Solve the following boundary value problem. if there is no solution, write none for your answer. y″−3y′=0; y(0)=2−2e3; y(1)=0

Answer:

m = -3

Step-by-step explanation:

The formula for slope is \(m=\frac{y2-y1}{x2-x1}\)

So use the x's and y's from the given points to solve for m

(3, -4) (1, 2)

\(m=\frac{2-(-4)}{1-3}\)

\(m= \frac{6}{-2}\)

\(m=-3\)

Given:

The equation is

\(2(x+14)=40\)

To find:

The solution of the given equation.

Solution:

We have,

\(2(x+14)=40\)

Using distributive property, we get

\(2(x)+2(14)=40\)

\(2x+28=40\)

Subtracting 28 from both sides.

\(2x=40-28\)

\(2x=12\)

On dividing both sides by 2, we get

\(x=6\)

Therefore, the solution of the given equation is x = 6.

Answer:

y = 2

Step-by-step explanation:

Using calculator, the value of  the angle 5 sin (20 +10°) -4 = 0​ where 0 <x<90 is 17.5 degrees

You should understand that the sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle

The given angle is 5 sin (20 +10°) -4 = 0

To find the angle, first open the bracket to have

5sin(30) - 4 = 0

Collecting like terms to have

5 sin 30 = 4

Dividing both sides by 5 we have

5 sin30/5 = 4/5

This means that sin30 = 0.8

⇒sin30 - 0.8 = 0

⇒ 0.5 -0.8 = 0

-0.3

Therefore sin⁻-0.3 = 17.5⁰

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The Latin square that is balanced for residual effects is Latin Square 1.

To determine whether a Latin square is balanced for residual effects, we need to check if the order effects and carryover effects are equal across all rows and columns.

In Latin Square 1:

Order effects: Each treatment appears once in each row and column. Therefore, there are no order effects.

Carryover effects: Each treatment follows every other treatment once in each row and column. Therefore, there are no carryover effects.

Since there are no order or carryover effects in Latin Square 1, it is balanced for residual effects.

In Latin Square 2:

Order effects: Treatment A appears twice in row 1, while treatment D appears twice in row 2. Therefore, there are order effects.

Carryover effects: Treatment C follows treatment A twice in row 3, but only once in row 2. Therefore, there are carryover effects.

Since there are order and carryover effects in Latin Square 2, it is not balanced for residual effects.

Therefore, the Latin square that is balanced for residual effects is Latin Square 1.

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A control system where the output variable is compared with an input parameter, and their difference is used to drive the output is called closed-loop control.

In closed-loop control, the output of the system is constantly compared to a desired setpoint, and any differences between the two are used to adjust the system's behavior to reduce or eliminate the error. This type of control system is also known as feedback control, and it is widely used in many different applications, including process control, robotics, and automatic temperature regulation. In contrast, open-loop control does not have feedback or error correction, and the output of the system is determined solely by the input parameters, without regard to the actual output of the system.

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You will need amount of 1.5 cups of butter if you plan to use 3 cups of flour in your recipe.

To calculate how much butter is needed for 3 cups of flour in a recipe, start by identifying that the recipe requires a ratio of 1 cup of butter for every 2 cups of flour. To get the amount of butter needed for 3 cups of flour, multiply 1 cup of butter by 1.5. This will give you 1.5 cups of butter, which is the amount needed for 3 cups of flour.  Therefore, you will need 1.5 cups of butter if you plan to use 3 cups of flour in your recipe.  To ensure accuracy, it is recommended to measure the ingredients carefully and double check your calculations before proceeding.

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The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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Answer:

-284

Step-by-step explanation:

If it's not im truly sorry

Answer:

8

Step-by-step explanation:

First, you want to substitute your a, b, c, and d, which you would get 3(2) + 3(8) divided by sign 2 - 2(5). According to PEMDAS, we will multiply our numbers in the parenthesis with the outside number next to it, so you should have gotten 6 + 24 divided by sign 2 - 10. Next, you will divided 24 by 2 to get 12, so the equation will now look like 6 + 12 - 10. Finally, just work it out 6 + 12 is 18 minus 10, is 8. I hope this helps :)

Answer:

Answer is 18

Step-by-step explanation:

a2+3b/c-2d

when

a=3

b=8

c=2

d=5

2*3+3*8/2-2*5

6+24/2-10

6+12-10

18-10

8. answer

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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The law of sines is solved for the triangle and C =28.7 units

Given data ,

Let the triangle be represented as ABC

Now , the measures of angles and sides are given as

Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

c / sin ( 60 )° = 14 / sin ( 25 )°

Multiply by sin 60° on both sides , we get

c = 0.86602540378 ( 14 / 0.42261826174 )

On simplifying , we get

c = 28.688 units

Hence , the measure of c of triangle is c = 28.7 units

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Answer:

The answer is $1,215

Step-by-step explanation:

I did $32,000 divided by 12 (months on an year) and got $2,700 per month, now we just do 0.45 x $2,700 and thats how I got the answer!

Answer:

29.85°

Step-by-step explanation:

To convert 29° 51' to decimal degrees, we need to convert the minutes (') to decimal form.

Since 1° is equal to 60 minutes ('), we divide the minutes by 60 to get the decimal representation.

29° 51' = 29 + 51/60 = 29.85°

Rounded to the nearest hundredth, 29° 51' is approximately equal to 29.85°.

Answer:

< i = 21.6 degrees

Step-by-step explanation:

Side KI = 5.3 ft

Side JK = 2.1 ft

To find :  = ?

Answer:

Step-by-step explanation:

to get the value of angle I, use the formula: x tan⁻¹Ф = h

where: x = 5.3

           h = 2.1

          Ф = ?

plugin values into the formula;

5.3 tan⁻¹Ф = 2.1

tan⁻¹Ф  = 2.1  

               5.3

           ≈ 22°

Answer:

If 20 more soldiers join it would last 48 days

Step-by-step explanation:

if 80 soldiers need 84000 food for 60 days it means that in 60 days one soldier eats 84000/80= 1050 each

then 1050/60=17.5 meaning they need 17.5 food a day each,

adding 20 soldiers means 80+20= 100 soldiers

100*17.5=1750 food is eaten every day

84000/1750= 48 which means that 100 soldiers will eat 84000 in 48 days

Take 2 points

Slope:-

\(\\ \sf\longmapsto \dfrac{-2}{7}=\dfrac{-2}{7}=m\)

Now find equation of line in point slope form

\(\\ \sf\longmapsto y=-2/7(x+7)\)

\(\\ \sf\longmapsto y=-2/7x-2\)

Put (0,0)

\(\\ \tt\Rrightarrow 0=0-2\)

\(\\ \tt\Rrightarrow 0\neq -2\)

shaded region is away from origin .

So the inequality is

\(\\ \sf\longmapsto y\leqslant -2/7x-2\)

Answer:

Take 2 points

(-7,0)

(0,-2)

Slope:-

Now find equation of line in point slope form

Put (0,0)

shaded region is away from origin .

So the inequality is

this answer is correct i got it right when i used it.

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

(i)  X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) x( x+4)=a

    (x+1)(x+3)= a+3  

Step-by-step explanation:

(i)  X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) (x+1)(x+3)=x^2+3X+X+3=x^2+4x+3;

x(x+4)=a

(x+1)(x+3)= a+3

Step-by-step explanation:

x is followed by x+1 so each time we add one

our sequence goes like this:

the first number is x and the fourth one is x+3

the second number is x+1 and the third one is x+2

the first product is x²+3x and the second one is x²+3x+2

Let P be x²+3x and P' be x²+3x+2

Anything times 1 = the same number so 696969x1=696969

Answer:

696969

Step-by-step explanation:

Answer:

Step-by-step explanation:

m represents the meters.

A company received 15 funding applications and want to select 8 of them to be funded. The number of different lists of successful applications is 6,435

Suppose we have n objects in total and we want to select r objects among total objects, the number of ways they can be selected is given by the combination formula:

ⁿCr = n! / [r! (n-r)!]

Data from the problem:

n = total applications = 15

r = number of selected applications = 8

Hence, the number of different lists of successful applications is:

¹⁵C₈ = 15! / [8! (15-8)!]

       = 15! / [8! 7!]

       = 6,435

Thus, the number of different lists can be selected is 6,435

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The median mark on the boxplot is 40, which means 50% of the data values are greater than or equal to 40.

The vertical line drawn within the box of a box plot represents the median which is the 50th percentile of the data represented by such boxplot.

The median mark in this case is 40. Which represents the 50th percentile or 50% mark.

Therefore, 50% of the data values are greater than or equal to 40.

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To maximize the area,

The radius of the semicircle, r = 124.6in

Height of the rectangle, h = 124.6in

Given,

Perimeter of the window, P = 890in

P = 2L + 2r + πr

From this Length of window,  \(L=\frac{P-2r-\pi r}{2}\)

Length is equal to the Height of window.

So, \(H=\frac{P-2r-\pi r}{2}\)

Radius of the semicircle,

\(r=\frac{P}{4+\pi }\)

\(r=\frac{890}{4+\frac{22}{7} }\)

\(r=124.6\)

Then,

\(H=\frac{P-2r-\pi r}{2}\)

\(H=\frac{890-2(124.6)-\frac{22}{7}(124.6) }{2}\)

\(H=\frac{890-249.2-391.6}{2}\)

\(H=\frac{249.2}{2}\)

\(H=124.6\)

Area  of the window,

\(A=Pr-2r^{2} -(\frac{1}{2})\pi r^{2}\)

\(A=890(124.6)-2(124.6)^{2} -(\frac{1}{2} )(\frac{22}{7})(124.6)^{2}\)

A = 110894 - 31050.32 - 24396.68

A = 55447

From the above calculations we have to conclude that:

To maximize the area,

The radius of the semicircle, r = 124.6in

Height of the rectangle, h = 124.6in

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Answer:

Step-by-step explanation:

423

Based on the given information, we can assume that the survey has a 95% confidence level, which means that the margin of error can be calculated using the formula:

Margin of Error = (maximum difference in percentage points / 2)

The maximum difference in percentage points between the two candidates is 53% - 47% = 6%. Dividing this by 2 gives us a margin of error of 3%. Therefore, we can say that the results of the phone survey indicate that between 44% and 56% of voters may choose candidate a over candidate b (with a margin of error of +/- 3%).

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The solutions for the systems of inequalities are:

a) (0, -50), (0, -100), (0, -125)

b)  (0, 20), (0, 23) , (0, 24).

When we have a system of inequalities, a solution is a point (x, y) that solves both ienqualities at the same time.

The first one is:

y ≤ x - 8

y < -3x - 9

Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -50, replacing that we will get:

-50  ≤ 0 - 8 = -8

-50 < - 3*0 - 9 = -9

Both of these are true, so (0, -50) is a solution, and trivially, other solutions of the system of inequalities can be things like (0, -100) and (0, -125) are other two solutions.

For the second system:

y > 5x + 1

y > 3

Let's do the same thing, x = 0 and y gets really large values, like y = 20

20 > 5* + 1 = 1  this is true.

20 > 3   this is true.

so (0, 20) is a solution, and also are (0, 23) and (0, 24).

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Answer:

102 beads will be used for each necklace.

Step-by-step explanation:

3,264/32=102

Answer:

as below

Step-by-step explanation:

1st  the difference is 4  b/c half of 4 = 2

and

2*smaller +greater = 13

so check out small number that are 4 apart.. like 2 and 6

2(2)+6 =10

2(3) +7 = 13  aahh hah..  that's it

3 and 7 are the numbers being hunted :P