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In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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Answer: x= -3

Hope this helps :)

Answer:x=-9

Step-by-step explanation: Simplify both sides of the equation 3/4x = 27/4

Multiply both sides by 4/3

4/3 • 3/4x = 4/3 • -27/4

Answer:

I think 15 I am sure

Step-by-step explanation:

The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.

Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.

The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.

Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.

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Answer:

If there are dotted lines available then use dotted lines for the range where its only greater than or less than, when there is no equals to sign then you use dotted lines

Step-by-step explanation:

Answer:

1. y=2x^2-8X-1

2. y=-6x^2+36x-63

3. y=-3x^2+18x-34

4. y=9x^2+54x+76

5. y=-x^2+8x-22

6. y=6x^2-48x+90

7. y=8x^2+16x+5

8. y=2x^2-8x+1

Have a great day :)

Answer:

\(x=3\)

Step-by-step explanation:

Because this line is parallel to the y-axis, it is a vertical line. This is a special case where the formatting of its equation is different:

\(x=d\) where d is the x-intercept, or the value of x when the line crosses the x-axis

We're given that the line passes through the point (3,-5). Because this is a vertical line, the x-coordinates of the points it passes through will always stay the same. Therefore, the x-intercept (d) is 3.

\(x=3\)

I hope this helps!

The main criticism of differential opportunity theory is that it overlooks the fact that most delinquents become law-abiding adults (option c).

Differential opportunity theory, developed by Richard Cloward and Lloyd Ohlin, focuses on how individuals in disadvantaged communities may turn to criminal activities as a result of limited legitimate opportunities for success.

However, critics argue that the theory fails to account for the fact that many individuals who engage in delinquency during their youth go on to become law-abiding adults.

This criticism highlights the idea that delinquent behavior is not necessarily a lifelong pattern and that individuals can change their behavior and adopt prosocial lifestyles as they mature.

While differential opportunity theory provides insights into the relationship between limited opportunities and delinquency, it does not fully address the complexities of individual development and the potential for desistance from criminal behavior.

Critics suggest that factors such as personal growth, social support, rehabilitation programs, and the influence of life events play a significant role in individuals transitioning from delinquency to law-abiding adulthood.

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Answer:

\(\sqrt{3}\cdot\sqrt{6}=3\cdot\sqrt{2}\)

Step-by-step explanation:

Radicals

We have the expression:

\(\sqrt{3}\cdot\sqrt{6}\)

Since 6=2*3, it can be rewritten as:

\(\sqrt{3}\cdot\sqrt{6}=\sqrt{3}\cdot\sqrt{2}\cdot\sqrt{3}\)

Joining like radicals:

\(\sqrt{3}\cdot\sqrt{6}=\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{2}\)

\(\sqrt{3}\cdot\sqrt{6}=\sqrt{9}\cdot\sqrt{2}\)

\(\boxed{\sqrt{3}\cdot\sqrt{6}=3\cdot\sqrt{2}}\)

This is the required form with b=2

The integer b for \(\rm b\sqrt{2}\) such as \(\rm \sqrt{3}\times \sqrt{6} = b\sqrt{2}\) holds good is 3 .

According to the property of square root for any  positive integer x

\(\rm \sqrt{x} \times \sqrt{x} = x....(1)\)

According to the  given condition

\(\rm \sqrt{3}\times \sqrt{6} = b\sqrt{2}\)

We can simplify the left hand side  of the equation as follows

\(\sqrt{3}\times \sqrt{6}\)

\(= \sqrt{3}\times \sqrt{2\times 3 }\)

\(= 3\sqrt{2}\)      ( By using equation (1))

So on comparing with right hand side of equation (1) we get

\(\rm 3\sqrt{2} = b\sqrt{2}\\hence \; on\; comparing\\b = 3\)

The integer b for \(\rm b\sqrt{2}\) such as \(\rm \sqrt{3}\times \sqrt{6} = b\sqrt{2}\) holds good is 3 .

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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To simplify the expression 5√8 + √3, we can simplify each radical term separately and then combine them.

First, let's simplify the radical terms:

√8 can be simplified as 2√2 because 8 can be factored into 4 * 2, and √4 is equal to 2.

√3 cannot be simplified further since 3 is a prime number.

Now, let's substitute the simplified radical terms back into the expression:

5√8 + √3 becomes 5(2√2) + √3.

Next, we can multiply the coefficients outside the radicals:

5(2√2) is equal to 10√2.

Putting it all together, the simplified expression is:

10√2 + √3.

So, 5√8 + √3 simplifies to 10√2 + √3.

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

4

Step-by-step explanation:

To solve for x in the equation:

√(2x - 7) = 1

We can start by isolating the square root by squaring both sides of the equation:

(√(2x - 7))^2 = 1^2

2x - 7 = 1

Next, we can isolate the variable by adding 7 to both sides of the equation:

2x = 8

Finally, we can solve for x by dividing both sides by 2:

x = 4

Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

22 hours

Step-by-step explanation:

So, 143 equals eleven hours. 143 plus 143 would equal 243. So, you have two 143s which means you should multiply the 11 hours by two. 11x2 equals 22.

The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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Answer:

$13.50

Step-by-step explanation:

You can use the simple interest formula here: I(interest)=P(principal amount)r(interest rate)t(years). I=Prt. So just plug in the numbers. I=90x.15x1=13.5

We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

Given that,

The number is either 1-digit or 2-digit.

In the case of 1-digit, the only 1-digit primes are 3 and 7, for a total of 2 primes.

In the case of 2-digit, We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield 12-4=8 prime numbers.

Thus, We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

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Answer: 9 on the x axis  and 18 on the y axis

Answer:

\(\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(\frac{3}{2},\:-3\right),\:\:\mathrm{semi-major\:axis}\:b=6,\:\:\mathrm{semi-minor\:axis}\:a=3\)

Step-by-step explanation:

\(\left(2x-3\right)^2+\left(y+3\right)^2=36\\\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1\:\mathrm{is\:the\:ellipse\:standard\:equation}\\\mathrm{with\:center}\:\left(h,\:k\right)\:\mathrm{and\:}a,\:b\mathrm{\:are\:the\:semi-major\:and\:semi-minor\:axes}\\\mathrm{Rewrite}\:\left(2x-3\right)^2+\left(y+3\right)^2=36\:\mathrm{in\:the\:form\:of\:the\:standard\:ellipse\:equation}\\\left(2x-3\right)^2+\left(y+3\right)^2=36\\\mathrm{Rewrite\:as}\\\left(2x-3\right)^2+\left(y+3\right)^2-36=0\)

\(\mathrm{Simplify}\:\left(2x-3\right)^2+\left(y+3\right)^2-36:\quad 4x^2-12x+y^2+6y-18\\4x^2-12x+y^2+6y-18=0\\\mathrm{Add\:}18\mathrm{\:to\:both\:sides}\\4x^2-12x+y^2+6y=18\\Factor\:out\:coefficient\:of\:square\:terms\\4\left(x^2-3x\right)+\left(y^2+6y\right)=18\\\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}4\\\left(x^2-3x\right)+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}\\\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}1\)

\(\frac{1}{1}\left(x^2-3x\right)+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}\\\mathrm{Convert}\:x\:\mathrm{to\:square\:form}\\\frac{1}{1}\left(x^2-3x+\frac{9}{4}\right)+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)\\\mathrm{Convert\:to\:square\:form}\\\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)\\\mathrm{Convert}\:y\:\mathrm{to\:square\:form}\)

\(\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y^2+6y+9\right)=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)+\frac{1}{4}\left(9\right)\\\mathrm{Convert\:to\:square\:form}\\\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y+3\right)^2=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)+\frac{1}{4}\left(9\right)\\\mathrm{Refine\:}\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)+\frac{1}{4}\left(9\right)\\\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y+3\right)^2=9\)

\(\mathrm{Divide\:by}\:9\\\frac{\left(x-\frac{3}{2}\right)^2}{9}+\frac{\left(y+3\right)^2}{36}=1\\\mathrm{Rewrite\:in\:standard\:form}\\\frac{\left(x-\frac{3}{2}\right)^2}{3^2}+\frac{\left(y-\left(-3\right)\right)^2}{6^2}=1\\\mathrm{Therefore\:ellipse\:properties\:are:}\\\left(h,\:k\right)=\left(\frac{3}{2},\:-3\right),\:a=3,\:b=6\\b>a\:\mathrm{therefore}\:b\:\mathrm{is\:semi-major\:axis\:and}\:a\:\mathrm{is\:semi-minor\:axis}\)

\(\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(\frac{3}{2},\:-3\right),\:\:\mathrm{semi-major\:axis}\:b=6,\:\:\mathrm{semi-minor\:axis}\:a=3\)

Debbie can buy a maximum of 4 t-shirts with the remaining $38 after purchasing the $22 jeans.

To determine the greatest number of t-shirts Debbie can buy, we need to find out how much money she will have left after purchasing the pair of jeans. Debbie has $60 to spend and the jeans cost $22. Therefore, she will have $60 - $22 = $38 left to spend on t-shirts.

Each t-shirt costs $8, so we divide the remaining amount by the cost per t-shirt: $38 / $8 = 4.75.

Since Debbie cannot buy a fraction of a t-shirt, we round down the decimal value to the nearest whole number. Therefore, Debbie can buy a maximum of 4 t-shirts with the remaining $38.

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Answer:

Exact form 2/11

Decimal form 0.18

Answer:

x = -2 - sqrt(3), -2 + sqrt(3) 

Step-by-step explanation:

We can rewrite the equation as

x² + 4x + 1 = 0

Now we can use the quadratic equation.

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 4, c = 1. Substituting these values ​​gives:

x = (-4 ± sqrt(4² - 4(1)(1))) / 2(1)

x = (-4 ± sqrt(16 - 4)) / 2

x = (-4 ± sqrt(12)) / 2

x = (-4 ± 2sqrt(3)) / 2

x = -2 ± sqrt(3)

So, from min to max, the solution is:

x = -2 - sqrt(3), -2 + sqrt(3) 

Hope this helps!