if anyone can help me that would be great

The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

To know more about antiderivative refer here:

https://brainly.com/question/33243567

#SPJ11

Answer:

21√7

Step-by-step explanation:

The actual length and width of the kitchen in the scale drawing is: 22.5 ft x 17.5 ft

A scale drawing is defined as an enlargement of an object. An enlargement changes the size of an object by multiplying each of the lengths by a scale factor to make it larger or smaller. The scale of a drawing is usually stated as a ratio.

Now, the scale factor of the given drawing is seen as 2 in : 5 ft

From the drawing the dimensions of the kitchen are:

9" x 7"

Thus:

True length = (9 * 5)/2 = 22.5 ft

True width = (7 * 5)/2 = 17.5 ft

Read more about Scale Drawing at: https://brainly.com/question/15891755

#SPJ1

Answer:

\(-\frac{2}{\sqrt{2}}\) or \(-\sqrt{2}\)

Step-by-step explanation:

\(\sec{x}\) is the reciprocal of \(\cos{x}\), or in symbols: \(\sec{x}=\frac{1}{\cos{x}}\). \(\tan{x}\) is also the ratio of \(\sin{x}\) to \(\cos{x}\), and we can multiply both sides of the equation \(\tan{x}=\frac{\sin{x}}{\cos{x}}\) by \(\frac{1}{\sin{x}}\) to get the equation \(\frac{\tan{x}}{\sin{x}}=\frac{1}{\cos{x}}\). Of course, this is just the definition of \(\sec{x}\), so we can rewrite this fact as \(\sec{x}=\frac{\tan{x}}{\sin{x}}\).

In this problem, we're given that \(\sin{x}=\frac{\sqrt{2} }{2}\) and \(\tan{x}=-1\), so plugging those two values into our equation gives us

\(\sec{x}=\dfrac{-1}{\frac{\sqrt{2}}{2}} =-\frac{2}{\sqrt{2}}\)

We could leave our solution as \(-\frac{2}{\sqrt{2}}\), or we could rationalize the denominator to get a solution of

\(-\frac{2}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=-\frac{2\sqrt{2}}{2}=-\sqrt{2}\)

Answer:

52

Complementary Angles:

Two angles that add up to 90.

The Weighted Average Cost of Capital (WACC) for Snuggly Baby Corp. is calculated based on the company's capital structure, including common equity, preferred equity, and bonds. The WACC is influenced by the expected returns and prices of these securities.

To calculate the WACC, we need to determine the proportion of each component in the capital structure and multiply it by its respective cost of capital.

For Snuggly Baby Corp., the capital structure consists of 6,130,000 shares of common equity, 1,006,000 shares of preferred equity, and 81,400 bonds.

The cost of common equity is calculated using the expected return and the price of the shares. Similarly, the cost of preferred equity is calculated using the expected return and the price of the preferred shares. The cost of debt, represented by the bonds, is calculated using the yield-to-maturity.

Once we have the costs of each component, we multiply them by their respective proportions in the capital structure and sum them up to determine the overall WACC. Please note that to provide an accurate calculation of the WACC, additional information is required, such as the market value of each component and the weights assigned to them in the capital structure. Without this information, it is not possible to provide an exact WACC calculation.

learn more about Weighted Average Cost of Capital (WACC) here:

https://brainly.com/question/30746642

#SPJ11

Answer:

Curl ups

Step-by-step explanation:

I'm not 100% sure, but it seems like the most logical answer to me.

Answer:

Trunk Lift

Step-by-step explanation:

To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

Learn more about maximum area click;

https://brainly.com/question/29635164

#SPJ12

Horizontal translation for a parabola is changed by the value of a variable, h, that is subtracted from x before the squaring operation.

Our reference parabola has the following equation:

And the equation that includes a horizontal translation looks like this:

The sign of h is determined by whether the translated parabola is on the right (positive sign) or on the left (negative sign) side of the reference parabola, in this case, the vertex of the parabola is translated 3 units to the left, then h equals -3, replacing this value for h, we get:

Then, the correct answer is option D, G(x) = (x+3)^2

Answer:

The value of tan(3π/4) is indeed -1.

Now, to evaluate tan(3π/4 - π), we can use the following trigonometric identity:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)*tan(b))

Applying this identity to the expression tan(3π/4 - π), we get:

tan(3π/4 - π) = (tan(3π/4) - tan(π)) / (1 + tan(3π/4)*tan(π))

Substituting the values of tan(3π/4) = -1 and tan(π) = 0, we get:

tan(3π/4 - π) = (-1 - 0) / (1 + (-1)*0) = -1

So the value of tan(3π/4 - π) is also -1, which is the same as the value of tan(3π/4).

In other words, the value of tan(3π/4 - π) is equal to the value of tan(3π/4) because π is equal to 180 degrees, which is a full rotation. Subtracting a full rotation from an angle simply results in an equivalent angle in the opposite direction. Thus, the values of tangent for both angles remain the same.

0, becous A (-1x2) can't be negative.

Answer:

y = 1/2x - 3

Step-by-step explanation:

The line intercepts with the y-axis at -3 and its pattern is going right two and up one.

Answer:

-4

Step-by-step explanation:

3/2 = k + 11/2

Add  -11/2 to each side using the addition property  of equality

3/2 + -11/2 = k + 11/2+ -11/2

-8/2 = k

Simplify

-4 =k

Solution of k = -4 after applying the property of equality of addition and subtraction operation.

"Properties of equality represents the relation between two equal quantities after applying any operation on left hand side same has to be applied on the right hand side to make the balance in the given equation."

According to the question,

(3 / 2) = k + (11 / 2)

Here given operation is addition,

Apply inverse operation of addition,

Case1: Subtract 11/2 from both the sides we have,

   (3 /2) - (11 / 2) = k + (11/ 2) - (11 / 2)

⇒ ( -8 /2) = k

⇒ k = -4

Case 2. Add  ( - 11 /2) to both the sides we have,

  ( 3/ 2) + ( -11 /2) = k +( 11 /2) + (-11/ 2)

⇒( -8 /2) = k

⇒k = -4

Hence, solution of k = -4 after applying the property of equality of addition and subtraction.

Learn more about properties of equality here

https://brainly.com/question/13130806

#SPJ2

f(t) = t and g(t) = \(e^{(2t)\) form a linearly independent set of functions.

To show that the functions f(t) = t and g(t) = \(e^{(2t)\) are linearly independent, we can calculate their Wronskian and verify that it is nonzero for all values of t.

The Wronskian of two functions f(t) and g(t) is defined as the determinant of the matrix:

| f(t) g(t) |

| f'(t) g'(t) |

Let's calculate the Wronskian of f(t) = t and g(t) = \(e^{(2t)\):

f(t) = t

f'(t) = 1

g(t) = \(e^{(2t)\)

g'(t) = 2\(e^{(2t)\)

Now we can form the Wronskian matrix:

| t \(e^{(2t)\)|

| 1 2\(e^{(2t)\) |

The determinant of this matrix is:

Det = (t * 2\(e^{(2t)\)) - (1 * \(e^{(2t)\))

      = 2t\(e^{(2t)\) - \(e^{(2t)\)

      = \(e^{(2t)\) (2t - 1)

We can see that the determinant of the Wronskian matrix is not zero for all values of t. Since the Wronskian is nonzero for all t, it implies that the functions f(t) = t and g(t) = \(e^{(2t)\) are linearly independent.

Therefore, f(t) = t and g(t) = \(e^{(2t)\) form a linearly independent set of functions.

Learn more about Linearly Independent at

brainly.com/question/30575734

#SPJ4

Answer:

D, \(w\geq 23\)

Step-by-step explanation:

The length is 6 inches longer than it's width, therefore:

\(l=w+6\)

The area of the rectangle is AT LEAST 667 square inches, so:

\(lw\geq 667\)

Now, we have a system of two equations:

\(\left \{ {{l=w+6} \atop {lw\geq 667}} \right.\)

We want to isolate the width, so substitute the first equation into the second to eliminate the length.

\((w+6)w\geq 667\)

Simplify:

\(w^2+6w\geq 667\)

Since we now have a polynomial equation that needs to be factored, set the value of one side to 0.

\(w^2+6w-667\geq 0\)

Now factor the equation:

\((w-23)(w+29)\geq 0\)

Taking each factor individually, we find the following:

\(w\geq 23\\w\geq -29\)

Since a negative width doesn't make any sense, we can eliminate that solution, and we are left with the correct answer!

\(w\geq 23\)

A number which is 15 more than twice a number is 37 is 11.

Let the number be N.

Let's set up the equation.

A number is 15 more than twice a number is 37,

2N + 15 = 37

Let's subtract 15 from both sides.

2N = 22

Divide both sides by 2, and you get

N = 11

So the number which is 15 more than twice a number is 37 is 11.

A number system is a means of representing numbers. It is a method of representing numbers in a set of numbers consistently by using digits or other symbols. Each number receives a unique representation as well as information about the arithmetic and algebraic structure of the numbers. Addition, subtraction, multiplication, and division are just a few of the mathematical operations we may carry out using it.

Learn more about Number problems:

https://brainly.com/question/4697588

#SPJ4

Answer:

your answer would be B I hope it's right

Answer:

B)

Step-by-step explanation:

I hope this helps:)

Growth Decay

2x, ƒ(x) = (1)²*, 3x, f(x) = (1.3)³x - Growth

f(x) = (0.8)*2, f(x) = (-²)*2 - Decay

(The functions are categorized as either representing growth or decay.)

Growth Decay

2x - Growth (The function 2x represents exponential growth because as x increases, the value of 2x also increases.)

ƒ(x) = (1)²* - Growth (The function ƒ(x) = (1)² represents exponential growth because any number raised to the power of 2 will always be positive.)

f(x) = (7)x-¹ - Decay (The function f(x) = (7)x-¹ represents exponential decay because as x increases, the value of (7)x-¹ decreases.)

3x - Growth (The function 3x represents exponential growth because as x increases, the value of 3x also increases.)

f(x) = (1.3)³x - Growth (The function f(x) = (1.3)³x represents exponential growth because as x increases, the value of (1.3)³x also increases.)

f(x) = (0.8)*2 - Decay (The function f(x) = (0.8)*2 represents exponential decay because any number raised to the power of 2 will always be positive, and multiplying by 0.8 reduces the value.)

f(x) = (-²)*2 - Decay (The function f(x) = (-²)*2 represents exponential decay because any number raised to the power of 2 will always be positive, but the negative sign in front indicates a decay.)

For more such questions on Growth Decay, click on:

https://brainly.com/question/29634879

#SPJ11

Answer:

i think 58, but if not, go to khan academy and watch a video!

Step-by-step explanation:

Answer:

you would see which bank has a good business and have loyal customers and which one is giving you a better offer

Step-by-step explanation:

HOPE THIS HELPED!

Answer:

e.

Step-by-step explanation:

Answer:

discount=30%

hope it helps.

Answer:

did you use google.if not use it it is good to use.

If it is not true, then the relation is not an implicit solution to the differential equation.

You have not provided the given relation and differential equation, so I will provide general steps to determine whether a given relation is an implicit solution to a differential equation using implicit differentiation and assuming that the relation defines y implicitly as a function of x.

1. Differentiate the relation with respect to x using implicit differentiation.

2. Substitute y' for dy/dx.

3. Simplify the resulting expression by collecting like terms.

4. Substitute the original relation into the simplified expression to obtain a statement that must be true if the relation is an implicit solution to the differential equation.

5. Check whether the resulting statement is true for all values of x and y that satisfy the original relation. If it is true, then the relation is an implicit solution to the differential equation.

To learn more about : equation

https://brainly.com/question/17145398

#SPJ8

The phase of inferential statistics which is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct is "data gathering".

Inferential statistics are frequently employed to compare treatment group differences.

Some characteristics of inferential statistics are-

To know more about the inferential statistics, here

https://brainly.com/question/4774586

#SPJ4

Therefore, if the 300th day of year N is a Tuesday, the 100th day of year N-1 will be a Sunday.

To determine the day of the week on the 100th day of year N-1, we need to analyze the given information and make use of the fact that there are 7 days in a week.

Let's break down the given information:

In year N, the 300th day is a Tuesday.

In year N+1, the 200th day is also a Tuesday.

Since there are 7 days in a week, we can conclude that in both years N and N+1, the number of days between the two given Tuesdays is a multiple of 7.

Let's calculate the number of days between the two Tuesdays:

Number of days in year N: 365 (assuming it is not a leap year)

Number of days in year N+1: 365 (assuming it is not a leap year)

Days between the two Tuesdays: 365 - 300 + 200 = 265 days

Since 265 is not a multiple of 7, there is a difference of days that needs to be accounted for. This means that the day of the week for the 100th day of year N-1 will not be the same as the given Tuesdays.

To find the day of the week for the 100th day of year N-1, we need to subtract 100 days from the day of the week on the 300th day of year N. Since 100 is a multiple of 7 (100 = 14 * 7 + 2), the day of the week for the 100th day of year N-1 will be two days before the day of the week on the 300th day of year N.

To know more about year,

https://brainly.com/question/28206231

#SPJ11

The value of x using Pythagoras theorem is: x = √118 mi

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Thus:

x = √(12² - (√26)²)

x = √(144 - 26)

x = √118 mi

Read more about Pythagoras theorem at: https://brainly.com/question/231802

#SPJ1

Answer:

16

Step-by-step explanation:

Answer:

The answer 14

Step-by-step explanation: