32 to find the corresponding points on the dilated triangle.

The center of dilation, P, serves as the reference point for the dilation. It acts as the anchor around which the triangle expands or contracts. To dilate each vertex, we draw a line segment from the original vertex to point P. This line segment represents the direction and distance of the dilation. By multiplying the length of each line segment by the scale factor of 32, we determine the new positions of the vertices on the dilated triangle. The scale factor of 32 indicates that the dilated triangle will be enlarged by a factor of 32, resulting in a significant increase in size compared to the original triangle.

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Answer:

102739

Step-by-step explanation:

Answer:

12739

Step-by-step explanation:

10000 + 2739 = 12739

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

The equation of an exponential function will be y = 7.68 × 2.5ˣ.

What is equation of line?

The equation of line with slope m and passes through the point (x₁, y₁) is calculated as;

y - y₁ = m (x - x₁)

Given that;

An exponential function passes through the points (2, 48) and (5, 750).

Now, The exponential function is;

y = abˣ

Where, a and b are unknowns.

Hence, For the point (2, 48), we get the equation;

48 = ab² .. (i)

And, For the point (5, 750), we get;

750 = ab⁵   .... (ii)

Solve the equation (i) for value of a, we get;

48 = ab²

a = 48/b²

Substitute in equation (ii);

750 = ab⁵

750 = (48/b²) b⁵

750 = 48 b³

b³ = 750/48

Take cube root both side;

b = 5/2

Hence, a = 48/b² = 48/(5/2)²

a = 48 × 4 / 25

a = 7.68

Thus, After substitute the value of a and b we get the exponential equation as;

y = 7.68 × 2.5ˣ

Therefore, The equation of an exponential function will be,

⇒ y = 7.68 × 2.5ˣ.

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Answer:

first find the area of the big rectangle = 12×14=168

area of the small unshaded rectangle =2×5×6=60

area of the shaded region = 168-60=108

ANSWER

My answer is in the photos above

Answer:

60 seconds/1 minute

Step-by-step explanation:

We are trying to convert 20.1 meters/second to per minute. Since we know there's 60 seconds in a minute, we would use the conversion factor 60 seconds/1 minute in order to find greyhounds speed per minute

Answer:

x  ⪯ 7

Step-by-step explanation:

5 + 2 = 7

The expression ********** can be represented as 3333333333 in base four, 4444444444 in base five, and 7777777777 in base eight, according to the respective numerical systems.

a) In base four, each digit can have values from 0 to 3. The symbol "*" represents the value 3. Therefore, when we have ten "*", we can express it as 3333333333 in base four.

b) In base five, each digit can have values from 0 to 4. The symbol "*" represents the value 4. Hence, when we have ten "*", we can represent it as 4444444444 in base five.

c) In base eight, each digit can have values from 0 to 7. The symbol "*" represents the value 7. Thus, when we have ten "*", we can denote it as 7777777777 in base eight.

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Answer:

3/2 = 1/ 1/2

Step-by-step explanation:

1 1/5   divided by 4/5 is 1 1/2

Answer:

1

Step-by-step explanation:

4/5n=1-1/5n

so we collect the like terms

4/5n+1/5n=1

n=1

Answer:

Step-by-step explanation:

9.23

Answer:

|x + 7| ≥ 2 is the inequality

Step-by-step explanation:

x - b ≥ c    or    x - b ≤ -c

x ≥ b + c = -5     or x ≤ b - c = -9

b + c = -5

b - c = -9

2b = -14

b = -7                             -7 + c = -5

                                             c = 2

x - (-7) = x + 7

So, |x + 7| ≥ 2 is the inequality

The answer is D. 2 over 5

Step-by-step explanation:

Took the test.

The maximum value of f(x,y) is e^27, and the minimum value of f(x,y) is approximately 203.64.

The method of Lagrange multipliers can be used to find the maximum and minimum values of f(x, y) subject to the constraint x^3 + y^3 = 54.

Let g(x,y) = x^3 + y^3 - 54 be the constraint equation. We need to solve the system of equations:

grad(f) = λ grad(g)

g(x,y) = 0

where λ is the Lagrange multiplier.

Taking partial derivatives of f(x,y), we get:

fx = ye^xy = λ 3x^2

fy = xe^xy = λ 3y^2

Taking partial derivatives of g(x,y), we get:

gx = 3x^2 = 0

gy = 3y^2 = 0

Solving for x and y, we get:

x = y = (54/2)^(1/3) = 3∛18

The value of λ can be found by substituting the values of x and y into the equation grad(f) = λ grad(g):

ye^xy = λ 3x^2

xe^xy = λ 3y^2

Substituting x = y = 3∛18, we get:

λ = e^(18) / (9∛2)

To find the maximum and minimum values of f(x,y), we need to evaluate f(x,y) at the critical point (x,y) = (3∛18, 3∛18) and at the endpoints of the constraint region. The constraint x^3 + y^3 = 54 is satisfied on the boundary of the region, which is a compact set, so we can apply the extreme value theorem.

At the critical point, we have:

f(3∛18, 3∛18) = e^(54/2) = e^27

On the boundary of the region, we have:

f(x,y) = e^xy = e^(54-x^3) at y = (54-x^3)^(1/3)

Taking the derivative with respect to x, we get:

f'(x) = -3x^2 e^(54-x^3) + ye^(54-x^3) = 0

Substituting y = (54-x^3)^(1/3), we get:

-3x^2 e^(54-x^3) + (54-x^3)^(1/3) e^(54-x^3) = 0

Solving numerically, we get:

x = 2.8964, y = 3.8406 or x = 3.8406, y = 2.8964

At these points, we have:

f(2.8964, 3.8406) ≈ 203.64

f(3.8406, 2.8964) ≈ 203.64

Therefore, the maximum value of f(x,y) is e^27, and the minimum value of f(x,y) is approximately 203.64.

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The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).

This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.

For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.

Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.

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He needs one more quart. That is half of a gallon.

Answer:

90

Step-by-step explanation:

each dot = 45 bc 540 / how many dots there are which is 12 = 45 then there are 2 dots worth of 45 making it 90

math

540/12=45

45 x 2 = 90

Answer: 135 students

Step-by-step explanation:

1. Divide 540 (total number of students) by the number of dots (12)

2. So then 540/12= 45

3. Then see how many dots are more then 5 miles away so that is 3 dots (2dots on 6 miles, and 1 dot on 7 miles)

4. After 45*3= 135

To find the equation of the tangent at the point (π/4, π/2) on the curve given by x * sin(2y) = y * cos(2x), we need to find the slope of the tangent at that point.

First, we find the derivative of the given curve with respect to x using the product rule and the chain rule:

d/dx [x * sin(2y)] = d/dx [y * cos(2x)]

sin(2y) + x * 2cos(2y) * dy/dx = cos(2x) - y * 2sin(2x) * dx/dy

At the point (π/4, π/2), we substitute x = π/4 and y = π/2 into the above equation. Also, since the slope of the tangent is dy/dx, we solve for dy/dx:

sin(π) + (π/4) * 2cos(π) * dy/dx = cos(π/2) - (π/2) * 2sin(π/2) * dx/dy

1 + (π/2) * (-2) * dy/dx = 0 - (π/4)

1 - π * dy/dx = -π/4

dy/dx = (1 - π/4) / (-π)

Finally, we have the slope of the tangent dy/dx = (1 - π/4) / (-π).

Using the point-slope form of a line, we can write the equation of the tangent as:

y - (π/2) = [(1 - π/4) / (-π)] * (x - π/4)

Simplifying this equation gives the final equation of the tangent at (π/4, π/2) on the given curve.

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Answer:

= − 3

Step-by-step explanation:

15−2x=−7x

− 2 + 15 = −7

−2+15−15=−7−15

−2=−7−15

so 1 . you rearrange the terms

     2. subtract 15 from both sides

     3 simpfly  subtract the number

Answer:

You will move - 2x to the other side to gather factores x with considering change the sign because the changing in side so it will became

15=2x-7x

15=-5x

To find x you need to remove its variable -5 and that happen by devided it just basic algebra

X=15/-5

X=-3

The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

The total amount of money that was spent on lunch on Tuesday is $45.94.

The total amount that was spent on food on Tuesday can be determined by adding the amount spent on breakfast, lunch and dinner. Addition is the mathematical operation that is used to determine the sum of two or more numbers.

Total amount spent = 22.13 + 12.02 + 11.79 = $45.94

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Explanation:

first term = 33

second term = first term + 16 = 33+16 = 49

third term = second term + 16 = 49+16 = 65

We're adding 16 to each term to get the next term.

Answer:

c is correct

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Answer: THE TOTAL AMOUNT TAKEN BY KEVIN IN MIXING, BAKING, AND COOLING THE MUFFINS IS 30 MINUTES.

Step-by-step explanation:

1. AMOUNT TAKEN BY KEVIN FOR MIXING=8MIN.

2. AMOUNT TAKEN BY KEVIN FOR BAKING=17 MIN.

3. AMOUNT TAKEN BY KEVIN FOR COOLING=5MIN.

IN TOTAL, (8+17+5)MIN. = 30 MIN.

Answer:

30 minutes

Step-by-step explanation:

8+7  =15 +5=20+ another 10 = 30