f the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11)

The value of the improper integral ∫[0 to 1] arctan(√(x/(1-x))) dx is π/4.

To evaluate the improper integral

∫[0 to 1] arctan(√(x/(1-x))) dx,

we can use a trigonometric substitution. Let's substitute x = sin²θ, which gives dx = 2sinθcosθ dθ and modifies the limits of integration as well.

When x = 0, sin²θ = 0, and when x = 1, sin²θ = 1. Therefore, the new limits of integration are θ = 0 to θ = π/2.

Now, let's substitute these expressions into the integral:

∫[0 to 1] arctan(√(x/(1-x))) dx

= ∫[0 to π/2] arctan(√(sin²θ/(1-sin²θ))) * 2sinθcosθ dθ

= 2∫[0 to π/2] arctan(√(sin²θ/cos²θ)) * sinθcosθ dθ.

Simplifying inside the arctan, we have:

√(sin²θ/cos²θ) = √tan²θ = tanθ.

Substituting this back into the integral, we get:

2∫[0 to π/2] arctan(tanθ) * sinθcosθ dθ.

Since arctan(tanθ) is equivalent to θ for 0 ≤ θ < π/2, the integral becomes:

2∫[0 to π/2] θ * sinθcosθ dθ.

We can rewrite sinθcosθ as (1/2)sin(2θ):

2∫[0 to π/2] θ * (1/2)sin(2θ) dθ

= ∫[0 to π/2] θ * sin(2θ) dθ.

Now, we can integrate by parts with u = θ and dv = sin(2θ) dθ:

∫ u dv = uv - ∫ v du.

Differentiating u = θ gives du = dθ, and integrating dv = sin(2θ) dθ gives v = -(1/2)cos(2θ).

Applying the formula for integration by parts:

∫[0 to π/2] θ * sin(2θ) dθ = [-(1/2)θ * cos(2θ)] from 0 to π/2 - ∫[0 to π/2] (-(1/2)cos(2θ)) dθ

= [-(1/2)(π/2) * cos(π)] - [-(1/2)(0) * cos(0)] - [-(1/2) ∫[0 to π/2] cos(2θ) dθ]

= [-(π/4)(-1)] - [0] - [-(1/2) ∫[0 to π/2] cos(2θ) dθ]

= π/4 + (1/4) ∫[0 to π/2] cos(2θ) dθ.

Now, let's integrate ∫[0 to π/2] cos(2θ) dθ:

∫ cos(2θ) dθ = (1/2)sin(2θ).

Evaluating this integral from 0 to π/2:

∫[0 to π/2] cos(2θ) dθ = (1/2)sin(π) - (1/2)sin(0)

= (1/2)(0) - (1/2)(0)

= 0.

Substituting this result back into the previous expression:

π/4 + (1/4) ∫[0 to π/2] cos(2θ) dθ = π/4 + (1/4)(0)

= π/4.

For more such questions on improper integral

https://brainly.com/question/33372635

#SPJ8

The calculated value of the improper integral [tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx[/tex] is 0.7853

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

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \arctan\left(\frac{\sqrt{x}}{\sqrt{1-x}}\right)\,x+\frac{\sqrt{1-x}\sqrt{x}+\arctan\left(\frac{\sqrt{1-x}}{\sqrt{x}}\right)}{2}[/tex]

When simplified, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \frac{\left(2x-1\right)\arctan\left(\sqrt{\frac{x}{1-x}}\right)+\left(1-x\right)\sqrt{\frac{x}{1-x}}}{2}[/tex]

Recall that the x values are from 0 to 1

This means that

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \frac{\left(2(1)-1\right)\arctan\left(\sqrt{\frac{1}{1-1}}\right)+\left(1-1\right)\sqrt{\frac{1}{1-1}}}{2}- \frac{\left(2(0)-1\right)\arctan\left(\sqrt{\frac{0}{1-0}}\right)+\left(1-0\right)\sqrt{\frac{0}{1-0}}}{2}[/tex]

When evaluated, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = 0.7853[/tex]

Hence, the value of the integral is 0.7853

Read more about derivatives at

brainly.com/question/5313449

#SPJ1

Answer:

Step-by-step explanation:

To determine the share of Winta in the profit, we need to calculate the ratio of her initial investment to the total initial investment and then apply that ratio to the total profit.

Winta's initial investment: Birr 21,000

Lensa's initial investment: Birr 17,500

Total initial investment: Birr 21,000 + Birr 17,500 = Birr 38,500

To find the share of Winta in the profit, we calculate:

Winta's share = (Winta's initial investment / Total initial investment) * Total profit

Winta's share = (Birr 21,000 / Birr 38,500) * Birr 24,600

Simplifying the calculation:

Winta's share = (0.5455) * Birr 24,600

Winta's share ≈ Birr 13,414.55

Therefore, Winta's share in the profit is approximately Birr 13,414.55.

Answer:

19.0285

Step-by-step explanation:

For this, we have to work backwards.

First, the equation for the circumference of a circle is:
[tex]2\pi r[/tex]

We already know the circumference, so we can solve for r:
[tex]119.56=2\pi r[/tex]

divide both sides by 2

[tex]59.78=\pi r[/tex]

divide both sides by pi

[tex]19.0285...=r[/tex]

So, depending on the answer choices, the answer is 19.0285 rounded to the according decimal place.

Hope this helps! :)

The fourth table of values represents an exponential function (Correct choice: D).

Herein we find four tables of values, three representing a linear function and one representing an exponential function. Each function is introduced below:

Linear equation:

n = m + r · n

Exponential function

n = m · rⁿ

Where:

Common rate is the most appropriate criterion to distinguish linear equations of exponential equations. Now we proceed to summarize the results of each table of values:

Case A: Linear equation, r = 8.

Case B: Linear equation, r = 1.

Case C: Linear equation, r = 5.

Case D: Exponential equation: r = 2.

To learn more on exponential functions: https://brainly.com/question/23729449

#SPJ1

Answer:

Step-by-step explanation:

Let x be 1 shirt price

Let y be 1 pant price

we have the following equation

3x+2y = 104.81$ (1)

2x+y = 61.33$ => multiply two sides by 2 => 4x + 2y = 122.66 (2)

=> (2) - (1) => x = 17.85$

So one shirt is 17.85$

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

For more such question on function. visit :

https://brainly.com/question/11624077

#SPJ8

By evaluating f(6) and confirming that it equals zero, we can determine that x - 6 is a factor of the polynomial f(x) = x^4 - 32x^2 - 144.

To determine if x - 6 is a factor of f(x) = x^4 - 32x^2 - 144 using the Factor Theorem, we need to check if f(6) equals zero. If f(6) is zero, then x - 6 is a factor of f(x); otherwise, it is not a factor.

Let's calculate f(6):

f(6) = (6)^4 - 32(6)^2 - 144

= 1296 - 32(36) - 144

= 1296 - 1152 - 144

= 0

Since f(6) equals zero, we can conclude that x - 6 is indeed a factor of f(x).

The Factor Theorem states that if f(c) equals zero, where c is a constant, then x - c is a factor of f(x). In this case, since f(6) is zero, x - 6 is a factor of f(x).

Therefore, the answer is: Yes, x - 6 is a factor of f(x).

For more such question on polynomial. visit :

https://brainly.com/question/4142886

#SPJ8

Answer:

324 cm³

Step-by-step explanation:

Square based pyramid volume formula:
[tex]V=a^2\frac{h}{3}[/tex]

with a being the base length and h being the height

We can substitute in our values:

[tex]V=a^2\frac{h}{3} \\V=9^2\frac{12}{3}\\V=81(4)\\V=324[/tex]

So, the volume is 324 cm³.

Hope this helps! :)

Answer:

1428

Step-by-step explanation:

Area=L×B/W

34×42

=1428

Answer:

Step-by-step explanation:  -3.655 hopefully that works

To simplify the expression 12(3k-3)k^5, we can use the distributive property and simplify each term.First, let's apply the distributive property:

[tex]12 * 3k * k^5 - 12 * 3 * k^5[/tex]

This simplifies to:

[tex]36k * k^5 - 36 * k^5[/tex]

To combine like terms, we add the exponents when multiplying variables with the same base. In this case, both terms have k as the base:

36k * k^5 can be simplified to 36k^6.

Therefore, the expression becomes:

[tex]36k^6 - 36k^5[/tex]

This is the simplified form of the expression 12(3k-3)k^5.

It's important to note that if you have any specific values for k, you can substitute those values into the expression to get the numerical result. Without a specific value for k, we can't simplify it further.

Remember to always double-check the original expression and any specific instructions or context given to ensure you've applied the correct simplification techniques.

For more such questions on distributive property

https://brainly.com/question/4077386

#SPJ8

The domain of the function shown in the graph is given as follows:

B. x ≥ 0.

The values of x in this graph are to the right of x = 0, including x = 0, hence the domain is given as follows:

B. x ≥ 0.

Learn more about domain and range at https://brainly.com/question/26098895

#SPJ1

Answer

a=93

b=74

Step-by-step explanation:

a=180-87=93 b=180-106=74

After 3 days, the two friends will earn the same profit.

To find the number of days after which the two friends will earn the same profit, we need to set the profit functions P(x) and Q(x) equal to each other and solve for x.

P(x) = Q(x)

−x^2 + 5x + 12 = 6x

Rearranging the equation:

−x^2 + 5x + 12 - 6x = 0

Combining like terms:

−x^2 - x + 12 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:

-(x - 3)(x + 4) = 0

Setting each factor equal to zero:

x - 3 = 0 or x + 4 = 0

Solving for x:

x = 3 or x = -4

Both x = 3 and x = -4 are solutions to the equation. However, we need to determine which one is a viable answer and which one is a nonviable answer.

The question asks for the number of days, which cannot be negative. Therefore, x = -4 is a nonviable answer since it represents a negative number of days. The viable answer is x = 3.

for such more question on profit

https://brainly.com/question/1078746

#SPJ8

Answer:

1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.

2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.

3. The solution to the initial value problem is y = t^2 + 4/3.

The farmer should use 660 pounds of the 75% protein supplement and 440 pounds of the 25% protein ration to make 1100 pounds of a high-grade 55% protein ration.

Let 75% protein supplement be x and 25% protein ration be y

The total weight of the mixture is x + y = 1100

The second equation related  to the protein in the mixture is 0.75x + 0.25y = 0.55 × 1100

= 0.75x + 0.25y = 605

By using the elimination method multiply the first equation by 0.25 to match the coefficients of y:

0.25x + 0.25y = 0.25 × 1100

0.25x + 0.25y = 275

by subtracting this equation from the second equation:

0.75 x + 0.25 y - {0.25 x + 0.25y} = 605 - 275

0.75 x - 0.25 x = 330

0.5x = 330

x = 660

by substituting this in the first equation:

660 + y = 1100

y = 440

Learn more about equations here:

https://brainly.com/question/15707224

The correct equation for the parabola is [tex]x^2 = 16(y - 4)[/tex].

The standard equation of the parabola in the graph can be determined based on its characteristics.

Given:

Vertex: (0, 4)

Focus: (4, 4)

P (the distance from the vertex to the focus or directrix): 4

We can conclude that the parabola opens to the right because the axis is horizontal.

The standard equation of a parabola with a horizontal axis and vertex (h, k) is given by:

[tex](x - h)^2 = 4p(y - k)[/tex]

In this case, the vertex is (0, 4), so the equation becomes:

[tex](x - 0)^2 = 4p(y - 4)[/tex]

Now, we need to determine the value of p. The distance from the vertex to the focus is p, which is 4 in this case.

Therefore, the standard equation of the parabola in the graph is:

[tex]x^2 = 4(4)(y - 4)\\x^2 = 16(y - 4)[/tex]

for such more question on parabola

https://brainly.com/question/9201543

#SPJ8

The graph can represent a normal curve because it represent a normal density function. The Option C.

The answer is yes. While these characteristics may deviate from the ideal properties of a normal distribution, they do not necessarily invalidate the possibility of the graph representing a normal density function.

A normal curve can have tails that extend indefinitely allowing for the graph to increase as x becomes very large or very small. Negative values can occur if the graph represents a standard normal distribution which is centered at zero.

Read more about normal curve

brainly.com/question/23418254

#SPJ1

Answer:

Let x be the number we are looking for.

We know that 12 is at most a number decreased by 7, which can be written as:

x - 7 >= 12

To solve for x, we add 7 to both sides of the inequality:

x - 7 + 7 >= 12 + 7

Simplifying, we get:

x >= 19

Therefore, the solution to the inequality is x >= 19.

The answer is:

Work/explanation:

Let w be the number. Now, let's write an inequality to solve for w.

Let's focus on the part that says "at most a number". At most means that the number can't be greater than something, it can only be less than. So the symbol for "at most" is ≤, which also means "less than".

Now, decreased by 7 means we subtract 7 from w.

With all this information, we are ready to write the inequality.

The inequality is:

[tex]\sf{12\leqslant w-7}[/tex]

Now, let's solve it for w.

_________________________

Add 7 on each side

[tex]\sf{12+7\leqslant w}[/tex]

[tex]\sf{19\leqslant w}[/tex]

Answer:

18

Step-by-step explanation:

[tex]\sqrt{x-2} =4\\x-2=16\\x=18[/tex]

Given equation :

[tex] \sqrt{x - 2} = 4[/tex]

Squaring both sides

[tex]( { \sqrt{x - 2} })^{2} = {(4)}^{2} [/tex]

[tex]x - 2 = 16[/tex]

Move all terms containing x to the left, all other terms to the right.

[tex]x = 16 + 2[/tex]

[tex]x = 18[/tex]

Verification:

Put value the x in the given equation.

[tex] \sqrt{x - 2} = 4[/tex]

[tex] \sqrt{18 - 2} = 4[/tex]

[tex] \sqrt {16} = 4[/tex]

[tex] \sqrt {4 \times 4 } = 4[/tex]

[tex]4 = 4[/tex]

Hence, The answer is 18.

The graph that correctly represents Marie's situation is the graph B or the second graph.

For the graph to correctly represent Marie's situation the followin elements are needed:

Note: This question is incomplete; below are the missing graphs:

Learn more about graphs in https://brainly.com/question/17267403

#SPJ1

Answer:

What is the equation?

Step-by-step explanation:

Can't solve it without knowing where c is in the equation

Answer:

First you draw the lines zjkl and then you make an archs to bisect the line using a compass and a pencil first you go to each point and it's corresponding letter you arch then draw a straight line which passes through the arch

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

For more such questions on triangle

https://brainly.com/question/1058720

#SPJ8

Answer:

------------------------

Use coordinates of endpoints, taken from the diagram, B(6, 2) and C(2, - 1) and the distance formula:

Substitute BC for d and given coordinates to find the radius:

Hence the segment BC is 5 units long.

Shan performed better in his science test than in his math test based on the respective scores of 15 out of 20 and 7 out of 10.

To determine which test Shan achieved better results in, we need to compare the scores he obtained in both the math and science tests.

Shan scored 7 out of 10 in his math test, which can be written as a fraction 7/10. This fraction can also be converted to a decimal by dividing 7 by 10, resulting in 0.7.

Similarly, Shan scored 15 out of 20 in his science test, which can be written as a fraction 15/20. This fraction can also be simplified by dividing both the numerator and denominator by 5, resulting in 3/4. Converting this fraction to a decimal by dividing 3 by 4 yields 0.75.

Comparing the decimal values, we can see that 0.75 (science test) is greater than 0.7 (math test). Therefore, Shan achieved better results in his science test compared to his math test.

for such more question on scores

https://brainly.com/question/15222372

#SPJ8

Answer:

37.5

Step-by-step explanation:

the therom of a parallelogram is width*height

so 7.5*5

=37.5

If you found this helpful, please consider giving a brainliest!

Answer:

A = 37.5

Step-by-step explanation:

The area of a parallelogram is:

Area = base × height

In your picture the base is 7.5 and the height is 5.

So multiply 7.5×5 and you get 37.5.

The area is 37.5cm^2

The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

for such more questions on width

https://brainly.com/question/28107004

#SPJ8