8 sin x cos3 x + 8 sin3 x cos x = ?

Double angle identity for sine:

[tex]\sin(2x) = 2 \sin(x) \cos(x)[/tex]

[tex]\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)[/tex]

Factorize the left side.

[tex]2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)[/tex]

Pythagorean identity:

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)[/tex]

so that

[tex]\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}[/tex]

Answer: B

Step-by-step explanation:

[tex](5x^2 -x-3)(2x+6)\\\\=2x(5x^2 - x-3)+6(5x^2 - x-3)\\\\=10x^3 - 2x^2 - 6x+30x^2 - 6x-18\\\\=\boxed{10x^3 +28x^2 - 12x-18}[/tex]

Answer:

x = 15

y = 60

Step-by-step explanation:

Angles (x + 50) and (3x + 20) follows corresponding angle theorem.

-----

⇒ x + 50 = 3x + 20

⇒ x - 3x = 20 - 50

⇒ -2x = -30

⇒ x = 15

The angles (x + 50) and (2y - 5) lies on a straight line which sum ups to 180°

⇒ (x + 50) + (2y - 5) = 180

⇒ 2y + x + 45 = 180

⇒ 2y + 15 + 45 = 180

⇒ 2y + 60 = 180

⇒ 2y = 120

⇒ y = 60

Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.

The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.

Equation for Rink A:

Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4

Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:

19 = 4(1) + b

19 - 4 = b

b = 15

Substitute m = 4 and b = 15 into y = mx + b:

y = 4x + 15 [equation for Rink A]

Equation for Rink B:

Unit rate (m) = (39 - 15)/(5 - 1) = 24/4 = 6

Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:

15 = 6(1) + b

15 - 6 = b

b = 9

Substitute m = 6 and b = 9 into y = mx + b:

y = 6x + 9 [equation for Rink B]

To find how many hours (x) both would cost the same (y), make both equation equal to each other

4x + 15 = 6x + 9

4x - 6x = -15 + 9

-2x = -6

x = 3

The hours Jeremy wants to skate is 3.

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The vertices of an inscribed square of a circle are located on the circumference and on perpendicular diameters

The vertices of a square inscribed in a circle can be located as follows;

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The number of students from the math club that went to the soap box derby.

From the question, we see that there are two vans and 6 students in each van.

Thus, to get the number of students from the math club that went to the soap box derby, we will solve as follows;

Number of students that went to derby = 2 × 6 = 12

Complete question is;

The entire school 250 students went to the soap box derby. The math club went in 2 vans and each van held 6 students how many students from the math club went to the soap box derby

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Answer:

[tex]\sqrt{269}[/tex] is ≈ 14.01

Step-by-step explanation:

If the table top is a square, to find the area, you would multiply one side times itself.

If you are given the area, and need to find the sides, you will take the square root of the area to find the side length.

Your question doesn't say to round, but 269 is not a perfect square.

[tex]\sqrt{269}[/tex] is ≈ 14.01

If the area of the base was 169, that is a perfect square. [tex]\sqrt{169}[/tex] = 13

Answer:

Jesse will need about 89.5 square inches of gift wrap.

Step-by-step explanation:

We need to find the amount of wrapping paper that will cover the entire outside surface of the cylindrical gift. This means that we need to find its surface area, which is the total area an object's surface occupies.

The formula for cylinder surface area is as follows:

[tex]A=2\pi rh+2\pi r^{2}[/tex] (where r = radius and h = height)

In this case, the radius, or r, is 1.5 in, and the height, or h, is 8 in. Plugging these values into our formula, we get a total surface area of:

[tex]A=2\pi rh+2\pi r^{2}\\= 2\pi *1.5*8+2\pi * 1.5^{2} \\= 24\pi +4.5\pi \\=28.5\pi \\ \approx \text{\bf 89.5 \bf $in^{2}$ }[/tex]

Hope this helps!

Answer:

28.5 pi square inches

Step-by-step explanation:

The surface area of a cylinder is the lateral area plus two times the area of the base circle. The lateral area is the perimeter of the base circle times the height, and the perimeter of a circle is 2*pi*r.

Therefore the lateral area is:

LA = Perimeter*Height

     = 2*pi*r*h

     = 2*pi*1.5*8

     = 24pi

The base area would be A = pi*r*r since the bases of cylinders are circles.

BA = pi*r*r

     = pi*1.5*1.5

     = 2.25 pi

Since there are two circles (top AND bottom) in a cylinder, the final surface area of the cylinder would be:

SA = LA + 2BA

     = 24pi + 2*2.25pi

     = 24pi + 4.5pi

     = 28.5 pi

In ancient civilization, the individuals with varying physical appearance were fill member of the society by adopting the cultural norms.

It should be noted that the physical variation means the range of values for the mental and physical characteristics of human beings.

Classical variations invested the most importance in tribal affiliation rather than the physical appearance.

Also, societies still equate physical characteristics like eye and hair color.

Anthropologists conclusion about human race is that there are no human biological races.

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The solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equations:

3x - 4y=12 and

2x+y=8

Multiplu by 4 on both side in equation  2x+y=8

8x + 4y = 32

Add the equaton 8x + 4y = 32 and 3x - 4y=12

3x - 4y=12

8x + 4y = 32

11x = 44

x = 4

Similarly, we can find the value of y:

y = 0

Thus, the solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0

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Answer:

puede ser su raiz que seria 90.79

Step-by-step explanation:

Answer:

a is to b,

a : b

w is to x,

w : x

a is to b as w is to x,

a : b : : w : x

In fraction form,

a/b = w/x

The first missing number in the sequence is 35, and the last missing number is 77.

The two missing numbers in the given sequence is calculated as follows;

= ?    49     63    ?

The given sequence is factor 7 which increases by 2

= 7 x 5      7 x 7       7 x 9     7 x 11

= 35         49          63          77

Thus, the first missing number in the sequence is 35, and the last missing number is 77.

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The sequence's initial missing number is 35, and its last missing number is 77.

The following number in the list is

The two missing numbers are determined as follows for the given sequence:

= ? 49 63 ?

The sequence is factor 7, which rises by 2 in the specified order.

= 7 x 5      7 x 7       7 x 9     7 x 11

= 35         49          63          77

Thus, the first missing number in the sequence is 35, and the last missing number is 77.

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According to the empirical rule, the percent of the data points that are below 100 is; 95.44%

We are given;

Mean; μ = 88

Standard deviation; σ = 6

Sample mean; x' = 100

Formula for z-score is;

z = (x' -  μ)/σ

z = (100 - 88)/6

z = 2

Now, from the empirical rule of normal distribution graph attached, we see that at z = 2, the percentage is 95.44%. However, we want to find the percentage that lie below 100. Thus, this is 95.44%

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Answer:

To find a

sin 30=a/6in

1/2=a/6in

2a=6in

a=6in/2

a=3in

To find b

cos 30=b/6in

/3/2=b/6in

2b=/3*6in

b=2/3(two radical three)

I don't get the radical sign so I use / sign on the last 3 steps on the second

Answer:

x=7

Step-by-step explanation:

3x + 0,25x + 0,10 (2x) +0,05 (x + 3) = 24,65

<=> 3x+0,25x+0,2x+0,05x+0,15=24,65

<=> 3,5x=24,5

<=> x=7

Answer:

[tex]sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]

Step-by-step explanation:

angles in II quadrant are found by solvig 180- ∅ where ∅ is the acute angle

Let us then find the acute angle: in[tex]cos^{-} (\frac{4}{5}) = 36.86^{0} \\\\so \ x \ the \ angle \ in \ the \ second \ quadrant \ is \ 180-36.86=143.13^{0} \\\\sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]

Answer: [tex]T=\frac{2}{F-5}[/tex]

Step-by-step explanation:

[tex]F=\frac{2}{T}+5\\\\F-5=\frac{2}{T}\\\\\frac{1}{F-5}=\frac{T}{2}\\\\T=\frac{2}{F-5}[/tex]

The equation of the function is f"(x) = 2x^2 - 3

The parent function is given as:

f(x) = x^4

When it is stretched vertically by a factor of 2, the rule is

f'(x) = 2f(x)

So, we have

f'(x) = 2x^2

When shifted down 3 spaces, the rule is

f"(x) = f'(x) - 3

So, we have:

f"(x) = 2x^2 - 3

Hence, the equation of the function is f"(x) = 2x^2 - 3

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Answer:

2444

Step-by-step explanation:

A half of 3916 is 1963.

A quarter of 1924 is 481.

Therefore, 1963 + 481 = 2444.

Answer:

Notice that the triangles ABC and AMN are similar.

Thus:

[tex]\frac{AC}{MN} = \frac{AB}{MB}\\\\\frac{AC}{6} = \frac{8}{4} = 2\\\\ AC = 12\,\,ft.[/tex]

Using the areas of the circles, the probability of landing in the shaded area of the picture is of 1/81.

The area of a circle of diameter d is given as follows:

[tex]A = 0.25\pi d^2[/tex].

For the smaller circle, the diameter is d = 6, hence the area is:

[tex]A_s = 0.25\pi \times 6^2 = 9\pi[/tex]

For the larger circle, the diameter is d = 54, hence the area is:

[tex]A_l = 0.25\pi \times 54^2 = 729\pi[/tex]

Hence the probability(desired area divided by total area) is:

[tex]p = \frac{9\pi}{729\pi} = \frac{1}{81}[/tex].

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Answer:

Step-by-step explanation:

The Crusades were a series of religious wars initiated, supported, and sometimes directed by the Latin Church in the medieval period. The best known of these Crusades are those to the Holy Land in the period between 1095 and 1291 that were intended to recover Jerusalem and its surrounding area from Islamic rule.

Answer: I am not so sure but I think it’s asking for the median so that would be ANSWER 9.2

Step-by-step explanation:

Answer:

B ∩ (¬A ∩ ¬C)

Step-by-step explanation:

You want to exclude the section C shares with A, the one C shares with B and the one it shares with both. Intersecting ¬A (not A) with ¬C (not C) you obtain the entire area except A and C, which then can be intersected with B to obtain the highlighted area.

Answer:

6

Step-by-step explanation:

most of them are rectangles

(a) The maximum displacement of the wave is 14 cm.

(b) The time for the wave to bounce opposite directions before coming to rest  is 3.0 s.

(c) The period of the wave is 3.0 s and the amplitude is 14 cm.

(d) The graph’s frequency is 0.33 Hz

(e) The wave attained maximum displacement at time 6 s and 7.5 s.

A) The maximum displacement of the wave is the point of maximum rise of the curve = 14 cm

B) Time of motion of the wave; This is the time for the wave to bounce opposite directions before coming to rest makes a complete cycle

It takes the wave 0.75s to bounce up and the 2.25 s to bounce down, and finally it came to rest at 3.0 s.

C) The period of the wave is the time taken for the wave to make a complete cycle = 3 s

Frequency of the wave

f = 1/T

f = 1/3 = 0.33 Hz

The frequency indicates the number of cycles in a second.

D) Position of the wave at time 6 s and 7.5 s

The wave attained maximum displacement at time 6 s and 7.5 s.

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The values have being matched to the variables that they represent here:

The equation of this form y = 12x-40

The variable y has been said to be the amount sam has after Daniel has been paid.

X is the amount that has to be multiplied by what he earns in dollars by the hour.

40 dollars is the amount that he owes which is going to be subtracted from what he earns by the hour.

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