Which of the following functions (there may be more than one) are solutions of the differential equation y'' – 4y' + 4y = e^t?

a. y= e^2t + e^t
b. y = e^2t
c. y = e^t
d. y = te^2t + e^t
e. y = e^2t + te^t

Answer:

80

Step-by-step explanation:

Answer:

80°

Step-by-step explanation:

I think all angles are 180°

so 60 +40 = 100

180 - 100 = 80

EXPLANATION

Given the circle, we can see the following facts:

Diameter= 24 ft ----> radius= 12 ft

Total arc length = 360°

The arc of a semi-circle is equal to 360/2 = 180 degrees

The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,

360° - 180° - 60° = 120°

So, representing this as a radian form:

Multiplying terms:

Simplifying:

So, the answer is 8π ft

Answer:

24 or 10

Step-by-step explanation:

unluckily, when you copied the text you did not paste well the value of x, but I assume it is 1.2 or 1/2

for the first value, the K (costant of variation) is 24, while for the second is 10, as the photo explains

Answer:

Mean: 20

Median: 16

Mode: No mode

Step-by-step explanation:

For the mean:

44 + 4 + 27 + 5 = 80

80/4 = 20

For the median:

5 + 27 = 32

32/2 = 16

For the mode:
None of the numbers are repeated.

Answer:

this is the order

-14/5, -11/5, -3/2, -2/3, 6/5, 4/2, 11/5, 16/5

Answer:

B

Step-by-step explanation:

can i have brainliest

Answer:

B

Step-by-step explanation:

You multiply 9 ×3 and get 27

Then you multiply 27×4 and get 108

And then you check your work.

Since 9×4 is 36 you multiply 36×3 and get 108.

So the new area is 3 times the old area.

423

To solve the above equation follow the BODMAS rule

That is,

Brackets of Division Multiplication Addition Subtraction

BODMAS rule states that mathematical expressions with multiple operations need to be solved from left to right in the order of BODMAS.

so,

first, calculate the value in the brackets

(144-4)*(12/4)+3 = (140)*(12/4)+3

=140*(3)+3

According to the rule, a division operation is to be performed but there is no division operation in the equation we skip this step and proceed to the next operation

so, multiply 140*3

=420+3

the next operation is the addition

=423

the next operation according to the rule is subtraction which is not required to be performed in the equation.

therefore,

(144-4)*(12/4)+3 = 423

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Answer:

426 cm^2

Step-by-step explanation:

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

Since φ satisfies all the conditions of the First Isomorphism Theorem, we conclude that K/(K ∩ N) is isomorphic to (K N)/N.

What is First Isomorphism Theorem?

The First Isomorphism Theorem is a fundamental result in group theory that establishes a connection between a group homomorphism and the structure of the groups involved. It states that if φ: G → H is a group homomorphism with kernel K, then the quotient group G/K is isomorphic to the image of φ, denoted as φ(G). In other words, the cosets of the kernel K in G form a group isomorphic to the image of G under the homomorphism φ

To prove that K/(K ∩ N) is isomorphic to (K N)/N, where K is a subgroup of G and N is a normal subgroup of G, we can use the First Isomorphism Theorem. The theorem states that if φ: G → H is a homomorphism with kernel K, then G/K is isomorphic to φ(G).

Let's define a homomorphism φ: K → (K N)/N, where φ(k) = kN. We need to show that φ is well-defined, injective, surjective, and preserves the group operation.

Well-defined: We need to show that if k1, k2 ∈ K and k1N = k2N, then φ(k1) = φ(k2). Since k1N = k2N, it implies that k1⁻¹k2 ∈ N. Since N is a normal subgroup of G and K is a subgroup of G, it follows that (k1⁻¹k2)k ∈ K for any k ∈ K. Hence, φ is well-defined.

Injective: We need to show that if φ(k1) = φ(k2), then k1 = k2. If φ(k1) = φ(k2), it implies that k1N = k2N, which means k1⁻¹k2 ∈ N. Since N is a subgroup of G, k1⁻¹k2 ∈ N implies k1⁻¹k2N = N. This implies k1⁻¹k2 ∈ K ∩ N. As K ∩ N contains only the identity element (since N is a normal subgroup and K is a subgroup), we have k1⁻¹k2 = e (identity element), which gives k1 = k2. Hence, φ is injective.

Surjective: We need to show that for every coset aN in (K N)/N, there exists an element k ∈ K such that φ(k) = aN. Since aN is a coset in (K N)/N, we can write aN = knN for some k ∈ K and n ∈ N. Hence, φ(k) = knN = aN. Therefore, φ is surjective.

Group operation preservation: We need to show that φ preserves the group operation. Let k1, k2 ∈ K. Then φ(k1k2) = (k1k2)N = (k1N)(k2N) = φ(k1)φ(k2). Hence, φ preserves the group operation.

Since φ satisfies all the conditions of the First Isomorphism Theorem, we conclude that K/(K ∩ N) is isomorphic to (K N)/N.

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The sine of 0 radians is 0.

In trigonometry, the sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse of a right-angled triangle.

When the angle is 0 degrees (or 0 radians), the opposite side has a length of 0, and thus the ratio is also 0. Therefore, the sine of 0 radians is 0.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 0 is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

Note that, the sine function maps an angle to a value which is between -1 and 1, with a periodic nature, meaning that the values repeat in a cycle as the angle increases.

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To find the unit rate for Start Fraction 182 dollars Over 14 feet End Fraction,

c. divide both 182 and 14 by 182.

A fraction is a mathematical concept that refers to a component of a whole or, more broadly, any number of equal parts.

An element of the whole is a fraction. The number is shown as a quotient in mathematics, where the numerator and denominator are split.Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.

Step 1: Divide 182 by 182

182 / 182 = 1

Step 2: Divide 14 by 182

14 / 182 = 0.07660818713450292

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Answer:

Independent = Milk left in the gallon jug

Dependent = cups of milk poured

Step-by-step explanation:

In an experiment or a research, a variable is defined as the thing or a phenomenon that you are trying to found out or measure. Variables can be independent variable as well as the dependent variable.

Independent variable is the variable that the researcher or the experimenter can change or manipulate in the research. This variable does not depend on others and thus stands alone. Its value can be change or altered to find the changes in the dependent variables. They are used as treatment variables.

Whereas, the dependent variables are those variables that are dependent on the values of the independent variables. It is considered as the effect of the independent variable. An independent variable is often manipulated to measure the outcome in the dependent variable.

In the context, the cups of milk poured is the dependent variable and the independent variable is the amount of milk left in the jug.  

A.68

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

Axiom-2

If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.

The two axioms given above together are called the linear pair axioms.

-----------------------------------------------------------------------------------------------------

Solution:

Given,

∠PQR = ∠PRQ

To prove:

∠PQS = ∠PRT

Proof:

∠PQR +∠PQS =180° (by Linear Pair axiom)

∠PQS =180°– ∠PQR — (i)

∠PRQ +∠PRT = 180° (by Linear Pair axiom)

∠PRT = 180° – ∠PRQ

∠PRQ=180°– ∠PQR — (ii)

[∠PQR = ∠PRQ]

From (i) and (ii)

∠PQS = ∠PRT = 180°– ∠PQR

∠PQS = ∠PRT

Hence, ∠PQS = ∠PRT

PLEASE MARK THIS AS A BRILLIANT ANSWER

Answer:

x = 2

Step-by-step explanation:

1 - 3x = -5

Subtract 1  from each side

1-3x-1 = -5-1

-3x = -6

Divide each side by -3

-3x/-3 = -6/-3

x = 2

The claim we need to check is that 16 is the 50% of 36.

Recall that if we add 50% and 50%, we should end up with 100%. In our case, we have that our 100% is 36. So, if it was true that 16 is the 50% of 36, then it should happen that if we add 16 with itself, we should get 36.

Note that

Since 16+16 is not 36, it is not true that 16 is the 50% of 36.

Answer:

Step-by-step explanation:

The sum of the angles in a triangle is always 180 degrees. Therefore,

2x + 3x + 22 = 180

Simplifying the equation,

5x = 158

Dividing by 5 on both sides,

x = 31.6

To find the actual measures of 2x and 3x, we substitute the value of x:

2x = 2(31.6) = 63.2 degrees

3x = 3(31.6) = 94.8 degrees

Therefore, the actual measures of 2x and 3x are 63.2 degrees and 94.8 degrees, respectively.

Answer:

Step-by-step explanation:

The experimental probability of the cube landing on three is 1/10.

Answer:

375 is greater than x.

Step-by-step explanation:

75>x/5

*5     *5 (this removes the five from the side with x)

375>x

Answer:It’s a x<1,125

Step-by-step explanation:

The function that possesses a period of 16 units, a midline at y=3, and a maximum at y=8 is f(x) = 5 sin(π/8 x) + 3

The sine function with a period of 16 units, a midline at y=3, and a maximum at y=8 can be written in the form:

y = A sin(Bx) + C

where A is the amplitude, B is the frequency (related to the period), and C is the vertical shift (related to the midline).

The frequency is related to the period by the formula: B = 2π/period.

So, in this case,

B = 2π/16 = π/8.

So, we have

y = A sin(π/8x) + C

Using the list of options as a guide the sine function that satisfies these conditions is f(x) = 5 sin(π/8 x) + 3

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Answer:

B. 12w + 62 = 242 is the answer  Happy to Help :)

Step-by-step explanation:

Answer:

-0.8 - 0.5b - 1.4c

Step-by-step explanation:

Take the b and the c away

Then times the 0.2 by all the numbers but don't add them

Once your done you and the b and c back to you equation

Answer:

$1.95 for one can of peanuts.

Step-by-step explanation:

It will cost $186.30 to run the resistance heater for 30 days with the given conditions.

Given data:

Power consumed by the resistance heater = 4.5 kW

Running time = 6 hours/day

Period of running = 30 days

Cost of electricity = Average price in Massachusetts

To calculate the total energy consumption during this time period,

we use the formula below:

Energy = Power × Time

Energy consumed in 6 hours

= 4.5 kW × 6 hours

= 27 kWh/day

Total energy consumed in 30 days

= 27 kWh/day × 30 days

= 810 kWh

To calculate the cost of running the resistance heater, we use the formula below:

Cost = Energy × Cost per unit of electricity

Cost of electricity per unit in Massachusetts is assumed to be $0.23/kWh

Cost of running the resistance heater

= 810 kWh × $0.23/kWh

= $186.30

Therefore, it will cost $186.30 to run the resistance heater for 30 days with the given conditions.

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Explanation:

AD = 15, DB = 12, AE = 10, and EC = 8

To determine if line BC is parallel to line DE, we will find the ratio of thier corresponding sides. if it is equal, they are parallelf

Answer:

Hey there!

Angle QRS is 70, and since it is located on the circle, we have a useful formula. If 141x-1 is called y, then 70 is half of that.

Thus, we have 141x-1=140

141x=141

x=1

Hope this helps :)

Answer:

\( \sf \: x = 25\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 11x - 24 = 7x + 76

Then the value of x will be,

→ 11x - 24 = 7x + 76

→ 11x - 7x = 76 + 24

→ 4x = 100

→ x = 100 ÷ 4

→ [ x = 25 ]

Hence, the value of x is 25.

Hello and greetings Brainly users.

It is an exercise of linear equations with one variable is a fundamental topic in the study of algebra. These types of equations are characterized by being first-degree polynomials in one variable, and can be found in various contexts, such as physics, economics, engineering, among others. Therefore, the ability to solve these equations is essential in the training of any mathematics student and in the development of their ability to solve problems in real life situations.

A linear equation with a variable can be solved by means of a series of algebraic operations that allow us to simplify the expression and clear the variable to be solved. These operations include adding, subtracting, multiplying, and dividing, always maintaining equality between both sides of the equation. The ultimate goal is to find the numerical value that satisfies the equation, that is, the value that makes the equality true.

Solving linear equations with one variable is an important skill not only for mathematics students, but also for professionals in various fields. For example, in engineering, linear equations are used to model physical systems and phenomena, and their resolution is necessary to perform calculations and make informed decisions. In the economy, they are used to analyze the behavior of financial variables and make projections for the future.

To solve the equation 11x - 24 = 7x + 76 we need to isolate the variable x on one side of the equation.

First, we can simplify both sides of the equation by combining like terms:

      11x - 7x = 76 + 24

Which gives us

       4x = 100

Next, we can solve for x by dividing both sides of the equation by 4:

       4x/4 = 100/4

       x = 25

Therefore, the solution to the equation is x = 25.

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Answer:

41.7

Step-by-step explanation:

\(10(2 + 3) - 8.3 \\ \\ = 10 (5) - 8.3 \\ \\ = 50 - 8.3 \\ \\ = 41.7\)