Integrate sin^9(x)dx ...?

The converse statement  interchange the hypothesis and the conclusion.

The converse of x=9 then [tex]x^{2} =81.[/tex]  is [tex]x^{2} = 81 then x=9.[/tex] is true.

A biconditional statement is defined to be true whenever both parts have the same truth value . combining  the statements as a biconditional we have

If [tex]x^{2}[/tex]. = 81, then x = 9.  

x = 9 if and only if [tex]x^{2} .[/tex] = 81

Option D is the right answer.

Answer:

41.57 unit²

Step-by-step explanation:

We know,

Area of a regular hexagon = [tex]3\times (sidelength)\times (apothem)[/tex].

The length of the apothem = [tex]2\sqrt{3}[/tex] units.

Since, we know, 'a regular hexagon splits into 6 identical equilateral triangles'.

As, the apothem of the regular hexagon = height of the equilateral triangle

So, height of the equilateral triangle = [tex]2\sqrt{3}[/tex] units.

As, in the equilateral triangle, 'One of the side length is the S, other will be [tex]\frac{S}{2}[/tex] and height is [tex]2\sqrt{3}[/tex] units'.

So, using Pythagoras Theorem, we have,

[tex]hypotenuse^{2}=perpendicular^{2}+base^{2}[/tex]

i.e. [tex]S^{2}=(\frac{S}{2})^{2}+(2\sqrt{3})^{2}[/tex]

i.e. [tex]S^{2}=\frac{S^2}{4}+12[/tex]

i.e. [tex]S^{2}-\frac{S^2}{4}=12[/tex]

i.e. [tex]\frac{3S^2}{4}=12[/tex]

i.e. [tex3S^2=48[/tex]

i.e. [texS^2=16[/tex]

i.e. S= 4 units

That is, the side length of the hexagon = 4 units.

Thus, the area of the hexagon is given by,

Area of a regular hexagon = [tex]3\times (4)\times (2sqrt{3})[/tex]

i.e. Area of a regular hexagon = [tex]12\times (2sqrt{3})[/tex]

i.e. Area of a regular hexagon = [tex]24sqrt{3}[/tex]

i.e. Area of a regular hexagon = 41.57 unit²

Hence, the area of the regular hexagon is 41.57 unit².

The length of the pantry is 3 feet.

To find the length of the pantry, we need to determine its area first. According to the question, the kitchen is 9 times the size of the pantry. With the kitchen's area being 81 square feet, the pantry's area would be 81 square feet divided by 9, which equals 9 square feet. Since we are given that the width of the pantry is 3 feet, we divide the total area of the pantry by its width to find the length.

The calculation is as follows:

Area of kitchen: 81 sq ft

Area of pantry: 81 sq ft / 9 = 9 sq ft

Width of pantry: 3 ft

Length of pantry: Area of pantry / Width of pantry = 9 sq ft / 3 ft = 3 feet long.

Answer:

1 gal

Step-by-step explanation:

The  larger down payment beneficial to a home investor is because of option C.

The following information should be considered:

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The trinomial [tex]2n^2[/tex]+3n-9 cannot be factored using integers as no two numbers exist that multiply to give -18 (the product of the leading coefficient and the constant term) and add up to 3 (the middle coefficient).

To factor the quadratic trinomial [tex]2n^2[/tex]+3n-9, one must find two binomials that, when multiplied together, give the original trinomial. Factoring complex trinomials can sometimes be achieved by finding two numbers that multiply to give the product of the leading coefficient (2 in this case) and the constant term (-9 in this case), and add to give the middle coefficient (3 in this case). However, for this particular trinomial, such numbers do not exist, and it cannot be factored using integers. This means that either the trinomial is prime (cannot be factored), or it would require the quadratic formula to solve for factors involving irrational or complex numbers.

Answer : The number of text messages that will result in the exact same charge from both companies is, 500

Step-by-step explanation :

Let the number of text messages be, 'x'

Cell phone company A charges $20 per month plus $0.05 per text message. Thus, the equation will be:

[tex]20+0.05x=0[/tex]     ............(1)

Cell phone company B charges $10 per month plus $0.07 per text message. Thus, the equation will be:

[tex]10+0.07x=0[/tex]        ............(2)

Now equating equation 1 and 2, we get:

[tex]20+0.05x=10+0.07x[/tex]

[tex]20-10=0.07x-0.05x[/tex]

[tex]10=0.02x[/tex]

[tex]x=\frac{10}{0.02}[/tex]

[tex]x=500[/tex]

Thus, the number of text messages that will result in the exact same charge from both companies is, 500

The zeros of the function y = 9x³ - 9x are x = 0, x = 1, and x = -1. There are no multiple zeros for this function.

The question seeks to identify the zeros of the function y = 9x^3 - 9x. To find the zeros, we set the function equal to zero and solve for x.

The zeros of the function are x = 0, x = 1, and x = -1.

Therefore, as per the above explaination, the correct answer is  x = 0, x = 1, and x = -1.

the picture in the attached figure

we know that

if ABC is an isosceles triangle

then

AB=BC

angle A=angle C=45 degrees

and

triangle ABD and triangle BDC also are isosceles triangles

AD=BD=x

DC=BD=x

the hypotenuse AC is equal to

[tex] AC=AD+DC\\ AC=x+x\\ AC=2x [/tex]

To find the length AB applying the Pythagorean Theorem

[tex] AC^{2} =AB^{2} +BC^{2} [/tex]

remember that AB=BC

[tex] AC^{2} =2AB^{2} [/tex]

[tex] AC^{2} =2AB^{2}\\\\ AB=\frac{AC}{\sqrt{2}}\\\\ AB=\frac{2x}{\sqrt{2}}\\\\ AB=x\sqrt{2} [/tex]

therefore

the answer is

the length of one leg of the large right triangle in terms of x is equal to [tex] x\sqrt{2} [/tex]

Answer:

b)x/2

Step-by-step explanation:

took the test

To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval. Using a graphing utility, we can plot the function and verify the result.

To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval.

Using a graphing utility, we can plot the function and verify the result. The integral will give us the area under the curve.

A graphing utility like Desmos or Wolfram Alpha can be used to plot the function and find the area under the curve.

Answer:

9,878,813

Step-by-step explanation:

First, make 0.6% into a decimal

0.6 / 100 = 0.006  

Then, multiply the number of people living in Michigan in 2000 by the number of people decreased (the percentage decrease) in 2010

9,938,444 x 0.006 = 59630.664

Last, subtract the percentage decrease by the original population in 2000

9,938,444 – 59630.664 = 9,878,813

In 2010 the approximate population in Michigan was about 9,878,813 (to the nearest whole person)

Answer: a

Step-by-step explanation: that person coulda said that

To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.

To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.

The distance between two points, (x1, y1) and (x2, y2), is given by the formula: √((x2-x1)² + (y2-y1)²).

In this case, the distance between the point (7/25, 24/25) and the origin (0, 0) can be calculated as: √((7/25-0)² + (24/25-0)²) = √((49/625) + (576/625)) = √(625/625) = 1.

Since the distance between the given point and the origin is indeed equal to 1, we can conclude that the point is on the unit circle.

Answer:

17 trips will it take him to move 51 boxes

Step-by-step explanation:

Given: Anton can carry 3 boxes per trip.

That's mean for 1 trip he carry 3 boxes .

To carry 51 boxes he make , [tex]\frac{51}{3}=17[/tex] trip

Therefore, 17 trips will it take him to move 51 boxes.

By using the rules of geometry, we can determine that if P is the midpoint of QN and MP is perpendicular to QN, then rectangles MRQ and MRN are congruent. The congruency is due to the properties of rectangles, triangles, midpoints, and the Hypotenuse-Leg Theorem.

The proof of the congruence of rectangles MRQ and MRN involves geometry rules, particularly the properties of rectangles, triangles, and midpoints. Let's consider rectangle MRQ and MRN. We know that in a rectangle, diagonals are congruent. If P is the midpoint of QN, that means QP = PN. Additionally, if MP is perpendicular to QN, PMQR and PMNR are right triangles with the same hypotenuse.

Using the properties of triangles, we can say that if two right triangles have a congruent hypotenuse and one leg (which is MP in both cases), then these triangles are congruent. Therefore, ∆PMQR is congruent to ∆ PMNR by the Hypotenuse-Leg (HL) Theorem.

Considering that ∆ PMQR ≅ ∆ PMNR and QP = PN, we can say that quadrilaterals MRQN and MRNP are each a parallelogram. Additionally, since MP is perpendicular to QN, quadrilaterals MRQN and MRNP are actually rectangles based on the definition of a rectangle (a parallelogram with a right angle). Therefore, rectangle MRQ is congruent to rectangle MRN.

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The triangle with side lengths of 14 cm, 48 cm, and 50 cm is a right triangle.

The lengths of the sides of the triangle are 14 cm, 48 cm, and 50 cm. To classify the triangle, we need to determine if it is acute, obtuse, or right.

Using the Pythagorean theorem, we can check if it satisfies the condition for a right triangle. If the square of the length of the longest side (50 cm) is equal to the sum of the squares of the other two sides (14 cm and 48 cm), then it is a right triangle.

In this case, (50)^2 = (14)^2 + (48)^2, which is true. Therefore, the triangle is a right triangle.

Final answer:

A triangle with side lengths of 14 cm, 48 cm, and 50 cm is classified as an acute triangle.

Explanation:

A triangle with side lengths of 14 cm, 48 cm, and 50 cm can be classified as an acute triangle.

To determine this, we need to check if the square of the longest side (50 cm) is less than the sum of the squares of the other two sides (14 cm and 48 cm).

502 < 142 + 482

2500 < 196 + 2304

2500 < 2500

This inequality is not true, so the triangle is not obtuse or right. Thus, it is classified as an acute triangle.