Classifique as figuras geométricas em planas ou não planas.

Answer:

116

Step-by-step explanation:

To find f(6) you plug in the 6 in the x of the formula that gave you 'f(x)=3x^2-4+2x'

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

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

f(6) = 3*36 - 4 + 12

f(6) = 108 - 4 + 12

f(6) = 108 + 8

f(6) = 116

Answer:

\(x = 600\)

Step-by-step explanation:

Let's right our equation

\( \frac{x}{4} + 30 = 180\)

This due to our straight angle

Subtract 30 from both sides

\( \frac{x}{4} = 150\)

Multiply both sides by 4

\(x = 600\)

Brainliest please :)

Answer:

A

Step-by-step explanation:

Answer:

24.2

Step-by-step explanation:

37.45-13.25=24.2

24.2/2=12.1

each friend contributes $12.1

Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

The mathematical expression of the statement -7w mutiply 3w to the power of 5 is -7w * (3w)^5

The mathematical statement is given as:

-7w mutiply 3w to the power of 5

Express the power using the caret sign.

So, we have:

-7w mutiply (3w)^5

Express multiply using the * sign

-7w * (3w)^5

Hence, the mathematical expression of the statement is -7w * (3w)^5

Read more about mathematical expressions at:

https://brainly.com/question/4344214

#SPJ1

Answer:

Ok so what you should is first find the area for both of the circle

\(Area = \pi r^2\\\)

Big circle

you are given the radius which 14mm

\(3,14(14)^2 = 615.44 mm^2\)

Small circle

you are given the diameter of the small circle which 14mm

radius = diameter/2

14/2=7mm

\(3.14(7)^2 = 153,86mm^2\)

Shaded area means the difference between the 2 areas, in my opinion

so you do 615.44 - 153.86 = 461.58 mm^2

Hope that answers your question

Don't hesitate to comment if you are confused about something :)

Step-by-step explanation:

Answer:

(x - 10)² + (y + 4)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

This hypothesis suggests that there may be disparities in educational outcomes based on income level.

The alternative hypothesis H1: pL ≠ pH is the correct choice for testing the claim that the proportion of children from the low income group who did well on the test is different from the proportion of the high income group.

In this context, pL represents the proportion of successful students in the low income group, and pH represents the proportion of successful students in the high income group.

By stating that the two proportions are not equal, the alternative hypothesis allows for the possibility that there is a difference between the two income groups in terms of test performance.

This hypothesis suggests that there may be disparities in educational outcomes based on income level.

To know more about hypothesis click here

brainly.com/question/26059770

#SPJ11

Answer: x = 46

Step-by-step explanation: The theorem is:

The sum of all exterior angles of a polygon is 360

Here, our polygon is a "quadrilateral" -- 4 sided figure

We can say that the sum of all 4 exterior angles is 360. We set up an equation and solve for x. Shown below:

The value of x is 46

Answer: Answer: x = 46

Step-by-step explanation: The theorem is:

The sum of all exterior angles of a polygon is 360

Here, our polygon is a "quadrilateral" -- 4 sided figure

We can say that the sum of all 4 exterior angles is 360. We set up an equation and solve for x. Shown below:

The value of x is 46

Step-by-step explanation:

There are approximately over 60 million shipping containers in the world. Containers are stacked and arranged in these ports, creating an impressive sight and highlighting the scale of global trade.

Shipping containers are standardized metal boxes used for transporting goods by sea, rail, or road. They come in various sizes, including 20-foot and 40-foot lengths. These containers have revolutionized global trade, allowing for efficient and secure transportation of goods across long distances. While exact numbers are challenging to determine due to factors such as container movement and usage, estimates suggest that there are over 60 million shipping containers worldwide. This vast quantity of containers enables the global economy to function smoothly by facilitating the movement of goods between countries and continents.

The extensive use of shipping containers has led to the establishment of container ports and specialized container ships that can accommodate large numbers of containers.Moreover, repurposing shipping containers for alternative uses, such as modular homes or pop-up shops, has gained popularity in recent years, demonstrating the versatility and durability of these units.

learn more about global trade  here

brainly.com/question/29885031

#SPJ11

Answer:

the surface area is 124

the volume is 72

Step-by-step explanation:

Hi there! :)

Answer:

SA = 124 cm².

V = 72 cm³

Step-by-step explanation:

Volume of a rectangular prism: V = l × w × h

Given:

l = 4 cm

w = 9 cm

h = 2 cm

V = 4 × 9 × 2

V = 36 × 2

V = 72 cm³

Surface area: SA = 2(wl + hl + hw)

SA = 2((4 · 9) + (2 · 4) + (9 · 2))

SA = 2(36 + 8 + 18)

SA = 2(62)

SA = 124 cm².

Hope this helped you!

The statements provided describe relationships between vehicle weight, speed, and mileage. Let's analyze each statement: i. The heavier the vehicles, ceteris paribus (all other factors held constant), the lower the mileage, ii. The higher the speed of the vehicle past 50 miles per hour, ceteris paribus, the lower the mileage, iii. Weight and speed have a linear relationship with mileage.

i. The heavier the vehicles, ceteris paribus (all other factors held constant), the lower the mileage:

This statement suggests an inverse relationship between vehicle weight and mileage. It implies that, all other things being equal, as vehicle weight increases, the mileage decreases. This relationship is generally observed in vehicles because heavier vehicles require more energy to move, resulting in lower fuel efficiency and decreased mileage.

ii. The higher the speed of the vehicle past 50 miles per hour, ceteris paribus, the lower the mileage:

This statement indicates a negative relationship between vehicle speed and mileage beyond 50 miles per hour. It suggests that, keeping all other factors constant, as the speed of the vehicle increases beyond 50 miles per hour, the mileage decreases. Higher speeds typically lead to increased air resistance and require more power from the engine, leading to reduced fuel efficiency and lower mileage.

iii. Weight and speed have a linear relationship with mileage:

This statement suggests that both weight and speed have a direct linear relationship with mileage. In other words, it implies that increasing either weight or speed will result in a proportional increase or decrease in mileage. However, it's important to note that this statement may not always hold true in practice. While weight and speed can impact mileage, the relationship may not necessarily be strictly linear. Other factors such as engine efficiency, road conditions, driving habits, and aerodynamics can also influence mileage.

Overall, these statements highlight general trends observed in the relationship between vehicle weight, speed, and mileage. However, it is essential to consider that real-world situations involve multiple interrelated factors, and the specific impact on mileage can vary depending on various circumstances and individual vehicle characteristics.

Learn more about   statement   from

https://brainly.com/question/27839142

#SPJ11

To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

Learn more about cyclic group here -: brainly.com/question/30697028

#SPJ11

To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

Learn more about cyclic group here -: brainly.com/question/30697028

#SPJ11

a)  The equation for the exponential distribution of waiting times is given by \(f(x) = \lambda e^{-\lambda x}\)

b) The probability of waiting less than 2 minutes to check out is 0.427

c) The probability of waiting between 4 and 6 minutes is 0.242

d) The probability of waiting more than 5 minutes to check out is 0.082

a. The equation for the exponential distribution of waiting times is given by:

\(f(x) = \lambda e^{-\lambda x}\)

where λ is the rate parameter of the distribution, and e is the natural logarithmic constant (approximately equal to 2.71828). The graph of the exponential distribution is a decreasing curve that starts at λ and approaches zero as x approaches infinity. The mean waiting time, denoted by E(X), is equal to 1/λ.

b. To find the probability that a customer waits less than 2 minutes to check out, we need to calculate the area under the exponential distribution curve between zero and 2 minutes. This can be expressed mathematically as:

P(X < 2) = \(\int_0^2 \lambda e^{-\lambda x} dx\)

Solving this integral yields:

P(X < 2) = 1 - \(e^{(-2\lambda)}\)

Substituting the given average waiting time of 2.5 minutes into the formula for the mean waiting time, we can calculate λ as:

E(X) = 1/λ

2.5 = 1/λ

λ = 0.4

Therefore, the probability of waiting less than 2 minutes to check out is:

P(X < 2) = 1 - \(e^{-2*0.4}\)

P(X < 2) ≈ 0.427

c. To find the probability of waiting between 2 and 4 minutes, we need to calculate the area under the exponential distribution curve between 2 and 4 minutes. This can be expressed mathematically as:

P(2 < X < 4) =\(\int_2^4 \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(2 < X < 4) = \(e^{(-2\lambda)} - e^{(-4\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(2 < X < 4) = \(e^{(-20.4)} - e^{(-40.4)}\)

P(2 < X < 4) ≈ 0.242

d. To find the probability of waiting more than 5 minutes to check out, we need to calculate the area under the exponential distribution curve to the right of 5 minutes. This can be expressed mathematically as:

P(X > 5) = \(\int_5^{ \infty} \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(X > 5) = \(e^{(-5\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(X > 5) = \(e^{(-5*0.4)}\)

P(X > 5) ≈ 0.082

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

Step-by-step explanation:

Finding Slope:

Finding Y-Intercept:

Answer:

1.  Slope = 20

2.  y-intercept = 60

Step-by-step explanation:

The slope of the line is found by dividing the change in y by the change in x or "rise over run":

\(\implies \textsf{slope}\:(m)=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{80-60}{2-1}=\dfrac{20}{1}=20\)

The slope of the line for the given situation is the fee per class. Therefore, there is a $20 fee for each class a customer at the gym attends.

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

The y-intercept is the y-value at the point at which the line intercepts the y-axis, so when x = 0.

From inspection of the given graph, y = 60 when x = 0.

\(\implies \textsf{$y$-intercept}=60\)

The y-intercept of the line for the given situation is the membership fee for the gym.  Therefore, the membership fee for the gym is $60.

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4\)

____________________________________

\( \large \tt Solution \: : \)

\( \textsf{First Inequality :} \)

\(\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4\)

\(\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4\)

\(\qquad \tt \rightarrow \: - 2x - 10 > x - 4\)

\(\qquad \tt \rightarrow \: - 10 + 4 > x + 2x\)

\(\qquad \tt \rightarrow \: - 6 > 3x\)

\(\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x\)

\(\qquad \tt \rightarrow \: - 2 > x\)

\(\qquad \tt \rightarrow \: \therefore x < - 2\)

\( \textsf{Second Inequality :} \)

\(\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)\)

\(\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24\)

\(\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x\)

\(\qquad \tt \rightarrow \: 36 < 9x\)

\(\qquad \tt \rightarrow \: \cfrac{36}{9} < x\)

\(\qquad \tt \rightarrow \: 4 < x\)

\(\qquad \tt \rightarrow \: \therefore x > 4\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Step-by-step explanation:

red

Answer:

15 ft

Step-by-step explanation:

This is another classic case of Pythagoras theorem. To start with, let's assume that the length of the ladder we're looking for is x

We're told that the height of the building the ladder is leaning on is, x - 3

Also we're told that the distance at an adjacent from the ladder is 9 ft.

If we use Pythagoras theorem, we have

x² = (x - 3)² + 9²

x² = x² - 6x + 9 + 81

On rearranging, we have

x² - x² = -6x + 90

6x = 90

x = 90 / 6

x = 15 ft

Therefore, the length of the ladder is found to be 15 ft

Answer:

D

Step-by-step explanation:

(6, 24)  this ordered pair has an x-value of 6 and a y-value of 24

The only equation, if you substitute those values into it, which works is D.

24 = 4(6)

24 = 24

The final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

To express the given description as a symbolic expression and then convert it into an exponential expression in fractional form, we'll follow these steps:

Step 1: Symbolic Expression

The description states "the eighth root of fifty-seven to the sixth degree." Let's denote this as √[57]^(1/8)^6.

Step 2: Removing Radical

To eliminate the radical (√), we can rewrite it as a fractional exponent. The numerator of the fractional exponent corresponds to the power (6) applied to the base, and the denominator corresponds to the index of the root (8).

So, the expression becomes (57^(1/8))^6.

Step 3: Simplifying Exponents

To simplify the exponent, we multiply the powers:

(57^((1/8)*6))

Simplifying further:

(57^(6/8))

Step 4: Fractional Form

The exponent 6/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(57^(3/4))

Therefore, the final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

This means that we raise 57 to the power of 3/4 to represent the original description. The fraction 3/4 indicates taking the eighth root of 57 and then raising it to the sixth power.

learn more about exponential expression here

https://brainly.com/question/26540624

#SPJ11

Given data:

The given number of names are n=5.

TEhe expression for the probability that Ross doesn't drew his

name is,

P(R')=4/5

Thus, the option (D) is correct.

Answer:

25 shaded tiles and 15 white tiles

Step-by-step explanation:

Added up these all make 40 tiles, making them the only answer. Hope this helps.

The given paragraph states that a stationery shop has been running for 10 years near campus in Jakarta.

Students like the asker often visit this store to purchase stationery, markers, rulers, and photocopiers.

The word "been" is a past participle of the verb "be." It is used to show the completion of an action in the past.

In this case, it implies that the stationery shop has been operating for the past 10 years near the campus.

The sentence can be rewritten as follows to make use of the word "been":

"The stationery shop has been providing stationery, markers, rulers, and photocopiers to students near the campus for 10 years."

To know more about the word implies visits :

https://brainly.com/question/2507296

#SPJ11

Answer:

It may take 20 to 30 seconds.

Step-by-step explanation: Hope this helped

brainliest?

The average time it took for a tablet to dissolve in water that was 22 °C in temperature was 28.3 seconds.

Any substance that, when consumed, alters the physiology or psychology of an organism qualifies as a drug.

The properties of the API (active pharmaceutical ingredient) such as

To learn more about tablet, pharmaceutical, and physiology here,

https://brainly.com/question/14551883

#SPJ2

Step-by-step explanation:

really ? there is nothing to solve. only to calculate.

you have no calculator ? even the included apps on every computer system can do that.

that is a waste of both of our time.

24 + 19 - 5 = ?

I am sure you can figure that out.

Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

To know more about competent communicators refer here:

https://brainly.com/question/18764706

#SPJ11

Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

https://brainly.com/question/36648176

#SPJ6

(i) Euler's method: At x = 0.05, y ≈ 1.05, At x = 0.1, y ≈ 1.107, At x = 0.15, y ≈ 1.174

(ii) Fourth-order Runge-Kutta method: At x = 0.05, y ≈ 1.05 , At x = 0.1, y ≈ 1.107, At x = 0.15, y ≈ 1.174

(i) Euler's Method:

Euler's method is a simple numerical method for approximating solutions to differential equations. It uses the formula:

yᵢ₊₁ = yᵢ + h * f(xᵢ, yᵢ),

where yᵢ is the approximate value of y at xᵢ and f(x, y) is the given differential equation.

Let's start by calculating the approximate solution using Euler's method.

Step size, h = 0.05

At x = 0.05:

x₀ = 0

y₀ = 1

Using the given differential equation: dy/dx = 2x + eˣʸ

We have: f(x, y) = 2x + eˣʸ

Using Euler's method:

x₁ = x₀ + h = 0 + 0.05 = 0.05

y₁ = y₀ + h * f(x₀, y₀)

   = 1 + 0.05 * (2(0) + e^(0*1))

   = 1 + 0.05 * (0 + e^0)

   = 1 + 0.05 * (0 + 1)

   = 1 + 0.05

   = 1.05

At x = 0.1:

x₂ = x₁ + h = 0.05 + 0.05 = 0.1

y₂ = y₁ + h * f(x₁, y₁)

 \(= 1.05 + 0.05 * (2(0.05) + e^(0.05*1.05)) = 1.05 + 0.05 * (0.1 + e^(0.0525))\)

   = 1.05 + 0.05 * (0.1 + 1.05383959925)

   = 1.05 + 0.05 * (1.15383959925)

   = 1.107691979963

At x = 0.15:

x₃ = x₂ + h = 0.1 + 0.05 = 0.15

y₃ = y₂ + h * f(x₂, y₂)

  \(= 1.107691979963 + 0.05 * (2(0.1) + e^(0.1*1.107691979963)) = 1.107691979963 + 0.05 * (0.2 + e^(0.1107691979963))\)

   = 1.107691979963 + 0.05 * (0.2 + 1.12281597877)

   = 1.107691979963 + 0.0661407989385

   = 1.173832778901

Approximate solution using Euler's method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

(ii) Fourth-order Runge-Kutta Method:

The fourth-order Runge-Kutta method is a more accurate numerical method

for approximating solutions to differential equations. It uses the formula:

k₁ = h * f(xᵢ, yᵢ)

k₂ = h * f(xᵢ + h/2, yᵢ + k₁/2)

k₃ = h * f(xᵢ + h/2, yᵢ + k₂/2)

k₄ = h * f(xᵢ + h, yᵢ + k₃)

yᵢ₊₁ = yᵢ + (k₁ + 2k₂ + 2k₃ + k₄)/6

Let's calculate the approximate solution using the fourth-order Runge-Kutta method.

Step size, h = 0.05

At x = 0.05:

x₀ = 0

y₀ = 1

k₁ = 0.05 * f(x₀, y₀)

   = 0.05 * (2(0) + e^(0*1))

   = 0.05 * (0 + e^0)

   = 0.05 * (0 + 1)

   = 0.05

k₂ = 0.05 * f(x₀ + 0.05/2, y₀ + k₁/2)

   = 0.05 * f(0 + 0.025, 1 + 0.025/2)

   = 0.054123529771

k₃ = 0.05 * f(x₀ + 0.05/2, y₀ + k₂/2)

   = 0.05 * f(0 + 0.025, 1 + 0.054123529771/2)

   = 0.05 * (1.08260731316)

   = 0.054130365658

k₄ = 0.05 * f(x₀ + 0.05, y₀ + k₃)

   = 0.05 * f(0 + 0.05, 1 + 0.054130365658)

   = 0.05 * (1.15381700056)

   = 0.057690850028

y₁ = y₀ + (k₁ + 2

k₂ + 2k₃ + k₄)/6

   = 1 + (0.05 + 2(0.054123529771) + 2(0.054130365658) + 0.057690850028)/6

   = 1 + (0.05 + 2(0.054123529771) + 2(0.054130365658) + 0.057690850028)/6

   = 1.04999993086

At x = 0.1:

x₁ = x₀ + h = 0 + 0.05 = 0.05

k₁ = 0.05 * f(x₀, y₁)

   = 0.05 * (2(0.05) + e^(0.05*1.04999993086))

   = 0.05 * (1.15382091332)

   = 0.057691045666

k₂ = 0.05 * f(x₀ + 0.05/2, y₁ + k₁/2)

   = 0.05 * f(0 + 0.025, 1.04999993086 + 0.057691045666/2)

   = 0.05 * f(0.025, 1.076845501196)

   = 0.05 * (1.08293606756)

   = 0.054146803378

k₃ = 0.05 * f(x₀ + 0.05/2, y₁ + k₂/2)

   = 0.05 * f(0 + 0.025, 1.04999993086 + 0.054146803378/2)

   = 0.05 * (0.05 + 1.03297648754)

   = 0.05 * (1.08297648754)

   = 0.054148824377

k₄ = 0.05 * f(x₀ + 0.05, y₁ + k₃)

   = 0.05 * f(0 + 0.05, 1.04999993086 + 0.054148824377)

   = 0.05 * f(0.05, 1.104148755237)

   = 0.

05 * (2(0.05) + e^(0.05*1.104148755237))

   = 0.05 * (1.15636272702)

   = 0.057818136351

y₂ = y₁ + (k₁ + 2k₂ + 2k₃ + k₄)/6

   = 1.04999993086 + (0.057691045666 + 2(0.054146803378) + 2(0.054148824377) + 0.057818136351)/6

   = 1.04999993086 + (0.057691045666 + 2(0.054146803378) + 2(0.054148824377) + 0.057818136351)/6

   = 1.10730401829

At x = 0.15:

x₂ = x₁ + h = 0.1 + 0.05 = 0.15

k₁ = 0.05 * f(x₁, y₂)

   = 0.05 * (2(0.1) + e^(0.1*1.10730401829))

   = 0.066134153561

k₂ = 0.05 * f(x₁ + 0.05/2, y₂ + k₁/2)

   = 0.05 * f(0.1 + 0.025, 1.10730401829 + 0.066134153561/2)

   = 0.05 * (1.40252551209)

   = 0.070126275604

k₃ = 0.05 * f(x₁ + 0.05/2, y₂ + k₂/2)

   = 0.05 * f(0.1 + 0.025, 1.10730401829 + 0.070126275604/2)

   = 0.05 * f(0.125, 1.13726868037)

   = 0.05 * (1.40260973286)

   = 0

.070130486643

k₄ = 0.05 * f(x₁ + 0.05, y₂ + k₃)

   = 0.05 * f(0.1 + 0.05, 1.10730401829 + 0.070130486643)

   = 0.05 * (1.49307437508)

   = 0.074653718754

y₃ = y₂ + (k₁ + 2k₂ + 2k₃ + k₄)/6

   = 1.10730401829 + (0.066134153561 + 2(0.070126275604) + 2(0.070130486643) + 0.074653718754)/6

   = 1.17379707103

Approximate solution using the fourth-order Runge-Kutta method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

Therefore, the approximate solutions using Euler's method and the fourth-order Runge-Kutta method at x = 0.05, 0.1, and 0.15 are as follows:

Euler's method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

Fourth-order Runge-Kutta method:

At x = 0.05, y ≈ 1.05

At x = 0.1, y ≈ 1.107

At x = 0.15, y ≈ 1.174

Learn more about Euler's method here:

https://brainly.com/question/32585329

#SPJ11