Need help I don’t understand new topic answers please

The given Cauchy-Euler equation is t²y'' - 6ty' + 10y = 0. To find the general solution, we can assume a solution of the form y(t) = t^r, where r is a constant.

Substituting this into the differential equation, we can solve for the values of r that satisfy the equation. The general solution will then be expressed as y(t) = c₁t^r₁ + c₂t^r₂, where c₁ and c₂ are arbitrary constants and r₁ and r₂ are the solutions of the equation. Next, we can use the given initial conditions to determine the specific values of the constants c₁ and c₂ and obtain the solution that satisfies the initial conditions.

To find the general solution to the Cauchy-Euler equation t²y'' - 6ty' + 10y = 0, we assume a solution of the form y(t) = t^r. Taking the first and second derivatives of y(t), we have y' = rt^(r-1) and y'' = r(r-1)t^(r-2). Substituting these into the differential equation, we get r(r-1)t^r - 6rt^r + 10t^r = 0. Factoring out t^r, we have t^r(r^2 - 7r + 10) = 0.

Since t^r cannot be zero, we solve the quadratic equation r^2 - 7r + 10 = 0. The solutions are r₁ = 5 and r₂ = 2. Therefore, the general solution to the Cauchy-Euler equation is y(t) = c₁t^5 + c₂t^2, where c₁ and c₂ are arbitrary constants.

To find the solution that satisfies the initial conditions y(1) = -2 and y'(1) = 7, we substitute these values into the general solution.

y(1) = c₁(1^5) + c₂(1^2) = c₁ + c₂ = -2

y'(1) = 5c₁(1^4) + 2c₂(1^1) = 5c₁ + 2c₂ = 7

We now have a system of two equations with two unknowns (c₁ and c₂). Solving this system of equations will yield the specific values of c₁ and c₂, giving us the solution that satisfies the initial conditions.

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Answer:

15.2

Step-by-step explanation:

Answer:

★ The answer would be 15.2

Step-by-step explanation:

We need to find

16 % of 95

Write it exactly as it is said.

16 % can be written as a fraction.

16/100×95=15.2

⇒If you check by inspection the line passes through the points (0,-3) and (2.-2)

⇒Note I only chose those points because they will help me figure out the gradient of the line . You van use the points of you choice to find the gradient using the formula

\(m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{-2-(-3)}{2-0} \\m=\frac{-2+3}{2} \\m=\frac{1}{2}\)

We know that the general equation to find the straight line equation is y=mx+c

⇒Now to find the value of the the unknown variable which in this case is c we can substitute the known (x,y) which is a point of your choice and m which is thew gradient you calculated above as variable m

⇒Note I will use the point (0,-3) to find the value of c

\(-3=\frac{1}{2} (0)+c\\c=-3\)

⇒This brings us to a conclusion of saying the equation of the straight line is :

⇒\(y=\frac{1}{2}x-3\)

The first option is the answer

GOODLUCK!!!!!!!!

Answer:

5.9 pounds

Step-by-step explanation:

3.8 + 2.1 = 5.9

Answer:

the tops coordinates are A(0,6) B(4,6) C(6,4) D(2,4)

bottom A(0,3) B(2,3)C(3,2)D(1,2)

Step-by-step explanation:

Answer:

the tops coordinates are A(0,6) B(4,6) C(6,4) D(2,4)

bottom A(0,3) B(2,3)C(3,2)D(1,2)

Step-by-step explanation:

Answer:

u can have max of 3 with remainder of 3

Step-by-step explanation:

Hence, the different groups of \(5\) can be formed from the \(18\) volunteers is

\(^{18}C_5=205632\).

What is the permutation and combination?

Permutation and Combination form the principles of counting and they are applied in various situations.

A permutation is a count of the different arrangements which can be made from the given set of things. In permutation the details matter, as the order or sequence is important.

Here given that,

A blood bank needs \(5\) people to help with a blood drive. \(18\) people have volunteered.

So,

\(^nC_r=\frac{n!}{r(n-r)!}\)

Here \(n=18, r=5\)

Then

\(^{18}C_5=\frac{18!}{5(18-5)!}\\\\^{18}C_5=\frac{18!}{5(13)!}\\\\^{18}C_5=\frac{(18)(17)(16)(15)(14)(13)}{5(13)}\\\\^{18}C_5=\frac{(18)(17)(16)(15)(14)}{5}\\\\^{18}C_5={(18)(17)(16)(3)(14)}\\\\^{18}C_5=205632\)

Hence, the different groups of \(5\) can be formed from the \(18\) volunteers is

\(^{18}C_5=205632\).

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If you are trying to find the missing measures of a rectangle, you should know that all rectangles have four sides, and each side has a length.

In other words, if you have a rectangle, two of the angles must be 90 degrees, and the other two angles must also be 90 degrees. To find the missing measures of a rectangle, you need to use the properties of rectangles.

First, find the length of each side. The length of all sides of a rectangle should be the same. Then, calculate the area of the rectangle. You can do this by multiplying the length of one side with the length of the other side.

Finally, you can use the Pythagorean Theorem to find the missing measures.

The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Using this theorem, you can find the length of the hypotenuse of the rectangle.

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Complete Question:

if each quadrilateral is given, then define the steps to find the missing measures a rectangle.

The solution to the expression 4+(−634) is -630

From the question, we have the following parameters that can be used in our computation:

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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Answer:

The correct option is C: the isotope of iodine contains 81 neutrons.

Step-by-step explanation:

The mass (A) of the iodine isotope is given by:

\(A = Z + N\)

Where:

Z: is the number of protons

N: is the number of neutrons

For iodine Z= 53, so if A = 134 the number of neutrons is:

\( N = A - Z = 134 - 53 = 81 \)

Therefore, the correct option is C. The isotope of iodine contains 81 neutrons.

I hope it helps you!

Answer:

40600151844.........

Answer:

40, 600, 151,844

Step-by-step explanation:

this is two million seven hundred and forty eight, times two hundred three, to get forty billion six hundred million one hundred fifty one thousand eight hundred forty-four.

Answer:

Maybe 30°

Cause 12:4 is 3

3x10 30

The central angle of a regular dodecagon is 30 degrees. Option A is the correct option.

The central angle - The angle created at the polygon's center by two adjacent radii—the lines that connect the polygon's center to its vertices—is known as the central angle.

We know it is a regular dodecagon, which means all the sides will be of equal size.

As it is a dodecagon there will be a total of 12 equal central angles added to give an angle of 360 degrees.

Let's assume the central angle is x.

12x = 360

x = 360/12

x = 30

Hence, the central angle in a regular dodecagon is 30 degrees.

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To determine if the value 5π/4 is a solution for the equation 3√(sin θ) + 2 = -1, we need to substitute the value of θ and verify if the equation holds true.

Let's substitute θ = 5π/4 into the equation:

3√(sin(5π/4)) + 2 = -1

Now, let's simplify the equation step by step:

First, let's evaluate sin(5π/4). In the unit circle, 5π/4 is in the third quadrant, where sin is negative. Additionally, sin(5π/4) is equal to sin(π/4) due to the periodic nature of the sine function.

sin(π/4) = 1/√2

Now, substitute the value of sin(π/4) back into the equation:

3√(1/√2) + 2 = -1

Simplifying further:

3√(1/√2) = 3 * (√(1)/√(√2)) = 3 * (1/√(2)) = 3/√2 = 3√2/2

Now the equation becomes:

3√2/2 + 2 = -1

To add fractions, we need a common denominator:

(3√2 + 4)/2 = -1

Since the left side of the equation is positive and the right side is negative, they can never be equal. Therefore, the equation is not satisfied, and 5π/4 is not a solution to the equation 3√(sin θ) + 2 = -1.

Thus, the statement "The value 5π/4 is a solution for the equation 3√(sin θ) + 2 = -1" is false.

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Answer:

8=73 degrees

5=107 degrees

Step-by-step explanation:

Please mark me brainliest :D

Answer:

Angle 5 is 107 degrees

Angle 8 is 7s degrees

Step-by-step explanation:

First find angle 5. Since the lines are parallel and cut by a transversal, we can say that Angle 3 and Angle 5 are congruent (same measure) since they are alternate interior angles.

Since Angle 3 is 107 degrees, Angle 5 would also be 107 degrees.

Angle 8 is supplementary to Angle 5.

Angle 5 + Angle 8 = 180

Since we know Angle 5 is 107: 107 + Angle 8 = 180

Angle 8 would then be 73 degrees.

The equation of the linear trendline is y = 0.5x + 2. The R-squared value is 0.85, which indicates that there is a strong positive correlation between the two variables.

The scatter plot shows a strong positive correlation between the two variables. The linear trendline fits the data well, and the R-squared value of 0.85 indicates that 85% of the variation in the dependent variable can be explained by the variation in the independent variable.

The positive correlation between the two variables means that as the independent variable increases, the dependent variable also tends to increase. The linear trendline shows that the relationship between the two variables is approximately linear. The R-squared value of 0.85 indicates that there is a strong linear relationship between the two variables. This means that the linear trendline is a good fit for the data, and that the variation in the dependent variable can be explained by the variation in the independent variable to a large extent.

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Answer:first is negative and positive im sure of it if i get im sorry tried my best

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(---------------------------------\)

\(Here's\) \(how\) \(we\) \(solve\) \(it\)

\(-2.5\cdot\frac{-3}{5}\) = \(1.5\) \(or\) \(\frac{3}{2}\)

\(1.5\cdot50\) = \(75\)

\(75\cdot\frac{1}{-4}\) = \(-18.75\) \(or\) \(-\frac{75}{4}\)

\(-18.75\cdot1.6\) = \(-30\)

\(-30\cdot-2\) = \(60\)

\(---------------------------------\)

\(Here's\) \(the\) \(answer.\)

\(-2.5\cdot\frac{-3}{5}\cdot50\cdot\frac{1}{-4}\cdot1.6\cdot-2\) = \(60\)

\(60\) \(is\) \(positive\) \(and\) \(is\) \(an\) \(even\) \(number.\)

\(---------------------------------\)

Hope this helps! <3

Given y = g(x) therefore,

y = -4.

Since there's no x. That means x = 0.

Therefore the value of x is 0

Answer:

It depends on what the question and or equation is that you are using if i knew why you where trying to solve for x I could tell you.

Step-by-step explanation:

Ted's work to evaluate the expression 21 ÷ 3 + 5* 3 is incorrect, as he evaluated the division before the multiplication. He follow the wrong order of operations. The correct answer is 22, not 36.

Ted's work is incorrect. In step 1, he evaluated the division before the multiplication, which is incorrect according to the order of operations (PEMDAS). According to the order of operations, multiplication and division should be done before addition and subtraction. Therefore, the correct way to evaluate the expression is as follows:

21 ÷ 3 + 5 * 3

= 7 + 15 (evaluating multiplication before addition)

= 22

Thus, the correct answer is 22, not 36 as Ted calculated. It is important to follow the order of operations in order to arrive at the correct answer.

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

Ted tried to evaluate the expression 21 ÷ 3 + 5* 3. Here, is his work:

21 ÷ 3 + 5* 3

= 7 + 5 * 3          step 1

= 12 * 3              step 2

= 36

Is his work correct?

Answer:

6

Step-by-step explanation:

37/37+5=1+5=6

The measure of angle A in the isosceles triangle ABC is 62.5 degrees.

In an isosceles triangle ABC, where AB = AC, we are given that angle B (denoted as ∠B) measures 55 degrees. We need to calculate the measure of angle A (denoted as ∠A).

Since AB = AC, we know that angles A and C are congruent (denoted as ∠A ≅ ∠C). In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.

Therefore, we have:

∠A ≅ ∠C

Also, the sum of the angles in a triangle is always 180 degrees. Hence, we can write:

∠A + ∠B + ∠C = 180

Substituting the given values:

∠A + 55 + ∠A = 180

Combining like terms:

2∠A + 55 = 180

Subtracting 55 from both sides:

2∠A = 180 - 55

2∠A = 125

Dividing by 2:

∠A = 125 / 2

∠A = 62.5

Therefore, the measure of angle A in the isosceles triangle ABC is 62.5 degrees.

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The volume of the solid S, where the base is a triangular region and cross-sections perpendicular to the y-axis are semicircles, can be found using calculus. The volume of S is (3π/8) cubic units.

In the first part, the volume of the solid S is (3π/8) cubic units.

In the second part, we can find the volume of S by integrating the areas of the cross-sections along the y-axis. Since the cross-sections are semicircles, we need to find the radius of each semicircle at a given y-value.

Let's consider a vertical strip at a distance y from the x-axis. The width of the strip is dy, and the height of the semicircle is the x-coordinate of the triangle at that y-value. From the equation of the line, we have x = (3/2)y.

The radius of the semicircle is half the width of the strip, so it is (1/2)dy. The area of the semicircle is then\((1/2)\pi ((1/2)dy)^2 = (\pi /8)dy^2.\)

To find the limits of integration, we note that the base of the triangle extends from y = 0 to y = 2. Therefore, the limits of integration are 0 to 2.

Now, we integrate the area of the semicircles over the interval [0, 2]:

V = ∫\((0 to 2) (\pi /8)dy^2 = (\pi /8) [y^3/3]\) (evaluated from 0 to 2) = (3π/8).

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Answer:

  -4/243

Step-by-step explanation:

Your calculator can do this.

You know that 3³ = 27 and (-3)³ = -27. You also know that 3² = 9, and that anything to the zero power is 1. With these facts, you can simplify the expression to ...

  \(\dfrac{\sqrt[3]{-27}-27^0}{3^3\times3^2}=\dfrac{-3-1}{27\times9}=\boxed{-\dfrac{4}{243}}\)

Answer -11r - 31

First you have to multiply the 4 to the numbers on parenthesis and also the 5 to the numbers of parenthesis.

Answer:

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Answer:

a) 3x=18

x=18/3

x=6

b) 2x=9

x=9/2

or 4.5

c) x/5=7

x=7×5

x=35

d) x/2=6.5

x=6.5×2

x=13

Answer:

Step-by-step explanation:

a) 3x = 18, value of x?

→ 3x = 18

→ x = 18/3

→ [ x = 6 ]

Thus, value of x is 6.

b) 2x = 9, value of x?

→ 2x = 9

→ [ x = 9/2 ]

Thus, value of x is 9/2.

c) x/5 = 7, value of x?

→ x/5 = 7

→ x = 7 × 5

→ [ x = 35 ]

Thus, value of x is 35.

d) x/2 = 6.5, value of x?

→ x/2 = 6.5

→ x = 6.5 × 2

→ [ x = 13 ]

Thus, value of x is 13.

To find the mass of the water in the tank, we need to multiply the volume of the tank by the density of water. The volume of the tank can be found by multiplying its height, length, and width. we can use the formula:

Mass = Density * Volume

First, let's calculate the volume of the tank. The tank has dimensions of 2.4 m (height), 6 m (length), and 1.5 m (width).

Volume = height * length * width
             = 2.4 m * 6 m * 1.5 m
             = 21.6 cubic meters

Now, let's substitute the density of water and the volume into the formula to find the mass:

Mass of water = Volume of the tank * Density of water

Mass = 1,000 kg/m³ * 21.6 m³
         = 21,600 kg

Therefore, the mass of the water in the tank is 21,600 kg.

The correct answer is D. 21,600 kg.

In summary, the mass of the water in the tank is determined by the volume of the tank and the density of water. By multiplying the volume by the density, we can find the mass. In this case, the mass is 21,600 kg.

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Step-by-step explanation:

refer to the picture.. hope this helps :)

The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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1. Potential problems: Political instability, legal and regulatory environment, economic factors, and cultural differences.

2. Potential advantages: Access to a new market, incentive packages, and local expertise and resources.

3. Recommendation: Cautiously consider the joint venture after thorough risk analysis and due diligence.

1. Potential problems that face the new venture:

2. Potential advantages of this venture for the company:

3. Recommendation on entering the joint venture:

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