Find the length L of the curve x = y (y - 25/96 cube root y^3, 0 lessthanorequalto y lessthanorequalto 243. Set up: L = integral^243_0 squareroot 1 + (f'(x))^2 dy, where f'(y) = Simplify L = integral^243_0 squareroot (g(y))^2 dy, where g(y) = Integrate L =

Rita numbered the circles of the figure from 1 to 8, so that the sum of the three numbers on each of the four sides of the square equals 13. The sum of the four numbers written on the colored circles is 10.

The figure is as shown below:

Now, let's check how the numbers are arranged:The sum of the numbers 1, 6, and 6 is 13, and they are written on the same side of the square as the circle labeled with 1.

Similarly, the numbers 2, 5, and 6 are on the same side of the square as the circle labeled with 2, and the numbers 2, 6, and 5 are on the same side of the square as the circle labeled with 3.

Now, the remaining number that has not been used in any of the sides of the square is 4.

Therefore, it should be placed at the center of the square, as shown below:

The numbers on the colored circles are: 1, 2, 3, and 4. Thus, their sum is:

1 + 2 + 3 + 4 = 10

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Answer:

5

Step-by-step explanation:

In the given question,

center of the circle C = (1, 2)

let P be the point (-3, -1) on the circle (on circumference)

radius of the circle is equal to the distance between the center and any point on its circumference.

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] (distance between two points)

therefore,

[tex]r = \sqrt{(-3 - 1)^2 + (-1 - 2)^2}[/tex]

[tex]r = 5[/tex]

Hopefully this answer helped you!

The number of possible ways you can distribute the balls among the three boxes so that each box contains at least one ball = 21

Here we have 3 empty boxes.

Let us assume that a, b and c be these empty boxes.

and the total number of balls = 8

We need to distribute the balls among the three boxes so that each box contains at least one ball.

This means that a + b + c = 8

By allotting 1 ball to each box so that no box remains empty.

We get an equation a + b + c = 5

So, the possible number of ways to by allotting 1 ball to each box so that no box remains empty would be:

⁷C₂

Using combination formula:

⁷C₂

= 7! / 2!(7 - 2)!

= 21

Therefore,  the required number of ways = 21

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Answer:

second option: 6

Step-by-step explanation:

The general term of a geometric sequence is given by: [tex]a_{n} = a_{1} r^{n-1}[/tex]

∴ [tex]a_{1}[/tex] is the first term

[tex]a_{8} = a_{1} (3)^{8-1}[/tex]

13122 = [tex]a_{1}[/tex] [tex](3)^{7}[/tex]

13122 = [tex]a_{1}[/tex] x 2187

13122/2187 = [tex]a_{1}[/tex]

6 = [tex]a_{1}[/tex]

In Linear equation, 5/8 golf balls per ounce are the number of golf balls per Ounce.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Number of golf balls (n) = 20

Total weight (w) = 32 ounces

total weight = number of balls (n) * weight of 1 golf ball

∴ weight of 1 golf ball = w/n =32/20 ounces

⇒ the weight distribution is 1.6 ounce per golf ball

Now, apply unitary method :

32 ounces is total weight of 20 golf balls

∴ 1 ounce amounts to 20/32 golf balls

⇒ there are 5/8 golf balls per ounce

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Answer:

Step-by-step explanation:

17/x = 30/84  1. Set up the proportion

30x = 1428     2. Cross multiply and solve for x

x=47.6            3. There's the solution

Answer:

So first you'll want to line your numbers in order. 0,3,4,6,6,7,7,7,

The median refers to number that is in the middle, so 6 is the median.

To find the range, you subtract the biggest number with the smallest. So 9 is the range.

And 7 is the mode because it's repeated the most.

hope this helps

median:6

range: 9

mode: 7

Answer:

False

Step-by-step explanation:

Point (D) (-7, 4) must be on the graph of the inverse function F¹(x)  if point (7,-4) is on the graph of the function F(x).

If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function.

The term "f inverse" is widely used to refer to this particular inverse function, which is singular.

A function's inverse will cause the input and output to be inverted.

If a function has an inverse, one can use algebra to find it by setting the function equal to y.

Then, swap x and y and solve for y in terms of x.

So, we have the coordinates:
(7, -4)

It lies in the 4th quadrant.

Then, its inverse would be in the 2nd quadrant.

Which would be:

(-7, 4)

Therefore, point (D) (-7, 4) must be on the graph of the inverse function F¹(x)  if point (7,-4) is on the graph of the function F(x).

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Answer:

Step-by-step explanation:

it's (-4,7)

Therefore , the solution of the given problem of triangle comes out to be    h/s = h/√(h² - s²)..

If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

Triangle ABC and triangle ACD are both right triangles with a common hypotenuse, as shown by the given diagram.

Let's write the lengths of the sides AB or AD as s and the hypotenuse AC as h. (since both triangles have a common side with length s).

The Pythagorean formula can now be used to determine the length of each triangle's third side:

Triangle ABC's third side's length (BC) can be calculated using this formula:

=> BC = √(h² - s²).

The third side's (CD) length in the triangle ACD is also determined by:

=> CD = √(h² - s²).

By dividing each triangle's hypotenuse's (h) length by one of its sides' (s) lengths, the following result is obtained:

In the triangular ABC,

=> h/s = h/ √(h² - s²).

In the triangular ACD

=>  h/s = h/√(h² - s²).

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The two sides of the triangle are equal the triangle is an isosceles triangle.

Triangles with two equal sides are known as isosceles triangles. Triangles are three-sided polygons that can be categorised as equilateral, isosceles, or scalene depending on how long their sides are.

The uneven side of this triangle is referred to as the base since the other two sides are equal in it. The triangle's two equal sides are always opposing equal angles. An isosceles triangle's height is calculated from its base to its vertex (topmost point). The third angle of a right isosceles triangle is 90 degrees.

The coordinates of the triangle are J(-2, 4), K(8, 4) and L (6, -2).

Using the distance formula we have:

The distance between J and K: √((8 - (-2))² + (4 - 4)²) = 10

The distance between K and L: √((6 - 8)² + (-2 - 4)²) = 6.324

The distance between L and J: √((-2 - 6)² + (4 - (-2))²) = 10

Since two sides of the triangle are equal the triangle is an isosceles triangle.

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bh, where b is the base and h is the height of the parallelogram.

In the case of the circle, the base of the parallelogram is the circumference of the circle, which is equal to 2πr, where r is the radius of the circle. The height of the parallelogram is the distance from the center of the circle to the edge of the circle, which is also the radius r. Therefore, we have:

b = 2πr

h = r

Substituting these values into the formula for the area of a parallelogram, we get:

Area = bh = (2πr)(r) = 2πr^2

So the formula for the area of a circle is derived from the formula for the area of a parallelogram by using the circumference of the circle as the base and the radius of the circle as the height.

Answer:

C

Step-by-step explanation:

given x = a is a solution of f(x) then (x - a) is a factor

here the solutions, where the graph crosses the x- axis, are

x = - 4 , x = - 2 , x = - 1 , then the corresponding factors are

(x - (- 4)) , (x - (- 2)) , (x - (- 1)) , that is

(x + 4) , (x + 2) , (x + 1)

f(x) is then the product of these factors, that is

f(x) = (x + 2)(x + 1)(x + 4) ← in factored form

Answer:

10%

Step-by-step explanation:

(517-470)/470x100

=10%

Find the difference after tax and divide by the original price and times 100%

Answer:

3.75 and B

Step-by-step explanation:

for the first one if the actual is 48 feet, and the image is 12.8, divide both by the image(12.8). The value you have for the image should then become one centimeter, therefore the value you have for the parking lot is the amount of feet/1cm. For the second image, its the same idea. In this case you want to know how tall the scale is, so divide by the amount of meters(just as 6/2=3 and 6/3=2 the real value/scale value=representation of 1 unit and real value/representation of 1 unit = scale value). You get 12.5, however that is per 1 unit, so multiply by five since(the value you get by simply dividing is the answer IF 30 meters were represented in the scale by 1centimeter, but its represented by 5 so you multiply by five)You get 63.5

We have two possible values for y, we have two possible Coordinates for point A: (-3, 1 + √((units)² - (3 - (-3))²)) and (-3, 1 - √((units)² - (3 - (-3))²)).

Here are the terms and steps we'll use in the solution:

1. Point B coordinates: (3, 1)
2. Point A x-coordinate: -3
3. Distance formula: √((x2 - x1)² + (y2 - y1)²)

Let's find the possible coordinates of point A:

Step 1: We know the x-coordinate of point A is -3, so its coordinates will be in the form (-3, y).

Step 2: Apply the distance formula to find the distance between point A (-3, y) and point B (3, 1):

Distance = √((3 - (-3))² + (1 - y)²)

Step 3: Square the distance equation to eliminate the square root:

Distance² = (3 - (-3))² + (1 - y)²

Step 4: Plug in the given distance value and solve for y:

(units)² = (3 - (-3))² + (1 - y)²

Step 5: Solve for (1 - y)²:

(1 - y)² = (units)² - (3 - (-3))²

Step 6: Take the square root of both sides:

1 - y = ±√((units)² - (3 - (-3))²)

Step 7: Solve for y:

y = 1 ±√((units)² - (3 - (-3))²)

Since we have two possible values for y, we have two possible coordinates for point A: (-3, 1 + √((units)² - (3 - (-3))²)) and (-3, 1 - √((units)² - (3 - (-3))²)).

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The product of 2 and 1 3/6 can be expressed as either 18/6 or 3

The product of 2 and 1 3/6 can be found by multiplying 2 by the mixed number 1 3/6. To do this, we need to convert the mixed number to an improper fraction, then multiply it by 2. Here are two possible expressions that are equal to the product of 2 and 1 3/6

Improper fractions

2 x 1 3/6 = 2 x (1 + 3/6) = 2 x (6/6 + 3/6) = 2 x 9/6 = 18/6

Therefore, the product of 2 and 1 3/6 is equal to 18/6.

Decimals

We can also convert the mixed number 1 3/6 to a decimal and then multiply it by 2. To convert the mixed number to a decimal, we divide the numerator (3) by the denominator (6), which gives us 0.5. Then we add the whole number (1) to get 1.5.

2 x 1.5 = 3

Therefore, the product of 2 and 1 3/6 is equal to 3.

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Answer:

[tex]2 \frac{10}{23} [/tex]

Step-by-step explanation:

[tex] \frac{4u - 7}{ - 7} = \frac{u - 4}{4} [/tex]

Use the property of the proportion:

4 × (4u-7) = -7 × (u-4)

16u -28 = -7u + 28

16u + 7u = 28 + 28

23u = 56 / : 23

u =

[tex] 2\frac{10}{23} [/tex]

Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

Answer:

Step-by-step explanation:

D.

Relief rainfall causes Port Antonio on the windward side of the Blue Mountains to receive an average of 430 mm (17 inches) of rain in November while Kingston, in the rain shadow, receives only 175 mm (7 inches).

Answer:

9.9

Step-by-step explanation:

Turn Fractions into decimals. 3 3/5 turns to 3.6 and 5 1/2 turns to 5.5

Multiply them and get 19.8 and divide by 2 to get 9.9

Answer:

Step-by-step explanation:

Area = s x s. So 3 3/5 x 5 1/2 = 99/5 = 19 4/5

Answer: y intercept = (0.6)

Step-by-step explanation:

plug in 0 for x since the y-intercept is when x=0. then solve the equation. 2y=12. divide both sides by 2. y=6

i’m sorry i’m not sure about the slope

Answer:

1. It's a quadratic expression bcs the highest power in a quadratic expression is 2. Hence its in standard form. basically anything that follows ax^2 + bx + c
2. x^2-6x+8 (separate the coefficient into 2, where they add to get the coefficient number (-6), and multiply to get the number (8)
x^2-4x-2x+8 (separate it into 2 parts, and factorize each part)
x(x-4)-2(x-4)
(x-2)(x-4)
Hence, x^2-4x-2x+8 is equivalent to (x-2)(x-4)

67 people can maximize the profit.

Let's aasume that x represent the number of people.

so, the number of people on the tour = x + 50

The cost function would be:

C = 6000 + 32x

and the revenue:

R = (200 - 2x)(50 + x)

R = 10000 - 100x + 200x - 2x^2

R = 10000 + 100x - 2x²

So, the profit would be:

P = R - C

P = 10000 + 100x - 2x² - 6000 - 32x

P = 4000 + 68x - 2x²

Now we take the derivative of profit function:

P' = 68 - 4x

Consider P'(x) = 0

68 - 4x = 0

4x = 68

x = 17

So, the number of people on tour: 50+17 = 67

This means that 67 people can maximize the profit.

and the profit would be:

P = 4000 + (68 × 17) - (2 × 17²)

P = $4578

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Answer:

-8

Step-by-step explanation:

-0.5(3q+15) = 1.5(q+11)

3q + 15 = -3q - 33

6q = -48

q = -8

The measure of angle x and y in the cyclic quadrilateral are 93 and 59 degrees.

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

The opposite angles in a cyclic quadrilateral add up to 180°. The opposite angles of a cyclic quadrilateral are supplementary.

Therefore, let's find the measure of x and y in the cyclic quadrilateral.

Hence,

x + 87 = 180

x = 180 - 87

x = 93 degrees

y + 121 = 180

y = 180 - 121

y = 59 degrees

Therefore,

x = 93°

y = 59°

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The double integral of sin(xy) over the rectangle r equals 1 when a is approximately equal to 0.986, with 0 ≤ a ≤ π.

The iterated integral to compute the double integral over the rectangle r = {(x,y) : 0 ≤ x ≤ π, 0 ≤ y ≤ a} of sin(xy) is given by:

∫∫r sin(xy) dA = ∫₀^a ∫₀^π sin(xy) dx dy

Integrating with respect to x first, we have:

∫₀^a ∫₀^π sin(xy) dx dy = ∫₀^a [-cos(πy) + cos(0)] dy

= ∫₀^a (1 - (-1)^n) dy

= a - (a/π)sin(πa)

For what values of a is ∫∫r sin(xy) dA equal to 1?

We need to solve the equation:

a - (a/π)sin(πa) = 1

Multiplying both sides by π, we get:

aπ - a sin(πa) = π

Now, let f(a) = aπ - a sin(πa) - π. We need to find the values of a such that f(a) = 0.

Using numerical methods, we can find that there is only one solution in the interval [0,π], which is approximately a = 0.986.

Therefore, the double integral of sin(xy) over the rectangle r equals 1 when a is approximately equal to 0.986, with 0 ≤ a ≤ π.

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a.the two-dimensional shape of the cross-section will be a square.

b. the two-dimensional shape of the cross-section will also be a square.

c .The shapes are the same because regardless of the orientation of the cut, the cross-section will always be a square since all sides of a cube are equal.

A two-dimensional shape is a geometric figure that has only two dimensions, namely length and width, but no thickness or depth. Examples of two-dimensional shapes include circles, squares, triangles, rectangles, and polygons. These shapes are typically represented on a flat surface such as a piece of paper or a computer screen.

a. If the cube is sliced horizontally, the two-dimensional shape of the cross-section will be a square.

b. If the cube is sliced vertically, the two-dimensional shape of the cross-section will also be a square.

c. The shapes are the same because regardless of the orientation of the cut, the cross-section will always be a square since all sides of a cube are equal. The orientation of the cut only affects which faces of the cube are visible in the cross-section, but the shape itself remains the same.

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