Evaluate using the integration by Parts formula
∫(2x+9)e^x
dx; u=2x+9, dv=e^x dx

The amount of soil needed to fill the garden box is given as follows:

1728 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

V = 19 x 12 x 6 + 10 x 3 x 12

V = 1728 ft³.

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We can use the Pythagoras theorem, to solve the right-angled triangle.

What is a right-angled triangle?

A right triangle is a type of triangle that has one 90-degree angle, also known as a right angle. The sides of a right triangle can be classified as the hypotenuse (the side opposite the right angle) and the legs (the two sides that form the right angle).

To solve a right triangle given the length of one leg and the measure of one acute angle, you can use the Pythagorean theorem or trigonometric functions.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This can be written as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

Hence, we can use the Pythagoras theorem, to solve the right-angled triangle.

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The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

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Work Shown:

1/500 = 0.002 is the probability of winning $390

3/500 = 0.006 is the probability of winning $230

16/500 = 0.032 is the probability of winning $170

Multiply the probabilities with their respective winnings

0.002*390 = 0.78

0.006*230 = 1.38

0.032*170 = 5.44

Then add up those results

0.78+1.38+5.44 = 7.60

which is the expected value.

Side note: This game is not a fair game because mathematically a "fair game" is defined as such where the expected value is 0; ie, neither the player nor the dealer win and things break even.

An appropriate theorem to show that the given set, W, is a vector space. A specific example can be

\(\left[\begin{array}{ccc}p\\q\\r\end{array}\right]\) , -p- -3q = s  and 3p = -2s - 3r

Sets represent values ​​that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.

The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.

The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.

The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.

Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is

S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties

u +v =y+ u and (u + v)+w=u + (v +W).

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Answer:

All the points are the same distance from the center of line AB, therefore it is just the same triangle but rotated. They are the same triangle .

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

IM NOT SUPER SURE

A piecewise function is a function that behaves differently in different intervals of its domain.

The answers are:

a)

f(x) = x*$2.00    if 0 ≤ x ≤ 100

f(x) = x*$1.75     if  100 < x ≤ 250

f(x) = x*$1.25     if    x > 250.

b)  $306.25

The given information is:

The first 100 cupcakes cost $2.00 each.

If the order is between 100 and 250 cupcakes, the cost is $1.75 each.

If the order is more than 250 cupcakes, the cost is $1.25 each.

a) Now we want to write the piecewise function, this will be:

f(x) = x*$2.00    if 0 ≤ x ≤ 100

f(x) = x*$1.75     if  100 < x ≤ 250

f(x) = x*$1.25     if    x > 250.

Above you can see the piecewise function, when you want to evaluate it, the first thing you need to do is to find at which interval the input belongs.

b) If you order 175 cupcakes you have x = 175.

This belongs to the second interval ( 100 < x ≤ 250) then we will use the second part of the function:

f(175) = 175*$1.75 = $306.25

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Recall that in Linear Functions, we wrote the equation for a linear function from a graph. Now we can extend what we know about graphing linear functions to analyze graphs a little more closely. Begin by taking a look at Figure 8. We can see right away that the graph crosses the y-axis at the point (0, 4) so this is the y-intercept.

Then we can calculate the slope by finding the rise and run. We can choose any two points, but let’s look at the point (–2, 0). To get from this point to the y-intercept, we must move up 4 units (rise) and to the right 2 units (run). So the slope must be

\displaystyle m=\frac{\text{rise}}{\text{run}}=\frac{4}{2}=2m=

​run

​

​rise

​​ =

​2

​

​4

​​ =2

Substituting the slope and y-intercept into the slope-intercept form of a line gives

\displaystyle y=2x+4y=2x+4

HOW TO: GIVEN A GRAPH OF LINEAR FUNCTION, FIND THE EQUATION TO DESCRIBE THE FUNCTION.

Identify the y-intercept of an equation.

Choose two points to determine the slope.

Substitute the y-intercept and slope into the slope-intercept form of a line.

EXAMPLE 4: MATCHING LINEAR FUNCTIONS TO THEIR GRAPHS

Match each equation of the linear functions with one of the lines in Figure 9.

\displaystyle f\left(x\right)=2x+3f(x)=2x+3

\displaystyle g\left(x\right)=2x - 3g(x)=2x−3

\displaystyle h\left(x\right)=-2x+3h(x)=−2x+3

\displaystyle j\left(x\right)=\frac{1}{2}x+3j(x)=

​2

​

​1

​​ x+3

Graph of three lines, line 1) passes through (0,3) and (-2, -1), line 2) passes through (0,3) and (-6,0), line 3) passes through (0,-3) and (2,1)

Figure 9

SOLUTION

Analyze the information for each function.

This function has a slope of 2 and a y-intercept of 3. It must pass through the point (0, 3) and slant upward from left to right. We can use two points to find the slope, or we can compare it with the other functions listed. Function g has the same slope, but a different y-intercept. Lines I and III have the same slant because they have the same slope. Line III does not pass through (0, 3) so f must be represented by line I.

This function also has a slope of 2, but a y-intercept of –3. It must pass through the point (0, –3) and slant upward from left to right. It must be represented by line III.

This function has a slope of –2 and a y-intercept of 3. This is the only function listed with a negative slope, so it must be represented by line IV because it slants downward from left to right.

This function has a slope of \displaystyle \frac{1}{2}

​2

​

​1

​​  and a y-intercept of 3. It must pass through the point (0, 3) and slant upward from left to right. Lines I and II pass through (0, 3), but the slope of j is less than the slope of f so the line for j must be flatter. This function is represented by Line II.

Now we can re-label the lines as in Figure 10.

Figure 10

Finding the x-intercept of a Line

So far, we have been finding the y-intercepts of a function: the point at which the graph of the function crosses the y-axis. A function may also have an x-intercept, which is the x-coordinate of the point where the graph of the function crosses the x-axis. In other words, it is the input value when the output value is zero.

To find the x-intercept, set a function f(x) equal to zero and solve for the value of x. For example, consider the function shown.

\displaystyle f\left(x\right)=3x - 6f(x)=3x−6

Set the function equal to 0 and solve for x.

⎧

⎪

⎪

⎨

⎪

⎪

⎩

0

=

3

x

−

6

6

=

3

x

2

=

x

x

=

2

The graph of the function crosses the x-axis at the point (2, 0).

Q & A

Do all linear functions have x-intercepts?

No. However, linear functions of the form y = c, where c is a nonzero real number are the only examples of linear functions with no x-intercept. For example, y = 5 is a horizontal line 5 units above the x-axis. This function has no x-intercepts.

Graph of y = 5.

Figure 11

A GENERAL NOTE: X-INTERCEPT

The x-intercept of the function is value of x when f(x) = 0. It can be solved by the equation 0 = mx + b.

EXAMPLE 5: FINDING AN X-INTERCEPT

Find the x-intercept of \displaystyle f\left(x\right)=\frac{1}{2}x - 3f(x)=

​2

​

​1

​​ x−3.

SOLUTION

Set the function equal to zero to solve for x.

\displaystyle \begin{cases}0=\frac{1}{2}x - 3\\ 3=\frac{1}{2}x\\ 6=x\\ x=6\end{cases}

​⎩

​⎪

​⎪

​⎪

​⎪

​⎪

​⎨

​⎪

​⎪

​⎪

​⎪

​⎪

​⎧

​​  

​0=

​2

​

​1

​​ x−3

​3=

​2

​

​1

​​ x

​6=x

​x=6

​​  

The graph crosses the x-axis at the point (6, 0).

Analysis of the Solution

A graph of the function is shown in Figure 12. We can see that the x-intercept is (6, 0) as we expected.

Figure 12. The graph of the linear function \displaystyle f\left(x\right)=\frac{1}{2}x - 3f(x)=

​2

​

​1

Answer:

Part A: 7n + 30= -5 and 8n + 40= 16

Part B: 7(8) + 30= 86 and 8(8) + 40= 104

Part C: Company A saves you 12.

Step-by-step explanation:

Company A: 7n + 30

Company B: 8n + 40

7n + 30= -5       8n + 40= 16

7(8) +30= 86     8(8) +40= 104

7(2) + 30= 44    8(2) + 40= 56

56 - 44= 12

The given expression, -7/8 - 2 1/6 in the simplest form will be -146/48..

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that, the expression is, -18/5-3 4/5.

We have to show the mixed number in simplest form.

We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

= -7/8 - 2 1/6

= -7/8 - 13/6

= (-42-104) / 48

= -146/48

Thus, the given expression, -8/15-3 4/5 in the simplest form will be -146/48.

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Answer:

13/2, 6 5/9, 6.99, 6.992

Step-by-step explanation:

Answer:

20/27

Step-by-step explanation:

Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( \(\frac{3-3}{2}\) , \(\frac{1-7}{2}\) ) = ( \(\frac{0}{2}\) , \(\frac{-6}{2}\) ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = \(\sqrt{(3-0)^2+(1-(-3)^2}\)  

 = \(\sqrt{3^2+(1+3)^2}\)

 = \(\sqrt{3^2+4^2}\)

 = \(\sqrt{9+16}\)

 = \(\sqrt{25}\)

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

Answer:

30

Step-by-step explanation:

To find the number of different outfits:

3*5*2 = 30

They can choose from 30 different outfits.

The sequence of transformations used to show the congruence of polygons JKLMN and PQRST is to reflect PQRST across the y-axis and then translate the result down 10 units.

We are given two polygons. Both the polygons are congruent, and to prove it, we can use the concept of transformations. The first transformation we need to perform is to reflect the polygon PQRST across the y-axis. The next transformation that needs to be performed is to translate the result down by 10 units. We find that the polygon PQRST now coincides with the polygon JKLMN. Hence, it is proved that the polygons are congruent to each other.

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The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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The sampling method commonly used for a life-work balance survey is probability sampling, specifically stratified random sampling. This approach involves dividing the target population into different strata or categories based on relevant characteristics (e.g., age, gender, occupation).

Limitations associated with this sampling method include:

1. Non-response bias: There is a possibility that not all selected individuals will participate in the survey, leading to non-response bias. Those who choose not to participate may have different perceptions of life-work balance, which can affect the generalizability of the findings.

2. Sampling error: Probability sampling aims to reduce sampling error by providing a representative sample of the population. However, there is still a chance that the selected sample may not perfectly reflect the entire population, resulting in sampling error. The extent of sampling error can be quantified using measures such as confidence intervals.

3. Limited generalizability: While probability sampling provides a more representative sample, the findings may still have limited generalizability to populations with different characteristics or contexts. It is important to consider the specific characteristics of the sample and the context in which the survey was conducted when interpreting and applying the results.

4. Cost and time constraints: Probability sampling can be time-consuming and expensive, especially when the target population is large or geographically dispersed. Practical constraints may limit the ability to survey a truly representative sample, and compromises may need to be made.

Overall, while probability sampling is a widely accepted method for achieving representative samples in surveys, it is essential to acknowledge and consider its limitations to ensure accurate interpretation and application of the survey findings.

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Answer:

y=-2.5-5/4x and no it doesn't pass through (4,12)

Step-by-step explanation:

5x-4y=10

-5x     +5x

-4y=10+5x

/-4     /-4

y=-2.5-5/4x

Answer:

The son age is 10 years

And, his mother age be 40 years

Step-by-step explanation:

Given that

The mother is four times the age of her son

And,  in 5 years, she will be three times as old as him

We need to find out the ages of both

Here we assume that the age of her son be x

So the mother age be 4x

Now in 5 years, her mother would be 3 times as old as his son

So,

4x + 5 = 3(x + 5)

4x + 5 = 3x + 15

x = 10

The son age is 10 years

And, his mother age be 40 years

Answer:

that is corresponding

Answer:

1.9  could  be 3/4 but 5.025 kilograms

Step-by-step explanation:

3/4 of the apples and pairs r the pairs since u said 1/4 of the apples and pairs r the apples so it is 3/4 for the fraction of the killiograms.

The given velocity components are:

u = 2xt - 3xyz + 4xyw = 3x - 5yzt + yz

To satisfy the continuity equation, the third velocity component must be of the form

v = -ux - wy

Thus,v = -2xt + 3xyz - 4xy (from u)v = -3x + 5yz t - yz (from w)

The third velocity component

v = -2xt + 3xyz - 4xy - 3x + 5yz t - yz

= -2xt + 3xyz - 4xy - 3x + 5yz (t - 1)

The velocity of the fluid particle is given by,

v = (u, v, w) = (2t, -2t + 3z, 3 - 5zt + y)at (1, 0, 1) and t = 1 (last digit),v = (2, -2, -2)

The acceleration of the fluid particle is given by,

a = (at, av, aw)

= (∂u/∂t, ∂v/∂t, ∂w/∂t)at (1, 0, 1) and t = 1 (last digit),a = (2, 3, -5)

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Answer:

The domain of the inverse of this function is the range of the function. So the domain of the inverse of this function is

-6 < x < 4.

Answer:

The domain of the inverse function is -6 ≤ x ≤ 4.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

From inspection of the given graph, the endpoints are (-1, -6) and (1, 4).

The closed circles indicate the values are included in the interval.

Therefore, the domain of the graphed function is -1 ≤ x ≤ 1.

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph, the endpoint (-1, -6) is the minimum point and the endpoint (1, 4) is the maximum point.

The closed circles indicate the values are included in the interval.

Therefore, the range of the graphed function is -6 ≤ y ≤ 4.

The domain of the inverse function is the range of the original function (and the range of the inverse function is the domain of the original function).

Therefore, the domain of the inverse function is -6 ≤ x ≤ 4.

\(\hrulefill\)

Note: There is an error in the answer options. The domain includes both endpoints: -6 ≤ x ≤ 4.

Answer:

j > 3  hope this helps =)

The rate of increase of the radius is 0.025 in/sec.

A three-dimensional object with a sphere-like shape. A sphere has no vertices or edges, unlike other three-dimensional shapes. The distances between each point on its surface and its center are equal.

In other words, the distance between any two points on the surface and the sphere's center is equal. The formula for the Volume of the sphere is given by

Volume of sphere = (4/3)πr³

Where, r = radius of the sphere

Here we have

A sphere is increasing in volume at the rate of 20 in³/s.  

Here we need to find at what rate the radius of the sphere increases when the radius is 4 in.

Let v = Volume of the sphere at time t

=> Change in Volume = dv/dt  = 20

r = Radius of the sphere at time t

As we know, the Volume of the sphere, v = (4/3)πr³

Differentiate the Volume of the sphere with respect to t

=> dv/dt = (4/3)3πr³⁻¹)(dr/dt)

=> dv/dt = 4πr² (dr/dt)

=>  20 = 4πr² (dr/dt)  

=>  5 = πr² (dr/dt)  

Given that radius, r = 4

=> 5 = π4² (dr/dt)  

=> 5 = (22/7) 64 (dr/dt)  

=> 5 = 3.14(64) (dr/dt)  

=> dr/dt = (5/3.14 × 64)  

=> dr/dt = 0.024880573

=> dr/dt = 0.025

Therefore,

The rate of increase of the radius is 0.025 in/sec.

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The equivalent under modulus 7 of 139 and 450 is not same. A modulus is the whole-number remainder in a division equation. It can be calculated using the modulo operation. It helps determine whether or not a given integer is odd or even. Therefore, we can solve this problem by utilizing the modulo function.

Modulus refers to the process of converting a decimal number into a whole number. It is used to determine if a number is even or odd by looking at the last digit. If the last digit is even, the number is even. If the last digit is odd, the number is odd. The remainder after division is the modulus.

The symbol for modulus is % .To see if 139 and 450 are equivalent under modulus 7 or not, we will do the following:

We'll convert 139 to its remainder under modulus 7 using the modulo function.

139 % 7 = 4

We'll convert 450 to its remainder under modulus 7 using the modulo function.

450 % 7 = 3

Now, since both remainders are not the same, we can say that 139 and 450 are not equivalent under modulus 7.

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The response of the system to a unit impulse input is given by \(.\)y(t) = -1 + 3e^(-3t) - 3e^(-t) + 2t e^(-t).

Given transfer function is:

G(s) = Y(s) / V(s) = S+6 / s(s + 3)(s + 1)²

a. Zeros and poles of sys.

Zeros are the values of s where the transfer function G(s) is zero. The zeros of the given system can be obtained by equating the numerator to zero,

so

S + 6 = 0

S = -6

Zeros of the system are -6.

Poles are the values of s where the transfer function G(s) is undefined.

The poles of the given system can be obtained by equating the denominator to zero, so

s(s + 3)(s + 1)² = 0

s = 0, -3, -1

Poles of the system are 0, -3, -1.

b. Find partial fraction expansion.

The given transfer function can be expressed in partial fractions as:

S+6 / s(s + 3)(s + 1)²

= A/s + B/(s + 3) + C/(s + 1) + D/(s + 1)²

Where A, B, C, and D are constants.To solve for these constants, we have to multiply both sides by the common denominator of the fractions and equate the coefficients of the terms with the same degree.

On doing so, we get:

S + 6 = A(s + 3)(s + 1)² + B s(s + 1)² + C s(s + 1)² + D s(s + 3)

On substituting s = -3, we get

B = 3

On substituting s = -1, we get

C - D = -5

On substituting s = 0, we get

A = -1

Simplifying the above equation, we get

C = -3 and D = 2

Substituting these values of A, B, C, and D in the partial fraction expansion, we get:

S+6 / s(s + 3)(s + 1)²

= -1/s + 3/(s + 3) - 3/(s + 1) + 2/(s + 1)²

c. Find the response of sys if the input is a unit impulse.

The Laplace transform of a unit impulse is 1.

Hence the response of the system to a unit impulse input can be obtained by evaluating the inverse Laplace transform of the transfer function G(s) multiplied by the Laplace transform of the input, which is 1.

G(s) = -1/s + 3/(s + 3) - 3/(s + 1) + 2/(s + 1)²

The inverse Laplace transform of the above transfer function is

y(t) = -1 + 3e^(-3t) - 3e^(-t) + 2t e^(-t).

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