I need to know what mistakes he made (if any)

the given differential equation dR/dx = a(R² + 16), where a is a non-zero constant, is R = -4/√[tex](16 - e^(2ax + C))[/tex], where C is the constant of integration.

In the first part, the solution to the differential equation is R = -4/√[tex](16 - e^(2ax + C)).[/tex]

In the second part, let's solve the differential equation step by step. We start by separating variables:

dR/(R² + 16) = a dx.

Next, we integrate both sides:

∫(1/(R² + 16)) dR = ∫a dx.

To integrate the left side, we can use a substitution. Let u = R² + 16, then du = 2R dR. This gives us:

(1/2) ∫(1/u) du = ∫a dx.

Simplifying the left side and integrating, we have:

(1/2) ln|u| = ax + C.

Substituting back for u and rearranging, we get:

ln|R² + 16| = 2ax + 2C.

Taking the exponential of both sides, we have:

|R² + 16| = [tex]e^(2ax + 2C).[/tex]

Considering the absolute value, we can rewrite it as:

R² + 16 = [tex]e^(2ax + 2C).[/tex]

Solving for R, we get:

R = ±√(e^(2ax + 2C) - 16).

Simplifying further:

R = ±√(e^(2ax + C) - 16).

Finally, we can rewrite it as:

R = -4/√(16 - e^(2ax + C)).

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The calculated value of the current price of the stock is $75

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

Growth = 5%

Required return = 12%

Last dividend payment = $5

The dividend is calculated as

D = Last dividend payment * (1 + Growth )

So, we have

D = 5 * (1 + 5%)

Evaluate

D = 5.25

the current price of the stock is calculated as

Price = D/(r - g)

So, we have

Price = 5.25/(12% - 5%)

Evaluate

Price = 75

Hence, the current price of the stock is $75

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Answer:

A prediction of 177 people.

Step-by-step explanation:

6x412=2472

2472/14=176.571428571

Rounded to nearest whole person=177

Please mark me as brainliest.

Answer:

-5/4 is the slope of the line.

Answer: 1176

Step-by-step explanation: 7 times as big is an ambiguous term; it could mean that each side is 7 times larger, or that the shape as a whole is made 7 times larger. We'll assume that each side is made larger, because that is typically the type of question asked. The area is given as base times height, and obviously, if you dilate the non-base side by 7, the height will also become 7, because those two lines from a triangle with the third side being the base extended. I wish I could draw you a diagram but i can;t. Either way, think of it as a square, and if we dilate each side by 7, then we have lx7xwx7=Area, which is lw*49=49 times the given area, which is 24; 24*49=1176

do it in your own answer

Answer:

7/17

Step-by-step explanation:

you add the number of students which is 34. Then you take the number of boys and put it over 34 which would be 14/34. when you reduce it the answer will be 7/17.

let me know if this helps!

There are a total of 9 possible sums. Suppose, the cards in the first set are 4, 5, and 6.

Similarly, the cards in the second set are 5, 6, and 7. A total of nine cards are there. If we choose one card from the first set and one card from the second set, then we get a total of nine possible pairs.

Hence, the sum of these pairs can be 4 + 5, 4 + 6, 4 + 7, 5 + 5, 5 + 6, 5 + 7, 6 + 5, 6 + 6, and 6 + 7. Therefore, there are nine possible sums possible.

Additionally, there are three possibilities in the first set (4, 5, and 6) and three possibilities in the second set (5, 6, and 7).

This means that there are 3 × 3 = 9 possible pairs of cards that we can choose, so there are 9 possible sums.We can list all of these sums as follows:4 + 5 = 96 + 5 = 116 + 5 = 116 + 6 = 127 + 5 = 127 + 6 = 137 + 7 = 14. Therefore, there are a total of 9 possible sums.

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Answer:

Radius = r

Diameter = 2r

Circumference = 2πr

Area = πr²

a diameter of a circle is a line drawn through the center of a circle.

Answer:

C) -6/12

Step-by-step explanation:

Sana nakatulong

Answer:

Length is 138 ft, area is 412 ft

Step-by-step explanation:

The length is determined by the perimeter, so add both side of the perimeter together, and you have your length. Area is determined by perimeter + Length, to add both sides of perimeter and length and you get 412 ft.

Based on the given statistics, we will shape each correlation to the corresponding scatterplot as follows:

13.True or False: r = 0.49 → (2)

14.True or False: r = -0.48 → (4)

15.True or False: r = -0.03 → (3)

16.True or False: r = -0.85 → (1)

Based on the given records, we need to match each correlation fee to the corresponding scatterplot. Let's analyze every correlation and its corresponding scatterplot in more detail:

13.True or False: r = 0.49 → (2)

A correlation coefficient of 0.49 shows a tremendous correlation among the variables. This means that as one variable will increase, the alternative variable tends to grow as nicely, albeit not flawlessly. In the scatterplot categorized as (2), we'd assume to look at a trendy upward fashion wherein the factors are quite scattered around the road of satisfactory fit.

14.True or False: r = -0.48 → (2)

A correlation coefficient of -0.48 indicates a bad correlation between the variables. This manner that as one variable increases, the opposite variable has a tendency to lower. In the scatterplot labeled as (2), we'd expect to see a standard downward fashion wherein the points are rather scattered around the line of fine match.

15.True or False: r = -0.03 → (4)

A correlation coefficient of -0.03 shows a very weak terrible correlation between the variables. This method that there is almost no relationship between the variables. In the scatterplot categorized as (four), we would count on seeing factors scattered randomly, with no discernible pattern or fashion.

16. True or False: r = -0.85 → (1)

A correlation coefficient of -0.85 shows a sturdy poor correlation between the variables. This method that as one variable increases, the other variable has a tendency to decrease substantially. In the scatterplot labeled as (1), we might count on to peer a clear downward trend in which the factors are tightly clustered around the road of the first-rate match.

By analyzing the strengths and instructions of the correlations, we can suit each correlation value to its corresponding scatterplot as follows:

13. True or False: r = 0.49 → (2)

14.True or False: r = -0.48 → (2)

15.True or False: r = -0.03 → (4)

16.True or False: r = -0.85 → (1)

Please notice that scatterplots provide visible representations of statistics and relationships between variables, and the interpretations might also vary relying on the context and the statistics being analyzed.

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Answer:

A VR car game and an iphone

Step-by-step explanation:

:)

Answer:

A) (2,5)

Step-by-step explanation:

longest side is between points (1,4) and (3,6)

so midpoint is ((1+3)/2), ((4+6)/2), which equals (2, 5)

The probabilities of:

A: Getting a number less than 4 on the dice is 1/2

B: Getting tails (T) on the coin is 1/2

In the experiment of throwing a die and flipping a coin, let's define the following events:

A: Getting a number less than 4 on the dice (possible outcomes: 1, 2, 3).

B: Getting tails (T) on the coin.

To determine the probabilities of these events, we need to consider the number of favorable outcomes and the total number of possible outcomes.

For event A:

Number of favorable outcomes: 3 (numbers 1, 2, 3)

Total number of possible outcomes on the dice: 6 (numbers 1 to 6)

So, P(A) = favorable outcomes / total outcomes = 3/6 = 1/2

For event B:

Number of favorable outcomes: 1 (tails T)

Total number of possible outcomes on the coin: 2 (heads H, tails T)

So, P(B) = favorable outcomes / total outcomes = 1/2

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The main cause of tides is the moon's gravitational pull.

Hope it helps you...

Answered by Benjemin ☺️

✅

Answer:

Yes, that equation is right

Step-by-step explanation:

I don’t know why this is a question, however

Answer:

0 = -3

Step-by-step explanation:

Distribution

− 2 ( 3 − 1 ) = − 6 − 1

− 6 + 2 = − 6 − 1

Subraction (2 from both sides)

− 6 + 2 = − 6 − 1

− 6 + 2 − 2 = − 6 − 1 − 2

Simplify

− 6 = − 6 − 3

Add 6 to both sides

− 6 +6 = − 6 − 3+6

Combine like terms

− 6 +6 = − 6 − 3+6

0=-(6)-3+(6)

0=-3

If dimensions of the globe that is 16 inches in diameter were reduced by half, then its volume would be [tex]$V= 267.9 \text{ in}^{3}$[/tex]

The volume of an object is a measure of the amount of space occupied by that object.

Here given that originally diameter was 16 inches but then dimensions of the globe was reduced by half

The new diameter is equal to

[tex]$$D=16 / 2=8 \mathrm{in}$$[/tex]

Hence radius is equal to

[tex]$$r=8 / 2=4 \mathrm{in}$$[/tex]

The volume of the reduced globe is

[tex]$V=\frac{4}{3}(\pi)(r)^{3}$[/tex]

[tex]$V=\frac{4}{3}(3.14)(4)^{3}$\\[/tex]

[tex]$V= 267.9 \text{ in}^{3}$[/tex]

If dimensions of the globe that is 16 inches in diameter were reduced by half, then its volume would be [tex]$V= 267.9 \text{ in}^{3}$[/tex]

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Answer:

267.9 in3

Step-by-step explanation:

I took the test and got it right!

Answer:

Step-by-step explanation:

-4m≥96

-m≥24

m≤-24

The Laplace transformation in the given function is = 5 - 8e⁻⁷ˣ/ x

Rewrite f in terms of the unit step function:

f(t) = { y = 5 for 0 ≤ t ≤ 7

    = { x = - 3 t > 7

f(t) = 5{u(t) -u(t -7) - 3u (t -7)}

     = 5u(t) - 8u (t-7)

Recall the time-shifting property of the Laplace transform:

L I u(t - c)f(t -c) I

= e⁻ᵃˣ L[f(t)]

and the Laplace transform of a constant function,

L(K) = k/a

So we have

L{f(t)} = 5u(t) - 8u (t-7)

       = 5 L[1] - 8e⁻⁷ˣ

       = 5 - 8e⁻⁷ˣ/ x

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The given question is incomplete, the complete question is below

Write the following function using unit step functions and then find its Laplace transform:

f(t) = { y = 5 for 0 ≤ t ≤ 7

    = { x = - 3 t > 7

Answer:

The height is 6.3

Step-by-step explanation:

Pythagorean Theorm: a² + b² = c²

5² + b² = 8²

25 + b² = 64

b² = 39

b = 6.2449979984

The given system y(0) = x(t)sin(wt) is linear, time-invariant, and causal. It satisfies the properties of superposition and homogeneity, exhibits the same time shift in the output as in the input, and the output at any given time depends only on the current and past values of the input.

a) Linearity: A system is linear if it satisfies the properties of superposition and homogeneity. In this case, the system is linear because it satisfies both properties. The input signal x(t) can be scaled or added together, and the corresponding output y(t) will also be scaled or added accordingly.

b) Time-invariance: A system is time-invariant if a time shift in the input signal results in the same time shift in the output signal. In this case, the system is time-invariant because shifting the input signal x(t) by a time delay will result in the same time delay in the output signal y(t).

c) Causality: A system is causal if the output at any given time depends only on the current and past values of the input. In this case, the system is causal because the output y(t) at any time t depends only on the values of the input x(t) for t' ≤ t.

In conclusion, the given system y(0) = x(t)sin(wt) is linear, time-invariant, and causal based on the justification provided above.

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Answer:

10 pages are in the page if im correct

Answer:

Step-by-step explanation:

hope it helps make brainliest

Answer:

42 minutes

Step-by-step explanation:

18/3= 6

6*7=42

Given z-score is z = 2.58 and the null hypothesis isH0: p = 0.85, where p is the true proportion, and we need to find the p-value.

We know that for a two-tailed test, the p-value is the probability that a z-score is greater than or equal to the absolute value of the calculated z-score or less than or equal to its negative value. So, the p-value for a two-tailed test is: p-value = P(z ≥ 2.58) + P(z ≤ -2.58)  ..............(1) Here, z = 2.58 represents the upper critical value, and the negative of it is the lower critical value (z = -2.58)

As the given hypothesis is a two-tailed test, we need to calculate the probabilities for both critical values. From the standard normal distribution table, the probabilities for these critical values are:

P(z ≥ 2.58) = 0.0049 (approx.)  P(z ≤ -2.58) = 0.0049 (approx.)

Substituting these values in equation (1), we get: p- value = 0.0049 + 0.0049 p-value = 0.0098Hence, the p-value is 0.0098 (approx.)

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Answer:

6, 0, 2

Step-by-step explanation:

Divide y by x.

Answer 10x8=80+3

Step-by-step explanation:

i.d.k 83?????

Answer:

Step-by-step explanation:

(a) The center of the circle is also the circumcenter of the triangle PQR.

Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:

Sum of the three angles is 360° as cover the full circle.

Each angle measure is:

(b) Each side is 16 cm and the radius is 12 cm.

The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.

The segment MO is:

ΔXYZ is isosceles with:

(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude

Find h:

(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.

Find ∠ZXM:

Find ∠ZOM:

Find the measure of the radius:

Find the measure of the diameter: