The circle above has a radius of 3 cm. What is the area of the circle?

Answer:

Step-by-step explanation:

The value of ||w - u || = 3 sqrt 2

Given:

u = 2i - 3j

w = - i - 6j

w - u = ( - i - 2i ) + ( - 6j - (-3j))

w - u = - 3i - 3j

|| w - u || = sqrt [ - 3^2 + - 3^2 ]

||w - u || = 3 sqrt 2

The concept of a radical in mathematics refers to the symbolic representation (√) of finding the roots of an expression or a number.

The widely known and frequently used kind is the square root (√), which reveals a positive value that, when multiplied by itself at once, generates the radicand.

Other forms may include cube roots (∛) or fourth roots (∜). To simplify radicals, one can factor out those factors within it that result in perfect cubes or squares from their corresponding radicands.

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Answer:

x = -31 maybe

Step-by-step explanation:

The maximum profit that can be made is $1737.82

An equation is an expression showing the relationship between numbers and variables using mathematical operators.

The profit function is the difference between the revenue and cost of a commodity. Given that:

Revenue, R(x) = 700x - 11.3x²

Cost, C(x) = 8068 - 34.25x

Profit, P(x) = Revenue - Cost

P(x) = (700x - 11.3x²) - (8068 - 34.25x)

P(x) = 665.75x - 11.3x² - 8068

The maximum profit is at P'(x) = 0; hence:

P'(x) = 665.75 - 22.6x

665.75 - 22.6x = 0

22.6x = 665.75

x = 29.45

P(29.45) = 665.75(29.45) - 11.3(29.45)² - 8068

P(29.45) = 1737.82

The profit to be made is $1737.82

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A conversion of 300 degrees to radians is equal to 5.24 radians.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

Next, we would convert degrees to radians;

300 = rads × 180/π

Radians = 300π/180 = 5.24 radians.

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The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)

The given vector function can be correctly expressed as:

r(t) = (t-2)i / (t+2) + sintj + ln(36-t²)k²

The domain of the given function can be determined by finding the domain of each respective component.

(t-2)i / (t+2)

Not defined, t = -2

Thus, the domain of the first component of the vector = (-∞, 2) ∪ (2, ∞)

The 2nd component = sin t

No restriction on t,

The 3rd component of the function is ㏑(36 - t²)

we know,

Natural number is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

thus, it satisfies the inequality -6 < t < 6

The third domain = (-6,6)

Hence, the domain of the vector function is : ( -6, -2) ∪ ( -2, 6)

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Answer:

2/3

Step-by-step explanation:

since a is 5 and b is 9.

so, 5+1( according to the expression given)/9

5+1/9 equals 6/9 and taking them down to the lowest terms that makes the answer 2/3

Since John cannot buy a fraction of a can, he needs to round up to the nearest whole number. So, John needs at least 5 cans of paint to cover the entire wall as per the height and length.

To calculate the area of the wall, we need to multiply the height and the length of the wall.

From the diagram, we can see that the height of the wall is 2 meters and the length is 5 meters.

So the total area of the wall is:

Area = height x length

Area = 2 meters x 5 meters

Area = 10 square meters

To convert this to square feet, we can use the conversion factor:

1 square meter = 10.764 square feet

So:

Area = 10 square meters x 10.764 square feet/square meter

Area = 107.64 square feet

Since 1 can of paint covers 24 square feet, John needs:

Number of cans = Area ÷ Coverage per can

Number of cans = 107.64 square feet ÷ 24 square feet/can

Number of cans = 4.485 cans

Thus, John needs at least 5 cans of paint to cover the entire wall.

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Your question seems incomplete, the probable complete question is:

John needs to paint one wall in his school. He knows that 1 can of paint covers an area of 24 square feet.

John uses a meter stick to measure the dimensions of the wall as shown.

[1 meter = approximately 39 inches]

What is the fewest number of cans of paint John can use to paint the wall?

The domain of the quadratic function in this problem is given as follows:

All real values.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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The direction angle of the vector with initial point (1, -1) and terminal point (7, 2) is approximately 26.57 degrees, found by calculating the arctangent of the ratio of the y and x components of the vector.

The direction angle of the vector v is the angle it makes with the positive x-axis, measured counterclockwise.

To find this angle, we need to calculate the difference between the y-coordinates and x-coordinates of the terminal and initial points of the vector, respectively. Then, we can use the arctangent function to find the angle.

Let's first find the components of the vector v

v = <7 - 1, 2 - (-1)> = <6, 3>

Now, we can find the direction angle as follows

θ = arctan(3/6)

θ = 0.4636 radians (in decimal form)

To convert this to degrees, we can multiply by 180/π

θ ≈ 26.57°

Therefore, the direction angle of the vector v is approximately 26.57 degrees.

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Answer: B) 1/2

Step-by-step explanation: Hope this helps! :)

The answer is 1/3. I looked it up on gpt and also got a 100 on this quiz

Answer:

1.5

Step-by-step explanation:

its a decimal number

Answer: the number 15/10 is a fraction.

Step-by-step explanation:

any two numbers that have a slash in the middle are fractons. :)

Step-by-step explanation:

k = a constant of proportionality

Putting m = 1kg, a = 1 ms-2

F becomes 1 N.

So, 1 N = 4 × 1kg × 1 ms-2

∴ k = 1

From equation (1), we have

F = ma

Answer:

Step-by-step explanation:

Complementary means angles that add up to 90°

Based on that you can write and equation by adding the 2 angles and making equal to 90

2x+6+1/2x=90          combine like terms on left

5/2x+6=90               subtract both sides by 6

5/2x=84                   multiply by the reciprocal of 5/2 => 2/5

x=168/5 or 33.6

Answer:correct answers are 3.96

2.32

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

-7u^2 + 4u + 6 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -7, b = 4, and c = 6. Substituting these values, we get:

u = (-4 ± sqrt(4^2 - 4(-7)(6))) / 2(-7)

u = (-4 ± sqrt(136)) / (-14)

u = (2 ± sqrt(34)) / 7

Therefore, either:

cos(θ) = (2 + sqrt(34)) / 7

or:

cos(θ) = (2 - sqrt(34)) / 7

Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:

θ = arccos((2 + sqrt(34)) / 7)

θ = arccos((2 - sqrt(34)) / 7)

Using a calculator, we find:

Answer: x is greater than or equal to 5 (I can't put the symbol in)

Step-by-step explanation:

Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.

Answer:

Step-by-step explanation:

3x+10<3

3x<3-10

3x<-7

x<-7/3

2x-5≥5

2x≥5+5

2x≥10

x≥10/2

x≥5

so x<-7/3 or x≥5

The measures of the three intercepted arcs from least to greatest are;

AC < BC < AB

We have,

We are given that

Angle ACB = 63 degrees

Arc BC is 118 degrees.

Now, from the Triangle angle sum theorem, we know that the sum of all interior angles of any triangle is always equal to 180 degrees.

Thus, the sum of the interior angles of the inscribed triangle given to us id also 180 degrees.

Now, since Angle ACB = 63 degrees

Then Arc AB = 63 * 2 = 126

Arc AC = 360 - (Arc BC + Arc AB)

We are given BC = 118 degrees

Thus;

Arc AC = 360 - (118 + 126)

Arc AC = 116°

Thus, the least arc angle is Arc AC while the greatest is Arc AB

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complete question:

Triangle ABC is inscribed in a circle centered at point O.

The figure shows triangle ABC is inscribed in a circle centered at point O and has an angle ACB is 63 degrees and arc BC is 118 degrees.

Order the measures of the three intercepted arcs from least to greatest.

The relation between lengths of AB and BC are,

⇒  Lenght of AB and BC are different.

We have to given that;

Triangles ABD and BDC are given.

Here, All the angles of a triangle ABD are different from angles of BDC.

Hence, We get;

Both triangle ABD and BDC are congruent.

So, All the sides of ΔABD are different from the sides of different from ΔBDC.

Hence, Lenght of AB and BC are different.

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Answer:

2.75

Step-by-step explanation:

To find the mean absolute deviation for a set of data, we first need to find the mean (average) of the data set. Then, for each data point, we find the absolute value of the difference between the data point and the mean. Finally, we take the mean of those absolute differences.

Step 1: Find the mean

Mean = (6+7+10+12+13+4+8+12)/8 = 72/8 = 9

Step 2: Find the absolute differences

|6-9| = 3

|7-9| = 2

|10-9| = 1

|12-9| = 3

|13-9| = 4

|4-9| = 5

|8-9| = 1

|12-9| = 3

Step 3: Find the mean of the absolute differences

Mean absolute deviation = (3+2+1+3+4+5+1+3)/8

Mean absolute deviation = 22/8

Mean absolute deviation = 2.75

Therefore, the mean absolute deviation for the given data set is 2.75.

The new area of the figure after the dilation with a scale factor of 4 will be 400 units²

We have,

When a figure is dilated by a scale factor of k, its area is multiplied by k².

So,

If the original area of the figure = 25 units²

Dilated by a scale factor = 4

The new area.

= (4²)(25 units²)

= 16(25 units²)

= 400 units²

Therefore,

The new area of the figure after the dilation with a scale factor of 4 will be 400 units².

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The requried value of x that satisfies the problem is 4.5,

Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:

Area = 9x² - 30x + 25

Side length = √(Area) = √(9x² - 30x + 25)

To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:

Perimeter = 4 * Side length

34 = 4 * √(9x² - 30x + 25)

8.5 = √(9x² - 30x + 25)

9x² - 30x - 47.25 = 0

We can solve this quadratic equation by using the quadratic formula gives,

x = 4.5 and -1.16

Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.

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The percentage of cars traveling slower than 62 mph during rush hour is 0.5 or 50%.

Since the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62 mph and a standard deviation of 5 mph, we can use the cumulative distribution function (CDF) of the normal distribution to find the percentage of cars traveling slower than 62 mph.

Let X be the speed of an automobile on the expressway during rush hour. Then, X follows a normal distribution with mean (µ) = 62 mph and standard deviation (σ) = 5 mph.

We want to find P(X < 62), which represents the probability that a car is traveling slower than 62 mph.

Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find the z-score corresponding to the value X = 62, using the formula;

z = (X - µ) / σ

Plugging in the given values;

z = (62 - 62) / 5 = 0

Now, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 0, denoted as Φ(0), which represents the probability that a standard normal random variable is less than or equal to 0.

Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find Φ(0) to be approximately 0.5.

So, P(X < 62) = Φ(0)

= 0.5

Therefore, the percentage of car is 0.5 or 50%

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Based on the rate of change, the total charge will be $ 12.60 in 4 days

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

Rate of change of investment = $3.15

Value of the investment = $12.60

Using the above as a guide, we have the following:

Number of days = Value of the investment/Rate of change of investment

Substitute the known values in the above equation, so, we have the following representation

Number of days = 12.60/3.15

Evaluate

Number of days = 4

Hence, the number of days is 4

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a) Based on the exponential function, p(t)=1200 (1.026)^t, the item's current price with a rate of inflation of 2.6% per year is $1,200.

b) In 8 years, the future price of the item would be $1,473.53.

An exponential function is a mathematical equation depicting the relationship between one variable and another with a periodic constant rate of growth or decline.

Exponential functions are classified into two:

Let the number of years from today = t

Annual inflation rate = 2.6%

Current price = $1,200

Time in years = 8 years

p(t)=1200 (1.026)^t

p(8) = 1,200(1.026)^8

= $1,473.53

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Answer:

x = 8.4

y = 23.6

Step-by-step explanation:

tan31 = x/14

x = tan31(14) = 8.412

y² = (8.412)² + (22)² = 554.7626

y = √554.7626 = 23.55

Answer: The IQR of this data set is 5.5

Step-by-step explanation: Ok so first you line the data set up in correct order.

Here's the correct order:

13, 15, 15, 16, 18, 19, 22, 28

Then you find the median and since there's even amount of numbers you add the two numbers in the middle which is 16 and 18 and divide that by 2 which is 17. So the median is 17. Then you split the data set into halves. The first quartile is 15 and the third quartile is 20.5. Then to find the IQR, you would minus 20.5 - 15 = 5.5. Hope this helps!

Answer: 1/2 cup oats 2/3 cup flower

The area of the rectangle in terms of x can be represented as (L . W)(x) = 24x³ - 30x² + 72x.

Given a rectangle.

Length of the rectangle, L(x) = 6x

Width of the rectangle, W(x) = 4x² − 5x + 12

The formula to find the area of the rectangle is,

Area = Length × Width

Substituting the given length and width,

Area of the rectangle = L(x) . W(x)

                                    = (L . W)(x)

                                    = (6x) (4x² − 5x + 12)

                                    = 24x³ - 30x² + 72x

Hence the area of the rectangle is represented as (L . W)(x) = 24x³ - 30x² + 72x.

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Answer:

(L . W)(x) = 24x³ - 30x² + 72x.

Step-by-step explanation: