The length of a room is 2 times it's breadth and 5 times of it's height.If the volume of the room is 800 m cube find the cost of papering it's wall at rs 6 per m cube

The given equation x^2 - y^2 represents a hyperbola.

A hyperbola is a conic section that has two branches, and its equation is typically of the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/b^2 - (x-h)^2/a^2 = 1. In this case, the equation x^2 - y^2 matches the general form of a hyperbola.

The equation x^2 - y^2 can also be written as (x - 0)^2/1^2 - (y - 0)^2/1^2 = 1, which represents a hyperbola centered at the origin with a horizontal transverse axis.

In summary, the equation x^2 - y^2 represents a hyperbola with a horizontal transverse axis.

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The equivalent fractions of 2/5 and 1/7 are 14/35 and 5/35

From the question, the fractions are given as

2/5 and 1/7

The denominators of the fractions are

Denominators = 5 and 7

Take the LCM of the denominators

LCM = 5 * 7

Evaluate

LCM = 35

This means that the denominators of the equivalent fractions must be 35

When this is done, we have

14/35 and 5/35

This is done by multiplying the numerator and the denominator by the same factor

Hence, the fractions are 14/35 and 5/35

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The equation (2 + 2i)^2 - 9(2 - 2i) = 0 can be written in polar form as r^2e^(2θi) - 9re^(-2θi) = 0.


To convert the equation to polar form, we need to express the complex numbers in terms of their magnitude (r) and argument (θ).

Let's start by expanding the equation:
(2 + 2i)^2 - 9(2 - 2i) = 0
(4 + 8i + 4i^2) - (18 - 18i) = 0
(4 + 8i - 4) - (18 - 18i) = 0
(8i - 14) - (-18 + 18i) = 0
8i - 14 + 18 - 18i = 0
4i + 4 = 0

Now, we can write this equation in polar form:
4i + 4 = 0
4(re^(iθ)) + 4 = 0
4e^(iθ) = -4
e^(iθ) = -1

To find the polar form, we determine the argument (θ) that satisfies e^(iθ) = -1. We know that e^(iπ) = -1, so θ = π.

Therefore, the equation (2 + 2i)^2 - 9(2 - 2i) = 0 can be written in polar form as r^2e^(2θi) - 9re^(-2θi) = 0, where r is the magnitude and θ is the argument (θ = π in this case).

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Answer:

9 1/2

Step-by-step explanation:

Add 2 1/2 plus 3 1/2 plus 3 1/2 to get 9 1/2.

Answer:

See below.

Step-by-step explanation:

I find autonomous robotics and fuzzy-related topics interesting. But it must include all the topics? I mean, Art as well? In the field of robotics, some interesting approaches involve building robots capable of moving in cluttered environments, places with humans efficiently. In this context the study of mapping algorithms and computer vision is interesting.

Answer:

6m

Step-by-step explanation:

the side of first square = 3 m

area of first square = 3^2= 9 m^2

let the side of second square = x m

since diagonal of first square = x m as per the question

in a square each angle is 90 degree

therefore by applying pythagorus theorem ,

diagonal ^2 = side^2 + side ^2

diagonal^2 = 3^2+3^2=9+9

DIAGONAL= square root of 18

diagonal= 3\(\sqrt{2}\) m = side of second square

therefore in second square ,

one angle is 90  degree , therefore by applying pythagorue theorem

diaqonal^2 = side ^2 + side ^2 = (3\(\sqrt{2}\))^2 + ( 3\(\sqrt{2}\))^2

diagonal ^2 = 18 + 18

diagonal = square root of 36

therefore diagonal of second square is 6m

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Answer:

6m explained it all hope it helps

Answer:

That is very difficult

Step-by-step explanation:

I hope you got help

The company can fence off a maximum square/rectangular area of 48,400 square meters. To find the maximum square/rectangular area that the company can fence off, they need to use all 880m of fencing available.

Let's call the length and width of the fenced area "L" and "W", respectively.
For a square, L = W, so we can write:
4L = 880
L = 220m
The maximum square area would be:
A = L x W = 220m x 220m = 48,400m²

For a rectangle, we need to use the fact that the perimeter (2L + 2W) equals 880m. We can solve for one variable (let's say L) in terms of the other (W), and then substitute it into the area equation:
2L + 2W = 880
L = 440 - W
A = L x W = (440 - W) x W = 440W - W²

To find the maximum area, we need to find the vertex of the quadratic equation. We can do this by finding the value of W that makes the derivative of the equation equal to 0:
dA/dW = 440 - 2W = 0
W = 220m
L = 440 - 220 = 220m
The maximum rectangular area would be:
A = L x W = 220m x 220m = 48,400m²
Therefore, the company can fence off a maximum square/rectangular area of 48,400 square meters.

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However, if the decisions drawn from both methods differ (e.g., one rejects the null hypothesis while the other does not), then the conclusions are not the same.

In order to compare the conclusions obtained using the p-value method with your initial conclusion, it is essential to first understand the p-value's role in hypothesis testing. The p-value is a probability that helps in determining the statistical significance of your test results. A smaller p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, leading to its rejection in favour of the alternative hypothesis. Conversely, a larger p-value (typically > 0.05) suggests weak evidence against the null hypothesis, and therefore, it cannot be rejected.
When comparing the conclusions, assess if both methods lead to the same decision regarding the null hypothesis. If your initial conclusion rejects the null hypothesis and the p-value method yields a p-value ≤ 0.05, then the conclusions are the same. Alternatively, if your initial conclusion does not reject the null hypothesis and the p-value method results in a p-value > 0.05, the conclusions also align.
However, if the decisions drawn from both methods differ (e.g., one rejects the null hypothesis while the other does not), then the conclusions are not the same. In such cases, it is crucial to revisit the methodology and ensure the correctness of the approach taken, as it is vital to have consistent and accurate results in any statistical analysis.

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Answer:

idk hff 8gciy ctcs 6rxtc igv6rx8

Answer:

the answer is c

Step-by-step explanation:

36x36 + 36x60

=3456 and add squared

The smallest integer value of c that ensures the function f(x) has a domain of all real numbers is c = 5.

For the function f(x) to have a domain of all real numbers, the denominator x^2 + 4x + c cannot be equal to zero. If the denominator equals zero, the function would have undefined values.

To find the smallest integer value of c that satisfies this condition, we need to find the values of c that make the quadratic x^2 + 4x + c = 0 have no real solutions.

For a quadratic equation ax^2 + bx + c = 0 to have no real solutions, the discriminant (b^2 - 4ac) must be negative.

In this case, we have a = 1, b = 4, and c is the variable we are trying to determine.

The discriminant is:

b^2 - 4ac = 4^2 - 4(1)(c) = 16 - 4c

To have no real solutions, the discriminant must be negative:

16 - 4c < 0

Solving this inequality, we find:

4c > 16

c > 4

Since c must be an integer, the smallest integer value of c that satisfies this condition is 5.

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The expression equivalent to the given expression is \(\frac{4}{x-9}\)

This are expressions written as a ratio of two expressions. Given the rational expression

\(f(x) = \frac{4(x-2)}{(x-2)(x-9)}\)

Since (x-2) is common in both numerator and denominator, they wil cancel out to have the function below;

\(f(x) = \frac{4(x-2)}{(x-2)(x-9)}=\frac{4}{x-9}\)

Hence the expression equivalent to the given expression is \(\frac{4}{x-9}\)

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Given:

Sides of a rectangle are 9.5x+14.3y cm and 11.7x+22.8y cm.

To find:

The perimeter of the cardboard in terms of x and y.

Solution:

We know that, perimeter of a rectangle is

\(Perimeter=2(length +width)\)

Now,

\(Perimeter=2[(9.5x+14.3y) +(11.7x+22.8y)]\)

On combining like terms, we get

\(Perimeter=2[(9.5x+11.7x) +(14.3y+22.8y)]\)

\(Perimeter=2[21.2x +37.1y]\)

using distributive property, we get

\(Perimeter=2(21.2x) +2(37.1y)\)

\(Perimeter=42.4x+74.2y\)

Therefore, the perimeter of the cardboard in terms of x and y is 42.4x+74.2y cm.

2×12=24

24+3= 27

12*12=144

144/24=6

Answer:

Step-by-step explanation:

We can show that for x = 0, both sides of the inequality get the value of 1.

With x > 0, the left side goes towards - ∞ with the negative slope and the right side is always positive.

I'll give a graphical solution.

Hope this helps.

Answer:

Step-by-step explanation:

let's rearrange the equation 3 x − 2 y = 2  a bit. (isolate y)

3x - 2 /2 = 2y /2

(3x-2)/2 = y

\(\frac{3}{2} x\) - 1 = y

The slope for the equation is 3/2.

Rule: Parallel lines have the same slope

So we know that the slope of the line we need to find is 3/2.

y = mx +b

y = (3/2)(x) + b

Now plug in the point (-6,-2) to find b

-2 = (3/2)(-6) + b

-2 = -9 + b

-2 + 9 = -9 + b + 9

7 = b

b = 7

Therefore the equation of the line we need to find: y = \(\frac{3}{2}x + 7\)

Answer:

7 science teachers

Step-by-step explanation:

42 and 14 in a ratio 3:1

if 42/2 =21 maths teachers then 7 science teachers

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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Answer:

40%

Step-by-step explanation:

The day the two bags will have the same weight is the 24th day.

The linear equation that can be used to determine the pound of dog food left is:

Amount of dog food left = capacity of the bag - (number of days x amount the dog eats per day)

Amount of dog food left = 34 - (1 x p)

Amount of dog food left = 34 - 1p

The linear equation that can be used to determine the pound of cat food left is:

Amount of cat food left = capacity of the bag - (number of days x amount the cat eats per day)

Amount of cat food left = 16 - (1/4 x p)

Amount of cat food left = 16 - 1/4p

On the day the two bags will have the same weight, the two above equations would be equal:

16 - 1/4p = 34 - 1p

p - 1/4p = 34 - 16

3/4p = 18

p = (18 x 4) / 3

p = 24 days

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Answer:

The cyclist can travel 0.9 miles in 2 minutes.

Step-by-step explanation:

1 hour = 60 minutes

Set up a conversion equation:

27 mi/1 hr × 1hr/60 mins

It is easier to see when writing it on paper, but the fractions are set up in a way to cancel the units out until the only units left are miles and minutes

After multiplying the numerators together and then multiplying the denominators together, you should reach the answer:

27 mi/60 mins

The cyclist can travel 27 miles in 60 minutes, but how many miles can he travel in 2 minutes?

Set up an equation:

Variable x = number of miles

27 mi/60 mins = x/2 mins

Cross multiply

27 × 2 = 60 × x

54 = 60x

Divide both sides by 60

0.9 = x

204.79

Step-by-step explanation:

Answer:

(3, - 28)

Step-by-step explanation:

f(x) = 4x² - 24x + 8

\(x = - \frac{ - 24}{2 \times 4} \)

x = 3

f(3) = -28

= (3, -28)

Step-by-step explanation:Step-by-step explanation:

For Sienna to be able to take the square root of both sides while solving a quadratic equation, she must have an expression with square on at least, the side that contains the variable she is trying to determine. Equation of the form:

(x + a) ² = b

'a' and 'b' could be any number, -1, 0, 1/3, -5/6, anything really.

So, she can take square roots of both sides then, like this

√(x + a)² = √b

x + a = ±√b

x = -a ± √b

Square roots always cancel out squares, and the '±' is because a square is satisfies by both + and -, 3² = 9, and (-3)² = 9.

It is the nature of the problem being solved that determines if we take just one or both of these answers.

As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.

Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.

Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.

Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.

Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.

Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.

By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.

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Answer: 6.32 (rounded)

Step-by-step explanation:

You need to use the pythagorean theorem. 2^2+6^2=c^2.

4+36=40

square root of 40 is 6.324 when rounded

1) The partial fraction decomposition of (x² + 2x + 1) / (x²(x + 3)²) is 1/(18x) + 1/(18x²) + 1/(18(x + 3)) + 1/(18(x + 3)²).   2) The partial fraction decomposition of (1 - x) / ((x² - 3x + 2)(x² + 4)) is A/(x - 1) + B/(x - 2) + (Cx + D)/(x² + 4).

1. To resolve (x² + 2x + 1) / (x²(x + 3)²) into partial fractions, we start by factoring the denominator.

The denominator can be factored as x²(x + 3)².

Now, let's express the fraction as:

(x² + 2x + 1) / (x²(x + 3)²) = A/x + B/x² + C/(x + 3) + D/(x + 3)²

To find the values of A, B, C, and D, we can multiply both sides of the equation by the common denominator (x²(x + 3)²):

x² + 2x + 1 = A(x + 3)² + B(x + 3)(x + 3) + C(x²)(x + 3) + D(x²)

x² + 2x + 1 = A(x² + 6x + 9) + B(x² + 6x + 9) + C(x³ + 3x²) + D(x²)

Now, equating the coefficients of the like terms on both sides:

For the term x² on the left side, we have: 1 = A + B + C + D.

For the term x on the left side, we have: 2 = 6A + 6B + 3C.

For the constant term on the left side, we have: 1 = 9A + 9B.

For the term x³ on the left side, we have: 0 = C.

Solving this system of equations, we find:

C = 0,

A + B + D = 1/9, and

6A + 6B = 2/3.

Solving further, we get:

A = 1/18,

B = 1/18, and

D = 1/18.

Therefore, the partial fraction decomposition of (x² + 2x + 1) / (x²(x + 3)²) is: (x² + 2x + 1) / (x²(x + 3)²) = 1/(18x) + 1/(18x²) + 1/(18(x + 3)) + 1/(18(x + 3)²).

2. To resolve the fraction (1 - x) / ((x² - 3x + 2)(x² + 4)) into partial fractions, we first factor the denominator as (x - 1)(x - 2)(x² + 4).

The partial fraction decomposition is expressed as A/(x - 1) + B/(x - 2) + (Cx + D)/(x² + 4), where A, B, C, and D are constants to be determined.

To find the values of A, B, C, and D, we multiply both sides of the equation by the common denominator (x - 1)(x - 2)(x² + 4) and simplify.

The equation becomes 1 - x = A(x - 2)(x² + 4) + B(x - 1)(x² + 4) + (Cx + D)(x - 1)(x - 2).

Expanding and simplifying the right side, we get 1 - x = (A + B)(x³ - 3x² - 6x + 8) + (Cx + D)(x² - 3x + 2).

By equating the coefficients of the like terms on both sides, we can solve for A, B, C, and D.

Solving the system of equations, we find A = 2/3, B = -1/3, C = -1/5, and D = 3/5.

Therefore, the partial fraction decomposition of (1 - x) / ((x² - 3x + 2)(x² + 4)) is (2/3)/(x - 1) + (-1/3)/(x - 2) + (-1/5)(x + 4)/(x² + 4).

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