Boyle's law states that if the temperature of a gas remains constant, then PV = c, where P=pressure, V = volume, and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 11 in^3 /sec, at what rate is P increasing when P = 90 lb/in^2 and V = 70 in^3?

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The name of the shape created by the cross section when a plane is parallel to the base of the rectangular prism is a rectangle.

Since the plane is parallel to the base, it will cut through the rectangular prism in a way that retains the original shape and dimensions of the base, which is a rectangle.
Summary for Part A: The shape created by a cross section parallel to the base is a rectangle.
For Part B: The shape of the resulting cross section when cut diagonal to the base of the rectangular prism is a parallelogram.
Explanation for Part B: When the cross section is cut diagonally to the base, it will cut through the rectangular prism at an angle, creating a shape with opposite sides parallel and equal in length, which is a parallelogram.

Summary for Part B: The shape created by a cross section diagonal to the base is a parallelogram.

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i) The dispersion relation for the given equation is ± (v / 6) * k.

ii) The group velocity for the given equation is ± v / 6.

iii) The phase velocity is ± v / 6.

To find the dispersion relation, as well as the group and phase velocities for the given equation, let's start by rewriting the equation in a standard form:

82y(x, t) - 8\(t^2\) + 84y(x,t) = -2 * 8\(x^4\)

Simplifying the equation further:

8(2y(x, t) - \(t^2\) + 4y(x,t)) = -16\(x^4\)

Dividing both sides by 8:

2y(x, t) - \(t^2\) + 4y(x,t) = -2\(x^4\)

Rearranging the terms:

6y(x, t) = \(t^2\) - 2\(x^4\)

Now, we can identify the coefficients of the equation:

Coefficient of y(x, t): 6

Coefficient of \(t^2\): 1

Coefficient of \(x^4\): -2

(i) Dispersion Relation:

The dispersion relation relates the angular frequency (ω) to the wave number (k). To determine the dispersion relation, we need to find ω as a function of k.

The equation given is in the form:

6y(x, t) = \(t^2\) - 2\(x^4\)

Comparing this with the general wave equation:

A * y(x, t) = B * \(t^2\) - C * \(x^4\)

We can see that A = 6, B = 1, and C = 2.

Using the relation between angular frequency and wave number for a linear wave equation:

\(w^2\) = \(v^2\) * \(k^2\)

where ω is the angular frequency, v is the phase velocity, and k is the wave number.

In our case, since there is no coefficient multiplying the y(x, t) term, we can set A = 1.

\(w^2\) = (\(v^2\) / \(A^2\)) * \(k^2\)

Substituting the values, we get:

\(w^2\) = (\(v^2\) / 36) * \(k^2\)

Therefore, the dispersion relation for the given equation is:

ω = ± (v / 6) * k

(ii) Group Velocity:

The group velocity (\(v_g\)) represents the velocity at which the overall shape or envelope of the wave propagates. It can be determined by differentiating the dispersion relation with respect to k:

\(v_g\) = dω / dk

Differentiating ω = ± (v / 6) * k with respect to k, we get:

\(v_g\) = ± v / 6

So, the group velocity for the given equation is:

\(v_g\) = ± v / 6

(iii) Phase Velocity:

The phase velocity (\(v_p\)) represents the velocity at which the individual wave crests or troughs propagate. It can be calculated by dividing the angular frequency by the wave number:

\(v_p\) = ω / k

For our equation, substituting the dispersion relation ω = ± (v / 6) * k, we have:

\(v_p\) = (± (v / 6) * k) / k

\(v_p\) = ± v / 6

Therefore, the phase velocity for the given equation is:

\(v_p\) = ± v / 6

To summarize:

(i) The dispersion relation is ω = ± (v / 6) * k.

(ii) The group velocity is \(v_g\) = ± v / 6.

(iii) The phase velocity is \(v_p\) = ± v / 6.

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Answer:

28%

Step-by-step explanation:

38.40 - 30 = 8.40

x : 100 = 8.40 : 30

x = 8.40 * 100 / 30

x = 840/30

x = 84/3 = 28%

volume of paper bag= 16×5×20=1600cmcube

volume of box= 8×3×10= 240

space left = 1600-240= 1360cmcube

hope it helps

\(\dfrac{1}{2} z+5=57\)

Subtract 5 from both sides:

\(\dfrac{1}{2} z+5-5=57-5\)

\(\dfrac{1}{2} z=52\)

Multiply both sides by 2:

\(2\times(\dfrac{1}{2} z)=2\times(52)\)

\(\fbox{z = 104}\)

Answer:

z=104

Step-by-step explanation:

1/2z=57-5

1/2z=52

1/2z*2=52*2

1z=104

1/1z=104/1

z=104

This is because the determinant is a measure of how much the matrix changes the area or volume of the space it is applied to, and if two columns are the same, then the matrix does not change the area or volume of the space.

According to Theorem 3 in Chapter 3, if two rows or two columns in a square matrix are the same, then the determinant of that matrix is 0. This is because the determinant is a measure of how much the matrix changes the area or volume of the space it is applied to. If two rows or two columns are the same, then the matrix does not change the area or volume of the space, so the determinant is 0.

To show this, let's consider a square matrix A with two identical rows:

A = [a1, a2, a3; a1, a2, a3; b1, b2, b3]

The determinant of A can be found using the formula:

det(A) = a1 * det([a2, a3; b2, b3]) - a2 * det([a1, a3; b1, b3]) + a3 * det([a1, a2; b1, b2])

Since the first two rows are the same, the first two determinants in this formula will be the same:

det([a2, a3; b2, b3]) = det([a1, a3; b1, b3])

So the formula simplifies to:

det(A) = a1 * det([a2, a3; b2, b3]) - a2 * det([a2, a3; b2, b3])

= (a1 - a2) * det([a2, a3; b2, b3])

Since a1 = a2, the determinant is 0:

det(A) = 0

The same is true for two identical columns. The determinant will also be 0 in that case. This is because the determinant is a measure of how much the matrix changes the area or volume of the space it is applied to, and if two columns are the same, then the matrix does not change the area or volume of the space.

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Answer:

C

Step-by-step explanation:

1. Change to improper fractions

4 6/8 -> Multiply 4 and 8. Add 6. = 38/8

2 3/5 -> Multiply 2 and 5. Add 3. 13/5

Denominators are different so we have to make the same.

38/8 = 190/40
13/5 = 104/40

190/40-104/40 = 86/40 -> 2 6/40

Answer:

20 Milk Chocolates and 15 Dark Chocolates

Step-by-step explanation:

Ratio of Milk to Dark Chocolates, 4 : 3

Therefore, the total number of units in the box is 4 + 3 = 7.

The box has 35 chocolates.

7 units = 35

1 unit = 35 ÷ 7 = 5

There are 4 units of Milk Chocolates.

4 * 5 = 20

There are 3 units of Dark Chocolates.

3 * 5 = 15

The solution of the algebraic expression (8h-1)-(h+ 3) is -25.

Given:

The given expression in the question is:

(8h-1)-(h+ 3); Value of h = -3​

Putting the value of h in the expression

8(-3)-1 - ((-3)+3)

= -24-1 -0

= -25

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The roots of f have the absolute value less than or equal to 1.

The roots of f have the absolute value less than or equal to 1 by using the Rouche's.

Let's consider the function g(x) = \(x^k\). Now, let h(x) = \(-x^{k-1} - x^{k-2} - ... - x - 1\).

On the unit circle |x| = 1, we have:

|g(x)| = \(|x^k|\) = 1,

|h(x)| ≤ \(|x^{k-1}| + |x^{k-2}| + ... + |x| + |1|\) ≤\(|x^{k-1}| + |x^{k-2}| + ... + |x| + 1\)= k.

Thus, for |x| = 1, we have:

|g(x)| > |h(x)|.

Now, we consider the function f(x) = g(x) + h(x) = \(x^k - x^{k-1} - x^{k-2} - ... - x - 1.\)

Let z be a root of f(x), that is, f(z) = 0.

Assume |z| > 1, then we have:

|g(z)| = \(|z^k|\) > 1,

|h(z)| ≤ k.

Thus, for |z| > 1, we have:

|g(z)| > |h(z)|,

Means that g(z) and h(z) have the same number of roots inside the circle |z| = 1 by Rouche's theorem.

The fact that f(z) = g(z) + h(z) has no roots inside the circle |z| = 1, since |z| > 1.

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Answer:

Step-by-step explanation:

40% of 18,000 gallons means

40 x 180= 7,200 gallons

Answer:

B. y = -6

Step-by-step explanation:

You can graph each line to see which one is horizontal since the y-axis is vertical. This would make the lines perpendicular since when a vertical and horizontal line meet, they form a 90-degree angle, which is by definition what perpendicular means.

Answer:

i think that the answer is b. y=-6

The hypothesis test to be used to test the relationship between x and y at 5% significance level. Slope indicates price-demand relationship.

To test the connection between the quantity of blaze drives sold each day (x) and their costs (y), we can direct a speculation test. The invalid speculation is that there is no critical connection between the two factors, while the elective theory is that there is a huge connection between them.

Expecting a direct relationship, we can play out a basic straight relapse examination to gauge the slant of the line, which addresses the adjustment of the quantity of blaze drives sold each day for each unit change in cost. A positive slant shows that the higher the value, the more blaze drives sold each day, while a negative slant demonstrates the inverse.

To decide if the slant is fundamentally unique in relation to nothing, we can compute the t-measurement and contrast it with the basic t-esteem at the 5% degree of importance. Assuming that the t-measurement is more noteworthy than the basic t-esteem, we can dismiss the invalid speculation and infer that there is a huge connection between the two factors.

As far as deciphering the slant of the line, a positive slant proposes that the interest for streak drives increments as their cost increments, which suggests that clients will pay something else for streak drives when they see a higher worth or quality. In any case, it is essential to take note of that the connection among cost and request may not be straight or might be impacted by different elements, for example, rivalry, market patterns, and shopper inclinations.

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The expression 3a² + 10a + 7 can be completely factored as (a + 7)(3a + 1).

The expression 3a² + 10a + 7 can be factored as a product of two binomials.

To factor this expression, we can find two numbers that multiply to 7 and add up to 10. The only pair of numbers that have this property is 1 and 7. So, we can write:

3a² + 10a + 7 = 3a² + 7a + a + 7

= a(3a + 1) + 7(1 + 3a)

= (a + 7)(3a + 1)

Factorization is the process of breaking down a mathematical expression into simpler, more manageable parts. There are various methods to factorize an expression, including:

Grouping: This method involves grouping terms in pairs and then factoring out a common factor.

Difference of Squares: This method involves factoring the expression into the difference of two squares.

Sum or Difference of Cubes: This method involves factoring the expression into the sum or difference of two cubes.

Using Factor Trees: This method involves finding the prime factorization of the expression and then grouping the factors to find the final answer.

Using Identities: This method involves using various mathematical identities to simplify the expression.

It's best to determine the method to use based on the specific expression you're trying to factorize.

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To check if the given differential equation is homogeneous. A first-order differential equation of the form M(x,y)dx + N(x,y) dy = 0 is said to be homogeneous if both M(x,y) and N(x,y) are homogeneous functions of the same degree.

In this case, we have 3x dy - 3y dx = 100 + 10(x^8y''). We can see that 3x and 3y are both homogeneous functions of degree 1, while 100 and 10(x^8y'') are both homogeneous functions of degree 0. So, the given differential equation is not homogeneous.

However, we can make it homogeneous by dividing both sides by x^3. This gives us:

3(dy/dx) - (y/x) = 100/x^3 + 10(x^5)(dy/dx)

Now, we can see that both 3(dy/dx) and (y/x) are homogeneous functions of degree 0, while 100/x^3 and 10(x^5)(dy/dx) are homogeneous functions of degree -3 and 5, respectively.

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Answer:

1. )0.35

2. )1.15

3.)0.5 (5 repeating's)

4.)2.72

Step-by-step explanation:

7 divide  20=0.35

-23 divide 20=1.15

-60 divide 22 = 2.727272 but it is 2.72

Answer:

C. Disagree

Step-by-step explanation:

Answer:

1. Sine ratio of angle ∠C = 12/13

2. cos ratio for ∠C = 6/10

Step-by-step explanation:

1. sin = perpendicular /hypotuse

=> 12/13

2. cos = base / hypotuse

=> 6/10

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Answer:

What's the question you're asking im very confused of what you're trying to ask

Step-by-step explanation:

Answer:

B) 5

Circle is 360 degr. So (21x+9) +(23x-5) +(26x+6)=360

Combine like terms 70x+10=360

Additive inverse -10 from both sides, 70x= 350

Divide both side by 70 division Property of Equality x=5.

Check your answer by substituting 5 back into original solution!

Step-by-step explanation:

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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the initial expression is:

Answer:

x=1

Step-by-step explanation:

3x+9 = 12

Subtract 9 from each side

3x+9-9=12-9

3x = 3

Divide by 3

3x/3 = 3/3

x=1

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(x = 1\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Calculating the answer...}}\\\\3x + 9 = 12\\-------------\\\rightarrow 3x + 9 - 9 = 12 - 9\\\\\rightarrow 3x = 3\\\\\rightarrow \frac{3x=3}{3}\\\\\rightarrow \boxed{x=1}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

$1.10

Step-by-step explanation:

Answer:

whatever amount of money Mai had first minus $9.60

Step-by-step explanation:

4.35+5.25= 9.60

Since this can't happen, let's suppose that P=150, then:

Now we have to move the 100 to the other side of the equation with a negative sign to get this:

Finally, to get w, we move the 2 that's multiplying to the other side dividing the 50:

Therefore, the width of the rectangle would be 25 ft if the perimeter is 150ft, and we can see how the rectangle would look:

1/3 is the probability of rolling either a 5 or a 6 using a normal six-sided die.

Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event.

Given:

Six-sided dice rolled once

Let n be the number of outcomes

let x be the number of favorable outcomes

We know that,

\(Probability=\frac{x}{n}\)

When the six-sided dice roll, The possible outcomes are,

\(\{1,\;2,\;3,\;4,\;5,\;6\}\)

Therefore,

\(Number\;of\;outcomes,\;n=6\)

\(Probability\;rolling\;5\;is\;\frac{1}{6}\)

\(Probability\;rolling\;6\;is\;\frac{1}{6}\)

Therefore, Probability of rolling either 5 or 6 is,

\(P(5\;or\;6)=\frac{1}{6} +\frac{1}{6}\)

\(P(5\;or\;6)=\frac{2}{6}\)

\(P(5\;or\;6)=\frac{1}{3}\)

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Answer:

I believe the answer is x less than > with a line under it 83.33.