Decompose the composite figure to find its total area.

Answer: To start with, we can admit that a water drop corresponds to 0.05ml. It is the same of saying that 1 litre of water contains closely to 20,000 drops.

The problem can be classified as a Combination problem. A combination is a way of selecting objects from a larger set without regard to their order. In other words, a combination is a selection of objects where the order in which they are selected does not matter.

In mathematics, permutations and combinations are techniques used to count the number of ways in which objects can be selected and arranged. The counting principle, also known as the multiplication principle, is used to count the number of ways in which independent events can occur. In this problem, the researcher needs to select 6 people from a group of 13 volunteers. The order of selection is not important, as long as the researcher ends up with a group of 6 people. Therefore, this problem can be solved using combination.

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The complete question is:

Identify the following as Permutations, Combinations or Counting Principle problems. (no need to solve):

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?

Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.

A straight line that only touches the circumference of a circle once is said to be the tangent to that circle. The point of tangency or contact point is the location where the tangent contacts a circle.

ABCD is a square having each side 8 units.

A center O of circle with radius r is passing through A and D such that it forms tangent to BC at E.

Joining OD, OA, OE and OF.

AD is the chord, having mid point F. Line OF meets at center of circle to point F.

Thus,  OF ⟘ AD.

In the right angle ODF,

OD=r

OF= 8—r

DF = FA = 4

OD² = OF² +FD²

r² = (8-r)² + 4²

Simplifying,

r² = 64 + r² - 16r + 16

16r = 80

r = 5

Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.

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Note that the triangle DEF should be congruent to triangle AED, since they have two sides and the included angle in common.

In geometry, a circle is a closed two-dimensional shape in which every point on the boundary is equidistant from a single fixed point inside the shape, called the center of the circle. The distance from the center to any point on the circle is called the radius of the circle. The set of all points that are equidistant from the center of the circle is called the circumference of the circle. The circumference is a one-dimensional object, and its length can be calculated using the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159.

Here,

Based on your instructions, it seems that you are performing a construction to copy a triangle using the SAS (side-angle-side) method. Here are the steps involved:

Draw line segment DE of the length you calculated in part B.

Using point E as the center, draw a circle with a radius equal to the length of DE.

Using point E as the vertex, draw an angle that is equal to the measure of angle AED using line segment ED as one of its sides. Draw ray EF from the vertex E to extend this angle.

Locate the intersection of ray EF and the circle, and label the point of intersection F.

Draw a line segment from point E to point F.

Finally, draw the triangle DEF by connecting points D, E, and F with line segments.

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Answer:

Step-by-step explanation: Pythagoras' theorem states that the square of the hypotenuse, (c2), is equal to the sum of the squares of the other two sides, (a2 + b2). c2 = a2 + b2 = 52 + 92 = 25 + 81 = 106 c = √106 = 10.30 (2dp.) The hypotenuse has length 10.30cm

The fraction (A) 1/2 will fill up the missing blank like:

6/10 > 1/2 > 1/3

Every number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.

So, we will multiply each fraction by a unit fraction to create a common denominator in order to compare fractions with various denominators:

= 6/10 * 6/6

= 36/60

Then,

= 1/3 * 20/20

= 20/60

Now, case (A): 1/2

= 1/2 * 30/30

Now, substitute and check:

36/60 > 30/60 > 20/60

Then, Yes it is the solution.

(Since we got our answer then we don't need to calculate more.)

Therefore, the fraction (A) 1/2 will fill up the missing blank like:

6/10 > 1/2 > 1/3

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Correct question:

Choose the fraction that goes in the blank.

6/10 >_______> 1/3

a- 1/2

b- 1/4

c- 2/3

d- 3/4

Answer: To find the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 4x - x^2 about the line y = 6, we can use the method of cylindrical shells.

The region enclosed by the graphs of the two equations looks like this:

         /|

 4x-x^2 / |

       /  |

      /   |

     /    |

y=x^2 ------

To rotate this region about the line y = 6, we need to shift the entire region 6 units upward, like this:

        /|  

       / |

      /  |

     /   |

    /    |

y=10 ------

 |  /|  

 | / |

 |/  |

y=6 ------

Now we can see that the solid we want to find is the result of rotating the region bounded by the two curves around the line y = 10 (which is the same as rotating the region bounded by the shifted curves around the line y = 6).

To use the method of cylindrical shells, we need to integrate over the range of x values that define the region. The limits of integration are where the two curves intersect, which can be found by setting them equal to each other:

x^2 = 4x - x^2

2x^2 - 4x = 0

2x(x - 2) = 0

x = 0 or x = 2

So the limits of integration are x = 0 and x = 2. The height of each cylindrical shell is the difference between the two curves at the given x value, so it is:

y = 4x - x^2 - x^2 = 4x - 2x^2

The radius of each cylindrical shell is the distance from the x-axis to the line y = 6, which is:

r = 6 - y = 6 - (4x - 2x^2)

Now we can set up the integral to find the volume:

V = ∫[0,2] 2πr y dx

V = ∫[0,2] 2π(6 - 4x + 2x^2)(4x - 2x^2) dx

V = ∫[0,2] 16πx - 24πx^2 + 8πx^3 dx

V = [8πx^2 - 8πx^3 + 2πx^4]₀²

V = 32π/3

Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 4x - x^2 about the line y = 6 is 32π/3 cubic units.

Step-by-step explanation:

After reading these two statements, we have both statements are false in nature but along with this these are logically equivalent. So, the right answer is option (d).

Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and a second statement can also be true in its own context, they just have to have the same meaning.

1) As we know, if there is exactly two lines or sides then these can't be make a closed figure. That's why it is not a polygon and statement is false one.

2) This statement is contrapositive of first one. In other words, if we consider the contrapositive of this statement that is if it is a polygon then it have two exactly two sides. Contrapositive of statement is false because polygon have more than two sides. This implies this conditional statement is also false. But, both of statements are satisfied the logical equivalent conditions (one true or false --> othe true or false respectively). Therefore, option (d) is answer.

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Answer:

BOTH STATEMENTS ARE FALSE

Step-by-step explanation:

The two statements are logically equivalent because they are BOTH false.

The possible formula for the transformation shown on the graph is given as follows:

y = f(x) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

From the graph, the function is translated four units up, hence the formula is given as follows:

y = f(x) + 4.

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