find the solution of the following differential equation. take the constants of integration to be zeros y ' ( 2 sin ( x ) cos ( x ) ) y = e − sin 2 ( x )

Factorize the quadratic.

\(2x^2 + 5x + 3 = (2x + 3) (x + 1)\)

We have \(|ab| = |a||b|\), so

\(|2x^2 + 5x + 3| = |2x + 3| |x + 1| > 0\)

Now, both \(|2x+3|\ge0\) and \(|x+1|\ge0\) (since the absolute value of any number cannot be negative), so we just need to worry about when the left side is exactly zero. This happens for

\((2x + 3) (x + 1) = 0 \implies 2x+3 = 0\text{ or }x+1 = 0 \\\\ \implies x = -\dfrac32 \text{ or } x = -1\)

So the solution to the inequality is the set

\(\left\{x \in \Bbb R \mid x\neq-\dfrac32 \text{ and } x\neq-1\right\}\)

Answer:

C) a quadrilateral, because angle C and angle X are acute

Step-by-step explanation:

It is a quadrilateral because angle C and angle X are acute angles and not right angles option third is correct.

It is defined as the four-sided polygon in geometry having four edges and four corners. It has two pairs of congruent sides and one pair of opposite congruent angles.

From the Pythagoras theorem:

\(14^2=12^2+8^2\)

196  ≠ 208

The angles C and X are not right angles since angles C and X are congruent and acute angles.

Thus, it is a quadrilateral because angle C and angle X are acute angles and not right angles option third is correct.

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Answer:

-8/7x-1

Step-by-step explanation:

perpendicular equations have opposite signs and are reciprocal.

Answer:

Hi... X=18....y=28...

Answer:

the height is 6 meters

Step-by-step explanation:

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

471 = 3.14(25)h

471 = 78.5h  Divide both sides by 78.5

\(\frac{471}{78.5}\) = \(\frac{78.5h}{78.5}\)

6 = h

Helping in the name of Jesus.

Answer:

b

Step-by-step explanation:

Um i dont knbow that

Answer:

\(( { - a}^{3}b)^{4} = ( { - a}^{3} )^{4} \times {b}^{4} = {a}^{12} {b}^{4} \)

Answer: y = mx + b

Step-by-step explanation:

i think this is what ur asking but “y” is the coordinate of the y-axis with “x” being the coordinate of the x-axis. m is the slope of the graph

The two probabilities for events U and V are:

A) P(U and V) = 0

B) P(U or V) =  0.67

We know that if two events A and B are mutually exclusive events, then these two events can't occur at the same time, this means that:

P(A and B) is always zero, and:

P(A or B) = P(A) + P(B)

Here we know the probabilities:

P(U)= 0.38

P(V) = 0.29

Then we can write:

P(U and V) = 0  (by definition)

And:

P(U or V) = P(U) + P(V) = 0.38 + 0.29 = 0.67

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To compute the value of α, we need more information about the context of the problem. α could represent different variables or parameters depending on the specific situation. Please provide additional details or clarify the context so that I can assist you further.

To compute the cumulative distribution function (CDF) for x, we need the probability density function (PDF) or the probability mass function (PMF) for x. The CDF gives the probability that a random variable takes on a value less than or equal to a specific value. If we have the PDF or PMF for x, we can compute the CDF by integrating or summing the PDF or PMF values from negative infinity up to the given value of x. This integration or summation gives us the area under the PDF or PMF curve up to x.

For example, if we have the PDF f(x) = 2x for 0 ≤ x ≤ 1, the CDF F(x) would be the integral of f(x) from 0 to x. The CDF would be F(x) = x^2 for 0 ≤ x ≤ 1. To compute the expectation for x, we need the probability distribution of x. The expectation, also known as the mean or average, represents the central tendency of a random variable. If we have the probability distribution of x, we can compute the expectation by multiplying each value of x by its corresponding probability and summing them up. This can be represented as E(x) = ∑(x * P(x)), where x represents the possible values of x and P(x) represents their corresponding probabilities. For example, if we have the probability distribution P(x) = {0.3, 0.5, 0.2} for x = {1, 2, 3}, the expectation E(x) would be E(x) = (1 * 0.3) + (2 * 0.5) + (3 * 0.2) = 1.9.

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Polynomial equation is an expression of two or more algebraic terms, which are added or subtracted from each other to form an equation. The resulting expression given polynomial function is,

\((6x^2-5)(x^2+2)\)

Hence, option 4 is the correct option.

Polynomial equation is an expression of two or more algebraic terms, which are added or subtracted from each other to form an equation.

The power of the variable is different but has the same variable.Given-the given polynomial equation is,

\(6x^4-5x^2+12x^2-10\)

Rearrange the given equation, we get,

\(6x^4+12x^2-5x^2-10\)

\(6x^2(x^2+2)-5(x^2+2)\)

\((x^2+2)(6x^2-5)\)

\((6x^2-5)(x^2+2)\)

Thus, the resulting expression given polynomial function is,

\((6x^2-5)(x^2+2)\)

Hence, option 4 is the correct option.

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Answer:

f(x) = 2(x + 1)² + 1

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

given

f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms

    = 2(x² + 2x) + 3

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 2x

f(x) = 2(x² + 2(1)x + 1 - 1) + 3

     = 2(x + 1)² - 2(1) + 3

     = 2(x + 1)² - 2 + 3

    = 2(x + 1)² + 1 ← in vertex form

The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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The question is asking us to make the denominator a rational function by finding a way to remove the square root without changing the value of the overall function.

We can do this by multiplying the denominator and numerator by the √(4x + 7), since multiplying a root term by that root term = the number being rooted  (√x × √x = x).

   - 5x⁴         ×      √(4x + 7)    =    (-5x⁴)(√(4x + 7))  

√(4x + 7)              √(4x + 7)                 4x + 7

The type of Balance Sheet Report showing information for today and a year ago is typically a C. Comparison.

A comparison balance sheet report compares the financial position of a company at two different points in time.

In this case, the current day and a year ago.

It presents the assets, liabilities, and equity of the company side by side, allowing for a comparison and analysis of the changes.

That have occurred over the specified period.

The other options mentioned are,

Balance Sheet A,

This is not a recognized classification for balance sheet reports.

Summary,

A summary balance sheet report provides a condensed overview of the financial position.

Usually presenting summarized categories of assets, liabilities, and equity.

It may not include specific details or comparisons with previous periods.

Detailed,

A detailed balance sheet report provides a comprehensive breakdown of all individual accounts.

Assets, liabilities, and equity, offering a more granular view of the financial position.

It may not necessarily include a comparison with a previous period.

Therefore, in the context of comparing the financial position for today and a year ago, the most suitable type of balance sheet report would be a C. Comparison.

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Step-by-step explanation:

n³/m²

remember, x^-n = 1/(x^n)

The two inequalities that define the shaded region in the diagram are:

y ≥ 4 and y < x

For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥"  because the shaded region is to the left and the boundary line is solid.

The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:

y ≥ 0(x) + 4

y ≥ 4

For the dashed line:

m = change in y / change in x = 1/1 = 1

b = 0

the inequality sign to use is: "<"

Substitute m = 1 and b = 0 into y < mx + b:

y < 1(x) + 0

y < x

Thus, the two inequalities are:

y ≥ 4 and y < x

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Answer:

1. 1

2.13

3. Brendan is correct

Answer:

1. The GCF is 1

2. THE GCF is 13

3. Brendan is correct

The mean lifetime of a bulb is 31. 57

Mean can be defined as the average of a given set of values or elements.

The formula for the mean of a given set of values is expressed as;

Mean = sum of the occurrence of the values/ number of values

Or

Mean = sum of terms/number of terms

From the information given, the frequency of the lifetime of the bulbs were given as;

34, 31, 94, 40 , 0 , 17, 5

The sum of the terms is given as:

= 34 + 31 + 94 + 40 + 0 + 17 + 5

= 221

The number of terms = 7

Substitute into the formula

Mean = 221/ 7

Mean = 31. 571

In 2 decimal place

Mean = 31. 57

Thus, the mean lifetime of a bulb is 31. 57

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Answer:

yes? im pretty sure yeah

Step-by-step explanation:

Considering the definition of an equation and the way to solve it, the number of miles in a day at which the rental costs for Company A and Company B are the same is 200.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.

The members of an equation are each of the expressions that appear on both sides of the equal sign.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

First, you define the variable "m" as the number of miles rented from a truck to a company in a day. You know that:

So the price of each company is:

If the rental costs for Company A and Company B are the same, the equation in this case is:

Price of company A= Price of company B

130 + 0.30m= 70 + 0.60m

Solving:

130 - 70= 0.60m - 0.30m

60= 0.30m

60÷0.30= m

200= m

In summary, the number of miles in a day at which the rental costs for Company A and Company B are the same is 200.

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Answer:

The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.

Step-by-step explanation:

It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).

It is asked to find the linear equation which passes through the given points.

To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,

\($m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$\)

Substitute b+1&b for \($y_{2}$\) and \($y_{1}$\) respectively, and a&a for \($x_{2}$\) and \($x_{1}$\) respectively in the above formula. Then simplify to get the slope as follows,

\(m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$\)

b+1. So the equation of the line cannot be found using the general point-slope form equation.

Step 2 of 2

Write the equation of the line.

So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.

Answer:

Step-by-step explanation:

To solve the inequality, we need to isolate y on one side of the inequality sign. We can do this by adding 21 to both sides of the inequality:

y - 21 + 21 < 85 + 21

Simplifying, we get:

y < 106

So, the solution to the inequality is y < 106.

When graphing the solution on a number line, we would put an open circle at 106 and draw the line towards the left, indicating that y can take on any value less than 106.

Answer:

15.62 feet

Step-by-step explanation:

If the flagpole is 10ft tall and the shadow is 12ft long, and you need to find the distance from the top of the flagpole to the far end of the shadow, to get your answer, you must use the pythagorean theorum.

\(a^{2} + b^{2} = c^{2}\)

let height of flagpole = a

let length of shadow = b

let distance between the two = c

\(10^{2} + 12^{2} = c^{2} \\100 + 144 = c^{2}\\244 = c^{2}\\\sqrt{244} = \sqrt{c^{2}} \\\sqrt{244} = c\\15.62 = c\)

The Value of the horizontal asymptote is 0

What is horizontal asymptote?

The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute \(x=\)±∞. We can also find the vertical asymptote.

now we are given a function

\(f(x)=2(3)^{-x}\)

Now substitute x=±∞ in the equation, as the x in denominator we get

f(x)= 0

This is the value of the horizontal asymptote

Hence the value of horizontal asymptote comes out to be 0

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the concentration of cells in the original sample is approximately 2.12 x 10^10 cells/mL.

To determine the concentration of cells in the original sample, we need to use the dilution factor and the count of colonies.

Given:

Number of colonies counted = 212

Volume plated = 0.1 mL

Dilution factor = 1 x 10^(-6)

The dilution factor represents the ratio of the volume of the original sample to the volume plated. To calculate the concentration of cells in the original sample, we can use the formula:

Concentration = (Number of colonies counted) / (Volume plated * Dilution factor)

Concentration = 212 / (0.1 mL * 1 x 10^(-6))

To simplify the calculation, we convert the volume from milliliters to liters:

Concentration = 212 / (0.1 L * 1 x 10^(-6))

Concentration = 212 / (1 x 10^(-8))

Concentration = 212 * 10^8

Concentration = 2.12 x 10^10 cells/mL

Therefore, the concentration of cells in the original sample is approximately 2.12 x 10^10 cells/mL.

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