Use a sketch to assist in transforming the following integral to polar coordinates. Then evaluate the resulting integral. ∫ -√6 √6 ∫ 0 √6-y^2 cos (x^2 + y^2) dx dy

Answer: -10

Step-by-step explanation:

Simplifying

-3(y + 5) = 15

Reorder the terms:

-3(5 + y) = 15

(5 * -3 + y * -3) = 15

(-15 + -3y) = 15

Solving

-15 + -3y = 15

Solving for variable 'y'.

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

Add '15' to each side of the equation.

-15 + 15 + -3y = 15 + 15

Combine like terms: -15 + 15 = 0

0 + -3y = 15 + 15

-3y = 15 + 15

Combine like terms: 15 + 15 = 30

-3y = 30

Divide each side by '-3'.

y = -10

Simplifying

In question 5, the segment lengths 2, 4, and 8 do not form a triangle. In question 6, the segment lengths 5, 6, and 7 do form a triangle, and it is an acute triangle. In question 7, the segment lengths 6, 8, and 15 do form a triangle, but it is an obtuse triangle. In question 8, the segment lengths 9, 12, and 15 do form a triangle, and it is a right triangle.

5. The sum of the two smaller sides (2 + 4) is less than the length of the largest side (8). Hence, a triangle cannot be formed.

6. The sum of any two sides (5 + 6 > 7, 5 + 7 > 6, 6 + 7 > 5) is greater than the length of the third side. Therefore, a triangle is formed. Since the square of the longest side (7) is less than the sum of the squares of the other two sides (5^2 + 6^2), it is an acute triangle.

7. The sum of the two smaller sides (6 + 8) is greater than the length of the largest side (15). A triangle is formed. Since the square of the longest side (15) is greater than the sum of the squares of the other two sides (6^2 + 8^2), it is an obtuse triangle.

8. The sum of any two sides (9 + 12 > 15, 9 + 15 > 12, 12 + 15 > 9) is greater than the length of the third side. Therefore, a triangle is formed. Since the square of the longest side (15) is equal to the sum of the squares of the other two sides (9^2 + 12^2), it is a right triangle.

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Answer:

The three given points are the vertices of a right triangle.

Step-by-step explanation:

Answer:

The three given points are the vertices of a right triangle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

When making a reflection of a triangle and describing it you would need to provide the following two details. First, over which axis the triangle is being reflected over. Secondly, the exact location of each reflected point of the triangle. Doing so would describe how the triangle is being reflected and which point is ending up in which location. Thus, letting the viewer/reader know exactly what is being done to the triangle.

Answer:

3

Step-by-step explanation:

These are similar triangle

We can use ratios to solve

12         12+4

------ = ----------

9         9+DC

Using cross products

12( 9+DC) = 9*(12+4)

12 (9+DC) = 9*16

Divide each side by 12

12/12 (9+DC) = 9*16/12

9+DC = 12

Subtract 9 from each side

9+DC-9 =12-9

DC =3

Answer:

3 units

Step-by-step explanation:

We can see that triangle ADE is similar to triangle ACB.

Therefore the ratios of the lengths of their sides must be equal.

We can write AD/AC = AE/AB

we are given AD = 9, AE = 12 and AB = 12 + 4 = 16

Substituting the above values into the equation:

AD/AC = AE/AB

9 / AC = 12/16  (rearranging)

(AC)(12) = (9)(16)

AC = (9)(16)/12

AC = 12

We can also see that

DC = AC - AD

DC = 12 - 9

DC = 3 units

The probability that the single server queuing system will contain 6 or more customers is 0.9779 (option d). This means that there is a high likelihood that the system will have at least 6 customers at any given time.

To calculate this probability, we can use the formula for the steady-state probability of the system being in state n or more, which is given by:
P(n or more) = (1 - ρ) * ρ^n / (1 - ρ^(N+1))
where ρ is the traffic intensity (arrival rate / service rate) and N is the number of servers. In this case, we have a single server, so N = 1.
First, we need to calculate the traffic intensity ρ. The arrival rate is 7 customers per hour, and the service rate is 15 customers per hour.
ρ = 7 / 15 = 0.4667
Next, we substitute the values into the formula:
P(6 or more) = (1 - 0.4667) * (0.4667^6) / (1 - 0.4667^(1+1))
P(6 or more) ≈ 0.9779
Therefore, the probability that the system will contain 6 or more customers is approximately 0.9779, or option d.

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Answer:

36x1.5=54

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

First you multiply the 36 by 1, which is 36.

Second you multiply 36 by 1/2 or 0.5. In other terms, that means what is half of 36? 18.

Last, add the two, 18 + 36 = 54

The area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.

To find the area of triangle OBC in terms of r and θ, we can utilize the formula for the area of a triangle: Area = (1/2) * base * height. In this case, the base of the triangle is the side BC, which has a length equal to r, and the height is the perpendicular distance from point O to side BC.

Considering that point O is the origin (0,0) and point B is located on the positive x-axis, the distance from the origin to the line BC is equal to the radius r. Thus, the height of the triangle is r.

To find the angle θ between the positive x-axis and the line BC, we can use trigonometry. Since the line BC forms an angle of θ with the positive x-axis, the perpendicular from point B to the x-axis creates a right triangle. Therefore, sin(θ) can be determined by dividing the height of the triangle (r) by the hypotenuse (also r), resulting in sin(θ) = r/r = 1.

Substituting the values into the formula for the area of a triangle, we have Area = (1/2) * r * r * 1 = (1/2) * r^2.

Therefore, the area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.

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Answer:

30

Step-by-step explanation:

6 - (-24) = 6 + 24 = 30

Method 1:  take the larger number and subtract the smaller number.

Method 2:  The scale on the number line has spaces every 6 units. There are 5 spaces between the two points.  5 x 6 = 30

The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable).

It is denoted by r-squared and typically takes values between 0 and 1. A value of 0 indicates that the independent variable does not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable explains all of the variance in the dependent variable. The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable). A higher R-squared value indicates a stronger regression relationship between the two variables.

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Answer:

Round (n-value):   0.      1.       2.     3.    4.

# of Teams (aₙ): 1024, 512,  256,  128,  64

Step-by-step explanation:

aₙ = a₁ · r ⁿ⁻¹

Someone please correct me if I'm wrong.  I learned this very recently.

To guarantee accuracy within 0.00002 for trapezoidal and midpoint rule approximations for ∫21 1x dx, we must take n ≥ 92 for the trapezoidal rule and n ≥ 65 for the midpoint rule.

To guarantee that the trapezoidal and midpoint rule approximations for ∫21 1x dx are accurate to within 0.00002, we need to find the value of n that satisfies the following inequalities:

|ET| ≤ (b-a)³ / (12n²) * M₂ for the trapezoidal rule
|EM| ≤ (b-a)³ / (24n²) * M₂ for the midpoint rule

Where M₂ is the maximum value of the second derivative of the function f(x) = 1/x on the interval [1,2], b-a = 2-1 = 1, and ET and EM are the true errors for the trapezoidal and midpoint rules, respectively.

Taking the second derivative of f(x), we get f''(x) = 2/x³. The maximum value of this function on the interval [1,2] is M₂ = 2.

Plugging in the values of M₂, b-a, and the desired accuracy into the inequalities, we get:

|ET| ≤ (1)³ / (12n²) * 2 ≤ 0.00002
|EM| ≤ (1)³ / (24n²) * 2 ≤ 0.00002

Solving for n, we get:

n² ≥ (1)³ / (12 * 0.00002) * 2 = 8333.33 for the trapezoidal rule
n² ≥ (1)³ / (24 * 0.00002) * 2 = 4166.67 for the midpoint rule

Taking the square root of both sides, we get:

n ≥ 91.29 for the trapezoidal rule
n ≥ 64.55 for the midpoint rule

Therefore, to guarantee that the trapezoidal and midpoint rule approximations are accurate to within 0.00002, we should take n ≥ 92 for the trapezoidal rule and n ≥ 65 for the midpoint rule.

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The graphs cross at x=-1 and x=1. Those are the solutions to to the equation

We know that, If two functions are equal then there solution is the intersection point of the curves.

When we determine the graph the intersection points are (0,2) and (1,1.25).

The values of x of the intersection points are the solutions of the system

Using a graphing tool, there are two intersection points and therefore the solutions are x = -1 and x [ 1.

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A line segment can be divided into ratios.

The coordinate of P on line segment AB is (5,1)

Given

\(A = (-3,-5)\)

\(B = (9,4)\)

The position of P from A to B is:

\(P_A = \frac 23\)

So, from P to B would be:

\(P_B =1 - \frac 23\)

\(P_B = \frac 13\)

So, the ratio is:

\(m : n = \frac 23 : \frac 13\)

Simplify

\(m : n = 2 :1\)

The coordinate of point P is:

\(P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

So, we have:

\(P = (\frac{2 \times 9 + 1 \times -3}{2 + 1},\frac{2 \times 4 + 1 \times -5}{2 + 1})\)

\(P = (\frac{15}{3},\frac{3}{3})\)

\(P = (5,1)\)

Hence, the coordinate of P is (5,1)

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\(\boxed{275.67+3(16.32)+24.39+27.40x \leq 560}\\\\27.40x +349.02 \leq 560\\\\27.40x \leq 210.98\\\\x \leq 7.7\)

Rounding down yields \(\boxed{x \leq 7}\).

Answer:

Step-by-step explanation:

560

To find the area between the curves, we need to determine the points of intersection between the curves and integrate the difference between the upper and lower curves with respect to x.

First, let's find the points of intersection. Setting the two y-values equal to each other:

4e^4x = 3e^4x + 1

Subtracting 3e^4x from both sides:

e^4x = 1

Taking the natural logarithm of both sides:

4x = ln(1)

4x = 0

x = 0

So the two curves intersect at x = 0. To find the limits of integration, we observe that the curve y = 4e^4x is the upper curve from x = -1 to x = 0, and the curve y = 3e^4x + 1 is the upper curve from x = 0 to x = 3. Now, we can calculate the area between the curves using integration:

A = ∫[a,b] (upper curve - lower curve) dx

For the first interval, from x = -1 to x = 0:

A1 = ∫[-1,0] (4e^4x - (3e^4x + 1)) dx

  = ∫[-1,0] (e^4x - 1) dx

For the second interval, from x = 0 to x = 3:

A2 = ∫[0,3] (4e^4x - (3e^4x + 1)) dx

  = ∫[0,3] (e^4x - 1) dx

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Answer:

3/10r+7/5

Step-by-step explanation:

khan <3

The system will be consistent and will have unique solution.

Given,

Coefficient matrix of 5 equation in 5 variables.

Here,

Let A be a 5x5 coefficient matrix such that its each column has a pivot element, then

Rank A = 5, rank of augmented matrix [A|b] = 5 and number of unknowns = 5

Rank A = rank of augmented matrix [A|b] = number of unknowns = 5

Hence , System is consistent

There is a unique intersection point of all three lines, so values of variables is unique.

Hence, solution of system if unique.

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Answer:

the clown plz mark brainliest

Answer:

TATE AND BROOKE THOMPSON or any of emma roberts characters

Answer:

Rate positively and give brainlist

The limiting reagent in a chemical reaction is a reactant that is totally consumed when the chemical reaction is completed. The amount of product formed is limited by this reagent, since the reaction cannot continue without it.

why is excess reagent used:

A good way to ensure that one reactant fully reacts is to use an excess of the other reactant. This is financially efficient when one of the reactants is very cheap. When one reactant is in excess, there will always be some left over.

how do you find the excess reagent:

The reactant that produces a lesser amount of product is the limiting reagent. The reactant that produces a larger amount of product is the excess reagent. To find the amount of remaining excess reactant, subtract the mass of excess reagent consumed from the total mass of excess reagent given

In the similar triangle, x = 67.5 ft

Similar triangles are triangles in which the ratio of their sides are equal.

Given the similar triangles, ΔMNP and ΔMAB

By the ratio of similar triangles, we have that

MP/MN = MB/MA

We observe that MN = MA + AN

So, MA = MN - AN

So, MP/MN = MB/MA

MP/MN = MB/(MN - AN)

Given that

We have that

MP/MN = x/(MN - AN)

Making x subject of the formula, we have that

x = (MN - AN)MP/MN

So, substituting the values of the variables into the equation, we have that

x = (MN - AN)MP/MN

x = (71.5 ft - 22 ft)97.5 ft/71.5 ft

x = 49.5 ft × 97.5 ft/71.5 ft

x = 4826.25 ft²/71.5 ft

x = 67.5 ft

So, the value of x = 67.5 ft

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Answer:

556 ft²

Step-by-step explanation:

The given information is,

→ Length (l) = 11 ft

→ Breadth (b) = 10 ft

→ Height (h) = 8 ft

Formula we use,

→ 2(lb + bh + lh)

The surface area of cuboid will be,

→ 2(lb + bh + lh)

→ 2{(11 × 10) + (10 × 8) + (11 × 8)}

→ 2(110 + 80 + 88)

→ 2 × 278

→ [ 556 ft² ]

Therefore, the TSA is 556 ft².

Here is sufficient evidence that revenue and the number of downloads are linearly related.

A computer software developer would like to use the number of downloads for the trial version of his new shareware to predict the amount of revenue.

The Null hypothesis is the common statistical theory that asserts that no statistical relationship or significance exist between two sets of observed data and measure phenomena based on a single observed variable.

Therefore the null hypothesis become,

H₀ : ρ₁ = 0

and the adjacent hypothesis will become,

H₁ : ρ ≠ 0

Now we will calculate test statistic,

t = r × \(\sqrt{\frac{n-2}{1-r^{2} } }\)

 = (0.8691) × \(\sqrt{\frac{30 - 2}{0.1309^{2} } }\)

t = 9.2974

we know that degree of freedom = n - 2 = 28

p-value at t = 9.2974 is 0.00

α = 0.05

since p-value < α

so null hypothesis will be rejected.

Hence we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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Answer:

C and D

atleast 20 characters to explain it well

Answer:

bring -18x to 2x

2x-18x

then bring -4 to +4

2x-18x+4-4

Given :

Diameter of pizza , \(D=10\dfrac{1}{3}=\dfrac{31}{3}\) .

To Find :

Is square box of size equal to diameter big enough to fit pizza inside it .

Solution :

Area of pizza :

\(A_p=\pi(\dfrac{D}{2})^2\\\\A_p=\pi\times (\dfrac{31}{3\times 2})^2\\\\A_p=83.86\ inch^2\)

Area of square with side equal to diameter :

\(A_s=D^2\\\\A_s=(\dfrac{31}{3})^2\\\\A_s=106.78\ inch^2\)

Since , the area of square is more than area of pizza .

Therefore , pizza can easily be fitted .

Hence , this is the required solution .