Find a possible solution to the equation cos(x+2)=sin(3x)


A.

x=0. 5 degrees

B.

x=1 degree

C.

x=22 degrees

D.

x=44 degrees

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

The equation for the tangent to the graph of y = arcsin(x/2) at the origin is y = x. This means that for any given x-value, the corresponding y-value is equal to that x-value, creating a line with a slope of 1. This line is tangent to the graph of y = arcsin(x/2) at the origin, which is (0, 0).

To find the equation for the tangent to the graph of y = arcsin(x/2) at the origin, we must first find the slope at the origin. We can do this by taking the derivative of the function y = arcsin(x/2) with respect to x.

The derivative of

y = arcsin(x/2) with respect to x is y' = (1/2)cos(x/2).

At the origin, x = 0, so the slope of the tangent at the origin is

y' = (1/2)cos(0) = 1.

Therefore, the equation for the tangent to the graph of

y = arcsin(x/2) at the origin is y = x, which has a slope of 1.

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The given expression is ∫∫(1-x^2)(62-y^2)^2 dxdy over the region R = {(x,y) | x^2 + y^2 ≤ 1}.

To evaluate this expression, we can use polar coordinates since the region R is a circle of radius 1 centered at the origin. So, we can write x = rcosθ and y = rsinθ, and the limits of integration become 0 to 2π for θ and 0 to 1 for r. Substituting these values, we get the integral expression as ∫0^2π ∫0^1 (1-r^2cos^2θ)(62-r^2sin^2θ)^2 rdrdθ.

Next, we can simplify the integrand by expanding the square of (62-r^2sin^2θ) and using trigonometric identities. This simplification leads to the expression ∫0^2π ∫0^1 (3844r^2 - 124r^4 + r^6)cos^2θsin^4θ rdrdθ.

Integrating this expression with respect to r and θ, we get the final result as 205π/128. Therefore, the value of the given expression is 205π/128.

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Answer:

x = 29

Step-by-step explanation:

\(2x - 2 + x + 5 = 90\)

\(3x + 3 = 90\)

\(3x = 87\)

\(x = 29\)

The solution of the given equation is y = y = e^(6x -∞) ,y = e^(6x)

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

\(I = e^(int (6 dy/6y)) = e^(ln y)\)

Multiplying both sides of the equation by I:

\(Iy' = 6y5/6 ⇒ dy/y = 6/6 dy ⇒ ln y = 6x + c\)

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

\(0 = e^(6(0) + c) ⇒ c = -∞\)

Therefore, the solution of the given equation is:

y = e^(6x -∞)

Solution 2:

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

\(I = e^(int (6 dy/6y)) = e^(ln y)\)

Multiplying both sides of the equation by I:

Iy' = 6y5/6

⇒ dy/y = 6/6 dy

⇒ ln y = 6x + c

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

0 = e^(6(0) + c)

⇒ c = 0

Therefore, the solution of the given equation is:

y = e^(6x)

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Answer:

13%

Step-by-step explanation:

the area of the flag is 4x6=24 the circle has an area of 3.14.  3.14/24 is 13%

The  percent of the flag is gold should be considered as the 13%.

Since

In a 4-by-6-foot Colorado state flag, the gold-colored disk has a 1-foot radius.

So here the area of the flag should be

= (4) (6)

= 24

Now the percentage be like

= 3.14/24

= 13%

hence, The  percent of the flag is gold should be considered as the 13%.

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After performing the test, the calculated p-value was 0.062. Since the p-value is greater than the significance level of 0.10 (α), the decision is to fail to reject the null hypothesis.

The χ² goodness of fit test was conducted to determine if the proportions of M&M colors in a selected bag match the claimed distribution by Mars Inc. The observed counts of each color were compared to the expected counts based on the claimed percentages.

After performing the test, the calculated p-value was 0.062. Since the p-value is greater than the significance level of 0.10 (α), the decision is to fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the proportion of M&Ms in the selected bag differs significantly from what Mars Inc. claims.

The χ² goodness of fit test is used to assess whether observed data follows an expected distribution. In this case, the expected distribution is based on the claimed proportions provided by Mars Inc.

The observed counts of M&M colors (Brown: 21, Red: 22, Yellow: 22, Orange: 12, Green: 17, Blue: 14) were compared to the expected counts derived from the claimed percentages (Brown: 30%, Red: 20%, Yellow: 20%, Orange: 10%, Green: 10%, Blue: 10%).

The χ² test statistic is calculated by summing the squared differences between observed and expected counts, divided by the expected counts. The degrees of freedom for this test are determined by the number of categories minus one (df = 6 - 1 = 5).

After calculating the χ² test statistic, the corresponding p-value is obtained. The p-value represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis (H0) is true. In this case, the null hypothesis is that the proportions of M&M colors in the selected bag match the claimed distribution.

Comparing the calculated p-value (0.062) to the predetermined significance level (α = 0.10), we find that the p-value is greater than α. Therefore, there is insufficient evidence to reject the null hypothesis. Consequently, the decision is to fail to reject the null hypothesis. This means that the observed proportions of M&M colors in the selected bag do not significantly differ from what Mars Inc. claims.

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Susan can make 8 distinct arrangements, according to the question.

Generally speaking, an arrangement of objects is just a collection of them. A combination (order is ignored) or permutation is used to determine the number of "arrangements" of the components (order is significant).

The number of possible arrangements or orders for a set of items is known as an arrangement number, also known as a permutation number or just a permutation.

The following formula calculates the number of combinations of n objects taken r at a time: C(n,r)=n! (n−r)! r!

According to the question,

We have the given information:

6 Tulips, 6 Roses, and 8 Daisies

Total number of plants to be arranged= 20

It means 20! ways

Dividing it by 6! 6! and 8! ways,

Total number of ways= 20!/6!6!8!

                                   = 116396280

Therefore, the total number of ways 116396280.

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The probability that the number of homicide deaths for a randomly selected day is:

a) 0: 0.18,

b) 1: 0.35,

c) 2: 0.27

The Poisson distribution is used to simulate the likelihood that a certain number of events will occur within a predetermined window of time or space.

In this instance, the Poisson distribution can be used to simulate the number of homicide deaths that occurred in Richmond, Virginia over the course of a year.

The Poisson distribution can be used to determine the likelihood of 0, 1, and 2 homicides happening on any given day.

One homicide occurs on a randomly chosen day with a 0.18 percent chance, one homicide occurs on a randomly chosen day with a 0.35 percent chance, and two homicides occur on a randomly selected day with a 0.27 percent chance.

Complete Question:

In one year, there were 116 homicide deaths in Richmond, Virginia. Using the Poisson distribution, find the probability that the number of homicide deaths for a randomly selected day is:

a) 0

b) 1

c) 2

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Answer:

1

Step-by-step explanation:

Hope this helps!

Lmk if you have any questions!

Have a great day! :)

Answer:

1

Step-by-step explanation:

the y intercept is where the line crosses the y = 0 mark and it crosses it at (1,0) so 1 would be your answer

The domain of f is the interval [-37, ∞).

For a function to have an inverse, it must be one-to-one, which means that it must pass the horizontal line test, i.e., each horizontal line should intersect the graph of the function at most once.

The derivative of the function is:

\(f'(x) = 6 + (1/2√(x+37))\)

f'(x) is always positive because 6 is positive and the square root is positive, so f(x) is an increasing function. This means that f(x) is one-to-one and therefore has an inverse.

To determine the largest interval on which f has an inverse, we need to find the domain of f. The square root can only take non-negative values, so we must have x+37 ≥ 0, which means x ≥ -37.

Therefore, the domain of f is the interval [-37, ∞).

Since f is increasing over this interval, its inverse will also be increasing, and the largest interval on which f has an inverse is [-37, ∞).

The proper question is "Let f(x)=6x+√(x+37)Choose the form of the largest interval on which f has an inverse and enter the value(s) of the endpoint(s) in the appropriate blanks. Then find (f−1)′(0)

Endpoints(a ,b)"

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

Answer:

\(\boxed{\tt v < 6.8}\)

Step-by-step explanation:

\(\tt 0.5v+0.06 < 3.46\)

Multiply both sides by 100:-

\(\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100\)

\(\tt 50v+6 < 346\)

Subtract 6 from both sides:-

\(\tt 50v < 340\)

Divide both sides by 50:-

\(\tt \cfrac{50v}{50} < \cfrac{340}{50}\)

\(\tt v < \cfrac{34}{5}\)

Or

\(\tt v < 6.8\)

Therefore, your answer is v < 6.8!!! :)

______________________

Hope this helps!

Have a great day!

Answer:

the answer is b

Step-by-step explanation:

9/10 minus 3/5 is 0.3. 0.3 as a fraction is 3/10

Answer: the answer is b which is 3 over 10

Step-by-step explanation: as a decimal it us 0.3 which is the same as 3 over 10 . Hope it is correct . Please give brainliest .Thanks .

The expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

g  = 2hm

To make m as the subject and solve it:

Divide the above expression by 2h on both sides:

g/2h = m  or

m = g/2h

Thus, the expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.

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Answer'

c

Step-by-step explanation:

The National Association of realtors reported that 26% of home buyers in the state of Florida are foreigners. When testing the validity of this report, a type I error would occur if it was concluded that the proportion of foreign buyers was not equal to 26% when in realty, the proportion is equal to 26%.

Hence the correct option is (B).

We would commit a Type I error if we rejected the null hypothesis even though it is true. Therefore, in this instance, Type I error would have occurred if we determined that the percentage of international buyers was less than 26% while in fact it was equal to 26%.

The correct choice is "not equal to 26% when in realty, the proportion is equal to 26%"

Hence the correct choice will be given by option (B).

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The question is incomplete. The correct question will be

Answer:

Step-by-step explanation:

Sp of an article= Rs 2300

profit%=15%

let Cost Price of an article be X

SP=CP+PROFIT %*CP

2300=X+15/100*X

2300=100X+15X/100

2300*100=115X

230000/115=X

2000=X

Therefore cost price of an article is Rs 2000.

Answer:

y= x+ 4

Step-by-step explanation:

use y= mx+b where m is the slope and y is the y intercept

in this case the slope is one and y intercept is four

The eigenvector for λ1 is (x1 x2) = ((√3 - 1)x2 x2), where x2 is a free parameter.

To compute \(e^A^t\) for the given coefficient matrices, we need to diagonalize the matrices and find the eigenvalues and eigenvectors.

Once we have the eigenvalues and eigenvectors, we can compute \(e^A^t\) using the formula \(e^At = P * diag(e^λt) * P^(-1)\), where P is the matrix of eigenvectors and diag(e^λt) is a diagonal matrix with the eigenvalues exponentiated by t.

Let's start with the first system:

X' = (4 3 -4 -4)X

To find the eigenvalues and eigenvectors, we solve the equation (A - λI)X = 0, where A is the coefficient matrix, λ is the eigenvalue, I is the identity matrix, and X is the eigenvector.

For the matrix A = (4 3 -4 -4), we have:

(A - λI)X = 0

(4 3 -4 -4 - λ)(x1 x2) = 0

Expanding the determinant, we get:

(4-λ)(-4-λ) - (3)(-4) = 0

λ^2 - 4λ + 4 - 12 = 0

λ^2 - 4λ - 8 = 0

Solving this quadratic equation, we find the eigenvalues:

λ1 = 2 + 2√3 ≈ 5.464

λ2 = 2 - 2√3 ≈ 0.536

Now, for each eigenvalue, we need to find the corresponding eigenvector by solving (A - λI)X = 0.

For λ1 = 2 + 2√3, we have:

(2 3 -4 -4 - (2 + 2√3))(x1 x2) = 0

(-2 - 2√3 3 -4)(x1 x2) = 0

Solving this system of equations, we find the eigenvector:

x1 = (√3 - 1)x2

Similarly, for λ2 = 2 - 2√3, we find the eigenvector:

x1 = (-√3 - 1)x2

Now that we have the eigenvalues and eigenvectors, we can compute \(e^A^t\) using the formula mentioned earlier. However, since the specific values of A are not provided, I cannot proceed with the computation.

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The solution for given equations are: z = 4, b = -12, w = 5, c = -11

An equation is a mathematical statement that expresses the equality of two expressions.

Variables are symbols or letters used to represent unknown values in equations.

To solve for a variable, one must first isolate the variable by performing the same operations on both sides of the equation until the variable is alone on one side of the equation.

For example, if the equation is 2x + 4 = 10, the first step would be subtracting 4 from both sides of the equation to get 2x = 6. The next step would be to divide both sides of the equation by 2 to get x = 3. This is how one would solve for the variable in this equation.

According to question:-

A. 3(7z-6)=-(-18z+6)

21z - 18 = 18z - 6

3z = 12

z = 4

B. -8b+2(-5b-2)=212

-8b - 10b - 4 = 212

-18b - 4 = 212

b = -12

C. 4/5w+5 = 1/5w+8

4/5w-1/5w = 8-5

3/5w = 3

w = 5

D. (-c-8)-(7c-6)= 18c+284

-c-8-7c+6 = 18c + 284

18c + 8c = -2-284

26c = -286

c = -11

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Answer:

D

Step-by-step explanation:

You have 2 5 12 13 right triangles.

x = 2 * 5

x = 10

Answer:

D. \(x=10\)

Step-by-step explanation:

You can use the Pythagorean Theorem, \(a^2+b^2=c^2\), where a and b are the legs and c is the hypotenuse.

\(12^2+b^2=13^2\\144+b^2=169\)

Subtract 144 from both sides

\(b^2=25\)

Square root both sides

\(b=5\)

\(2b=x\\b=5\\x=10\)

At an angle of 270 degrees (or 3π/2 radians) on a circle with a radius of 2 and center at (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

To find the x and y coordinates at an angle of 270 degrees (or 3π/2 in radian measure) on a circle of radius 2 with center (0, 0), we can use the trigonometric definitions of sine and cosine.

The x-coordinate (x-value) represents the horizontal position on the circle, while the y-coordinate (y-value) represents the vertical position.

For a point on the unit circle (circle with radius 1) at a given angle θ, the x-coordinate is given by cos(θ) and the y-coordinate is given by sin(θ).

In this case, the circle has a radius of 2, so we need to multiply the cosine and sine values by 2 to get the x and y coordinates, respectively.

Using the angle 270 degrees (or 3π/2 in radian measure):

x-coordinate = 2 * cos(3π/2)

y-coordinate = 2 * sin(3π/2)

Evaluating these expressions:

x-coordinate = 2 * cos(3π/2) = 2 * 0 = 0

y-coordinate = 2 * sin(3π/2) = 2 * (-1) = -2

Therefore, at an angle of 270 degrees (or 3π/2 radians) on the circle of radius 2 with center (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

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Answer:

y = 4 x + 24 i think thats the answer if not im sorry

Step-by-step explanation:

The total cost of the tent is 409.86

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

explanation:

230×0.65=149.50

230+149.50=379.50×.08=30.36

379.50+30.36=409.86

(Hope this helps :) )

============================================================

Explanation:

65% = 65/100 = 0.65

65% of 230 = 0.65*230 = 149.50

When applying markup, the store increases the cost by $149.50 to get the retail price of 230+149.50 = 379.50, which is the price the customer sees. This is the price before tax.

As a shortcut, we can say 1.65*230 = 379.50 because 1.65 = 1 + 0.65 = 100% + 65%. So 1.65 effectively means "increase the value by 65%"

Similarly, the multiplier 1.08 means "increase by 8%". The cost after tax would be 1.08*379.50 = 409.86 which is the answer

----------

As an even quicker shortcut, we can do both increases at once to say:

1.65*1.08*230 = 409.86

The order of multiplication doesn't matter. The two multipliers 1.65 and 1.08 can be combined into 1.65*1.08 = 1.782 which represents a 78.2% increase overall. After the mark up and tax are considered, the jump from $230 to $409.86 is 78.2%

We can apply the percent change formula to confirm this

A = old value = 230

B = new value = 409.86

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (409.86-230)/230 ] * 100%

C = 0.782 * 100%

C = 78.2%

So it might be tempting to say 65% + 8% = 73%, but as you can see above, that calculation is not true.

Answer:

yes

Step-by-step explanation:

because they both are equal.

The false statement is: "The researchers would come to the conclusion that the programme was successful if they used a significance level of 1%."

What is significance level?

A significance level, denoted by α, is the threshold chosen by researchers to determine the level of evidence required to reject the null hypothesis. It represents the maximum acceptable probability of making a Type I error (incorrectly rejecting the null hypothesis when it is true).

In this case, the given p-value is 0.003. If the null hypothesis is true, the p-value represents the likelihood of obtaining a test statistic that is equally extreme to or more extreme than the one that was observed. It offers proof that the null hypothesis is false.

We can conclude that there is strong evidence to reject the null hypothesis in favour of the alternative hypothesis because the p-value is 0.003, which is lower than any often used significance level like 0.05 or 0.01. Thus, if the researchers apply a 5% level of significance, they would draw the conclusion that the programme was successful.

However, if the researchers use a significance level of 1%, they would require even stronger evidence to reject the null hypothesis. Since the p-value of 0.003 is greater than 0.01, they would not be able to reject the null hypothesis at the 1% significance level and would not conclude that the program was effective.

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Answer:

Here x=20 so

15+20=35

18+80=98

47

35+98+47=180