√4x²+9 dx Consider the integral using trigonometric substitution? cos √4x²+9 dx 8 x4 = 9 sin4 0 |||||||||||| sec 0 = Which of the following statement(s) is/are TRUE in solving the integral √4x²+9 dx de (4x² +9)³ 27x3 cos e de sin4 0 √4x²+9 3 √4x²+9 dx = + C

The isolated form of the given formula for n be,

⇒ n = PV / RT

The given formula is,

PV = nRT,

To isolate n,

we have to divide both sides by RT.

Therefore,

⇒ n = PV / RT

We can interpret this formula as the number of moles of a gas, n,

being equal to the product of pressure, volume, and the number of gas molecules divided by the gas constant and temperature.

This formula is derived from the ideal gas law, which relates temperature, pressure, volume, and the number of molecules in a gas to one another.

To learn more about division visit:

https://brainly.com/question/2273245

#SPJ4

A company that manufactures children's toys calculates that its costs and revenue can be modeled by the equations:

C = 5000 + 1.3x and R = 300x - 0.02.x.

(a) Find the Profit function.The profit is the difference between revenue (R) and cost (C). Therefore,

P = R - C

Here

P = (300x - 0.02.x) - (5000 + 1.3x)

On simplifying,

P = 298.7x - 5000

(b) Find the rate of change of the profit per week if the company is making 2000 toys, and sales are increasing at a rate of 300 toys per week.

To find the rate of change of profit per week, we differentiate the profit function with respect to x. That is,

dP/dx = d/dx (298.7x - 5000)

dP/dx = 298.7

The rate of change of the profit per week is constant and equal to 298.7.

To know more about revenue visit:

https://brainly.com/question/14952769

#SPJ11

Answer:

Coronavirusss

Step-by-step explanation:

Stay at home :D

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

To know more about trigonometric expressions refer here:

https://brainly.com/question/12676341#

#SPJ11

The correct probabilities are P(at least two tails) = 0. 5 and P(at least one heads) = 0. 875.

Let's calculate the probabilities based on the given sample space:

Total number of outcomes (sample space) = \(2^{3}\) = 8

P(one tails):

From the sample space, there are four outcomes that have exactly one tails: HTT, THT, TTH, TTT.

So, P(one tails) = 4/8 = 0.5

P(three heads):

From the sample space, there is only one outcome that has three heads: HHH.

So, P(three heads) = 1/8 = 0.125

P(one heads and two tails):

From the sample space, there are three outcomes that have one heads and two tails: HHT, HTH, THH.

So, P(one heads and two tails) = 3/8 = 0.375

P(at least two tails):

From the sample space, there are four outcomes that have at least two tails: TTH, THT, HTT, TTT.

So, P(at least two tails) = 4/8 = 0.5

P(at least one heads):

From the sample space, there are seven outcomes that have at least one heads: HHH, HHT, HTH, THH, THT, TTH, TTT.

So, P(at least one heads) = 7/8 = 0.875

Therefore, the correct probabilities are:

P(one tails) = 0.5

P(three heads) = 0.125

P(one heads and two tails) = 0.375

P(at least two tails) = 0.5

P(at least one heads) = 0.875

To learn more about probabilities here:

https://brainly.com/question/31828911

#SPJ4

The force that must be applied by the pulley system to lift the load is 228.02N.

When the pulley system lifts the load, the force is applied vertically upwards, so θ = 0, and cos(θ) = 1.

So, we can write the Work Done formula as :

⇒ Work = Force × Distance

The work done against gravity is equal to the change in potential energy of the load:

⇒ Work = Potential Energy = mgh

Where, "m" = mass of the load, g = acceleration due to gravity (9.81 m/s²), and "h" = height through which the load is lifted.

So, we can write:

⇒ Force × Distance = mgh

⇒ Force = mgh / Distance

In this case, the load has a weight of 900 N,

So its mass (m) is = (900 N)/(9.81 m/s²) = 91.75 kg

Substituting the given values in the Force formula,

We get,

Force = [(91.75 kg) × (9.81 m/s²) × (0.19 m)]/0.75 ≈ 228.02N

Therefore, a force of approximately 228N must be applied to the rope to lift the load.

Learn more about Force here

https://brainly.com/question/20354940

#SPJ4

Answer:

The distance is 8.6

Step-by-step explanation:

^^^

Answer:

48.6

Step-by-step explanation:

If you use 8.1g of sugar for 1 cake then 6 cakes will be 48.6g of sugar

Just do 8.1*6 and you will get 48.6

Sure! Here's the 99.5% confidence interval for the true population mean textbook weight: (49.433, 60.567) ounces.

To construct a confidence interval for the true population mean textbook weight, we can use the formula:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √(sample size))

Given the information provided:

- Sample mean = 55 ounces

- Population standard deviation = 11.4 ounces

- Sample size = 32 textbooks

First, we need to find the critical value corresponding to a 99.5% confidence level. Since the sample size is relatively small (32 textbooks), we can use a t-distribution instead of a normal distribution.

The degrees of freedom for a t-distribution are given by (sample size - 1). In this case, the degrees of freedom will be (32 - 1) = 31.

Using a t-table or a statistical calculator, we find the critical value for a 99.5% confidence level and 31 degrees of freedom is approximately 2.750.

Now, we can calculate the confidence interval:

Confidence Interval = 55 ± 2.750 * (11.4 / √32)

Confidence Interval = 55 ± 2.750 * (11.4 / 5.657)

Confidence Interval = 55 ± 5.567

Therefore, the 99.5% confidence interval for the true population mean textbook weight is approximately (49.433, 60.567) ounces.

To know more about interval,

https://brainly.com/question/29126055#

#SPJ11

Given :

Gary made a scale drawing of his game room.

The scale drawing has a length of 3 inches and a width of 5 inches.

To Find :

If the game room has an actual length of 12 feet, which equation could be used to determine w, the width of the game room.

Solution :

We know, during making scale drawing of any thing the shape of the object is same as the real one i.e. the ratio of each dimension remains constant.

Let, width of the gaming room is w.

\(\dfrac{w}{5}=\dfrac{12}{3}\\\\w = 20\ inches\)

Therefore, the width of the game room is 20 inches.

Answer:

g(x) = x^2 - 7

Step-by-step explanation:

Put u=17

Answer:

59.5.

Step-by-step explanation:

h = 3.5u

When u = 17,

h = 3.5*17

= 59.5

The length of the segment MQ is 29.4

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

The circle and the intersecting chords

Using the equation of intersecting chords, we have

MQ * QN = OQ * QP

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

MQ * 17 = 20 * 25

So, we have

MQ = 20 * 25/17

Evaluate

MQ = 29.4

Hence, the length of the segment MQ is 29.4

Read more about intersecting chords at

https://brainly.com/question/13950364

#SPJ1

The price elasticity of demand at any point on a demand curve with a slope equal to negative 1 is C greater than 1, but less than infinite. This is because price elasticity of demand measures the percentage change in quantity demanded in response to a percentage change in price.

The price elasticity of demand at any point on a demand curve with a slope equal to negative 1 would be C) greater than 1, but less than infinite. This is because a slope of negative 1 indicates that for every one unit increase in price, there is a one unit decrease in quantity demanded. This means that the demand curve is relatively steep, indicating that small changes in price will result in larger changes in quantity demanded. Therefore, the price elasticity of demand would be greater than 1, but not infinite, as there is still some level of responsiveness to price changes.

When the elasticity is greater than 1, it indicates elastic demand, where the quantity demanded is highly responsive to price changes.

To know more about price elasticity visit:-

https://brainly.com/question/13691796

#SPJ11

Answer:

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Step-by-step explanation:

You’re only supposed to have one number to the left of the decimal point in scientific notation.

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Answer: X 0 1 2 3 4 5 6 7 8 P(X=k) 0.05 0.07 0.13 0.12 0.20 0.25 0.07 0.03 0.08  the probability that more than 5 patients arrive at the hospital

What is the probability that more than 5 patients arrive at the hospital with flu-like symptoms between 12:00pm and 12:20pm?

Step-by-step explanation:

Group of answer choices

A. 0.43

B. 0.18

C. 0.82

D. 1

Part two of the question:

using the same information as stated before,

Match the probability statements with the correct probabilities.

(choose one answer)

The probability that X is less than or equal to 5.

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

The probability that X is greater than 7.

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

The probability that X is between 3 (noninclusive) and 7 (noninclusive).

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

The probability that no patients arrive in that interval.

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

Answer:

2/3

Step-by-step explanation:

Take each side of ABCD and divide it on each side of LMNO

AB/LM = 4/6=2/3

AD/LO =2/3

DC/ON = 4/6 =2/3

BC/MN = 2/3

Answer:

Approximately \(0.7\; {\rm ft}\).

Step-by-step explanation:

If the current bounce is of height \(h\; {\rm ft}\), the next bounce would be of height \((78\%\, h)\; {\rm ft}\), which is equal to \((0.78\, h)\; {\rm ft}\).

It is given that the first bounce is of height \(6.5\; {\rm ft}\). Relative to this first bounce:

In general, the \(n\)th bounce would have been dampened \((n - 1)\) times. The height of that bounce would be \(((0.78)^{n - 1}\, 6.5)\; {\rm ft}\).

Thus, the \(10\)th bounce would have been dampened \((10 - 1) = 9\) times. The height of that bounce would be \(((0.78)^{10 - 1} \, 6.5)\; {\rm ft} \approx 0.7\; {\rm ft}\) (rounded to the nearest tenth, one digit after the decimal point.)

The answer is a² + 6. "Sum of a squared and 6" means you square a value and then add 6 to it.

\(e-\frac{1}{e} +\frac{4}{3} 0r 3.687\)  is the value when the equation is to integrate with respect to x or y

we integrate with respect to x

Area = \(\int\limits^b_a{(f(x)-g(x))} \, dx\)

       = \(\int\limits^1_-1{e^{x}-x^{2} +1 } \, dx\)

        =\(e^{x} -\frac{x^{3} }{3} +x\)

   substitute 1 and -1 in place of x

  = \((e-\frac{1}{3}+1-\frac{1}{e} -\frac{1}{3} +1)\)

  = \(e-\frac{1}{e} + \frac{4}{3} or 3.6837\)

The diagram was attached in the given below.

Learn more about integration here

https://brainly.com/question/18125359

#SPJ4

Answer:

obtion b and d

Step-by-step explanation:

4x + 5 = -4x + 5

4x + 4x = 5 - 5

8x = 0

x = 0/8

x = 0     (this has solution)

-4x + 5 = -4x - 4

-4x + 4x = -4 + 5

0 = -1   (this has no solution)

5x + 5 = -4x - 4

5x + 4x = -4 - 5

9x = -9

x = -9/9

x = -1                   (this has solution)

-4x + 5 = -4x - 5

-4x + 4x = -5 -5

0 = -10       (this has no solution)

There is no non-zero 2x2 matrix b that satisfies the equation ab = 0 for any non-zero 2x2 matrix a.

To find a non-zero 2x2 matrix b such that ab equals the 2x2 zero matrix, we can set up the following equation:

a * b = 0

where a is any non-zero 2x2 matrix. To solve for b, we can use the fact that matrix multiplication is distributive, associative, and has a zero property. This means that if any element in the product of two matrices is zero, then either one or both of the matrices must have a corresponding row or column that is all zero.

So, let's choose a specific non-zero 2x2 matrix for a, such as:

a = [ 1 2
     3 4 ]

Then, we can solve for b as follows:

a * b = [ 1 2
         3 4 ] * [ x y
                   z w ]

      = [ (1*x + 2*z) (1*y + 2*w)
          (3*x + 4*z) (3*y + 4*w) ]

We want this product to equal the 2x2 zero matrix:

[ 0 0
 0 0 ]

This means that each element in the product must be zero. We can start by setting the top-left element to zero:

1*x + 2*z = 0

This equation can be rearranged to solve for z:

z = (-1/2)*x

Next, we can set the top-right element to zero:

1*y + 2*w = 0

This equation can be rearranged to solve for w:

w = (-1/2)*y

Now, we can substitute these expressions for z and w into the bottom row of the product:

3*x + 4*(-1/2)*x = 0

3*y + 4*(-1/2)*y = 0

These equations simplify to:

x = 0

y = 0

So, we have found that the only solution for b that satisfies the equation ab = 0 is:

b = [ 0 0
     0 0 ]

However, this matrix is not non-zero, as required by the original question. Therefore, there is no non-zero 2x2 matrix b that satisfies the equation ab = 0 for any non-zero 2x2 matrix a.

To know more about non-zero matrices refer here :

https://brainly.com/question/31040801#

#SPJ11

Answer:

x

2

−

13

x

+

20

x

2

−

13

x

+

20

x

2

−

13

x

+

20

.

Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.

A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.

How to solve?

she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.

To learn more about fraction, visit:

https://brainly.com/question/20593515

#SPJ4