8(−5d−9)−3(−6d+10) in simplest terms?

Answer:

[tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]

Step-by-step explanation:

Given that

curve [tex]y = \dfrac{\pi x}{3}, 0 \leq x \leq 3[/tex]

The objective is to find the area of the surface obtained by rotating the above curve about the x-axis.

Suppose f is positive and posses a continuous derivative,

the surface is gotten by the rotating the curve about the x-axis is:

[tex]S = \int ^b_a 2 \pi f (x) \sqrt {1 + (f' (x))^2 } \ dx[/tex]

The derivative of the function [tex]y' = \dfrac{\pi}{3} cos \dfrac{\pi x}{3}[/tex]

As such, the surface area is:

[tex]S = \int ^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt {1 +(\dfrac{\pi}{3}cos \dfrac{\pi x}{3})^2 } \ dx[/tex]

Suppose ;

[tex]u = \dfrac{\pi}{3}cos \dfrac{\pi x}{3}[/tex]

[tex]du = -( \dfrac{\pi}{3})^2 sin \dfrac{\pi x}{3} \ dx[/tex]

If x = 0 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (0)}{3} = \dfrac{\pi}{3}[/tex]

If x = 3 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (3)}{3}[/tex]

[tex]u = \dfrac{\pi}{3}(-1)[/tex]

[tex]u = -\dfrac{\pi}{3}[/tex]

The equation for S can now be rewritten as:

[tex]S = \int^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt{1+(\dfrac{\pi}{3} cos \dfrac{\pi x}{3})^2 }\ dx[/tex]

[tex]S = 2 \pi \int ^{-\frac{\pi}{3} }_{\frac{\pi}{3}}(-\dfrac{9 \ du }{\pi^2} ) \sqrt{1+u^2}[/tex]

[tex]S = 18 \pi * \dfrac{1}{\pi ^2 } \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]

[tex]S = \dfrac{18} {\pi} \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]

[tex]S = \dfrac{18} {\pi} (2 \int ^{-\frac{\pi}{3}}_{0} \sqrt{1+u^2} \ du)[/tex]

since [tex](\int ^a_{-a} fdx = 2\int^a_0 fdx , f= \sqrt{1+u^2} \ is \ even )[/tex]

Applying the formula:

[tex]\int {\sqrt{1+x^2}} \ d x= \dfrac{x}{2} \sqrt{1+x^2}+ \dfrac{1}{2} In ( x + \sqrt{1+x^2})[/tex]

[tex]S = \dfrac{36}{x}[ \dfrac{u}{2} \sqrt{1+u^2}+ \dfrac{1}{2} \ In (u+ \sqrt{1+u^2}) ] ^{\frac{\pi}{3}}_{0}[/tex]

[tex]S = \dfrac{36}{x}[ \dfrac{\dfrac{\pi}{3}}{2} \sqrt{1+\dfrac{\pi^2}{9}}+ \dfrac{1}{2} \ In (\dfrac{\pi}{3}+ \sqrt{1+\dfrac{\pi^2}{9}})-0 ][/tex]

[tex]S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})[/tex]

Therefore, the exact area of the surface is [tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]

The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex].

Given that,

The exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx\3 , 0 ≤ x ≤ 3.

We have to determine,

Area of the surface obtained by rotating the curve.

According to the question,

Suppose f is positive and posses a continuous derivative,

The surface is gotten by the rotating the curve about the x-axis is:

Area of the surface is given by,

[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+ (f'(x))} } \, dx[/tex]

The given curve is x-axis,

[tex]y = \dfrac{sin\pi x}{3}[/tex]

The derivative of the function is,

[tex]\dfrac{dy}{dx} =\dfrac{\pi }{3} \dfrac{ cos\pi x}{3}[/tex]

The surface area is,

[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]

Substitute the value of f(x),

[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]

Suppose;

[tex]u = \dfrac{\pi }{3}cos\dfrac{\pi x}{3}dx\\\\\du =( \dfrac{-\pi }{3})^2 sin\dfrac{\pi x}{3}dx\\\\if \ x = 0, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (0)}{3} = \dfrac{\pi }{3}\\\\if \ x = 3, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (3)}{3} = \dfrac{\pi }{3}(-1)= \dfrac{-\pi }{3}[/tex]

Then,

[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\\\\S = 2\pi \int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} (\dfrac{-9du}{\pi ^2})\sqrt{1+u^2} \ du\\\\S = 18\pi \times \dfrac{1}{\pi ^2}\int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} \sqrt{1+u^2} \ du\\\\S = \dfrac{18}{\pi}\int\limits^{\frac{-\pi}{3}}_ {0} 2\sqrt{1+u^2} \ du\\\\\\[/tex]

Since,

[tex](\int\limits^a_{-a}{f} \, dx = 2\int\limits^a_0 {f} \, dx , \ f = \sqrt{1+u^2}\ is \ even)[/tex]

By applying the formula to solve the given integration,

[tex]\int {\sqrt{1+x^2} } \, dx = \dfrac{x}{2}\sqrt{1+x^2} + \dfrac{1}{2} \ ln(x+\sqrt{1+x^2})\\\\S = \dfrac{36}{2} [ \dfrac{u}{2} \sqrt{1+u^2} + \dfrac{1}{2} \ ln(u+\sqrt{1+u^2})}]^{\frac{\pi }{3}}_0\\\\[/tex]

[tex]S = \dfrac{36}{2} [ \dfrac{\dfrac{\pi }{3}}{2} \sqrt{1+\dfrac{\pi^2 }{9}} + \dfrac{1}{2} \ ln(\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}}-0)]\\\\S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]

Hence, The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]

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Answer:

-8 degrees

Step-by-step explanation:

4-12 = -8

It dropped 12 degrees in 7 hours.

Answer: -8°

Step-by-step explanation:

4 - 12

Answer:

D. 327.25

Step-by-step explanation:

You start out with a gross pay of $415.00. When you have a deduction from your gross pay, it means it gets subtracted. So subtract the deductions of 48, 31.25, and 8.50 from 415 and it leaves you with 327.25.

415 48-31.25-8.50 = 327.25

Answer:

approximately 26.7 million

Step-by-step explanation:

Let x be the number of cruise passengers in 2017.

6.7% increase of x gives us 28.5 m cruise passengers in 2018.

Thus, 106.7 % of x = 28.5

[tex] \frac{106.7}{100} * x = 28.5 [/tex]

[tex] \frac{106.7x}{100} = 28.5 [/tex]

Multiply both sides by 100

[tex] \frac{106.7x}{100} * 100 = 28.5*100 [/tex]

[tex] 106.7x = 2850 [/tex]

Divide both sides by 106.7

[tex] \frac{106.7x}{106.7} = \frac{2850}{106.7} [/tex]

[tex] x = 26.7 [/tex] (approximated)

Number of passengers in 2017 must have been approximately 26.7 million

Answer:

B

Good luck in Geometry my guy!

Answer:

50

Step-by-step explanation:

8 + 10a - 3 + 5a   when a=3

8+10(3)-3+5(3)=

8+30-3+15=

38+15-3=50

Answer:

not equal

Step-by-step explanation:

Answer:

4/5 is not equal to 5/4.

4/5 x 4 = 16/20

5/4 x 5 = 25/20

25/20 > 16/20

Answer:

Hey there!

There are actually multiple answers.

7 and 14 have a GCF (greatest common factor) of 7, and so do 7 and 7.

Let me know if this helps :)

Answer:

answers are:

7 and 14

The factors of 7 is:  1, 7

The factors of 14 is:  1, 2, 7, 14

28 and 7

Factors of 28:  1, 2, 4, 7, 14, 28

Facotrs of 7:  1, 7

Step-by-step explanation:

others:  

21, 3 is GCF is 3

The factors of 3 are: 1, 3

The factors of 21 are: 1, 3, 7, 21

7, 1 is GCF is 1

The factors of 1 are: 1

The factors of 7 are: 1, 7

Answer:

Cosec θ = – 25/24

Step-by-step explanation:

From the question given, we obtained the following information:

Tan θ = – 24/7

Cosec θ =?

Tan θ is negative in the forth quadrant.

Please see attached photo.

Tan θ = Opposite /Adjacent

Opposite = – 24

Adjacent = 7

Hypothenus = x

Thus, we can obtain the value of x by using the pythagoras theory as illustrated below:

x² = (–24)² + 7²

x² = 576 + 49

x² = 625

Take the square root of both side

x = √625

x = 25

Next, we shall determine Sine θ. This can be obtained as follow:

Opposite = – 24

Hypothenus = 25

Sine θ = ?

Sine θ = Opposite /Hypothenus

Sine θ = –24/25

Finally, we shall determine the Cosec θ. This can be obtained as follow:

Cosec θ = 1 /Sine θ

Sine θ = –24/25

Cosec θ = 1 ÷ –24/25

Cosec θ = 1 × – 25/24

Cosec θ = – 25/24

Answer:

2 works

-3 is extraneous

Step-by-step explanation:

sqrt(x + 7) - 1 = x                      Add 1 to both sides

sqrt(x + 7) = x + 1                     Square both sides

(x + 7) = (x + 1 )^2

x + 7 = x^2 + 2x + 1                Subtract x from both sides

0 = x^2 + x + 1 -7                    

0 = x^2 + x - 6                        This will factor

(x + 3)(x - 2)  = 0                      Find the values for x

x + 3 = 0

x = - 3

x - 2 = 0

x = 2

Now you must check this to see if both values work

sqrt(-3 + 7)  - 1 = -3

sqrt(4) - 1 = -3

2 - 1 =? - 3

1 does not equal - 3. Therefore - 3 is extraneous. Try x = 2

sqrt(2 + 7) - 1 = 2

sqrt(9) - 1 = 2

3 - 1 = 2

2 = 2

Answer:

t-t

Step-by-step explanation:

Answer: 11 stamps per page

Step-by-step explanation: 132 divided by 12

Answer:

A. 18

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

12(20 - 18) - 3(6)

Step 2: Multiply parenthesis

12(20 - 18) - 18

Step 3: Parenthesis

12(3) - 18

Step 4: Multiply

36 - 18

Step 5: Subtract

18

Answer:

[tex]0 \leq x \leq 100[/tex]

0, 40, and 80 are the values that work for this compound inequality.

Step-by-step explanation:

To create a compound inequality, we have to examine the conditions for [tex]x[/tex] to work.

Since [tex]x[/tex] can not be below 0° C, that means that [tex]x[/tex] must be greater than or equal to 0.

Which is represented as [tex]x\geq 0[/tex], or [tex]0\leq x[/tex].

Since [tex]x[/tex] can not be above 100° C, that means [tex]x[/tex] must be less than 100.

Which is represented as [tex]x \leq 100[/tex].

We can combine both inequalities into one, where [tex]x[/tex] is shared between the two. This creates [tex]0\leq x \leq 100[/tex].

Let's test each value of [tex]x[/tex] .

0 is equal to 0 and less than 100, so it works.

40 is greater  than 0 and less than 100, so it works.

80 is greater  than 0 and less than 100, so it works.

120 is greater  than 0 and greater than 100, so it doesn't work.

160 is greater  than 0 and greater than 100, so it doesn't work.

Hope this helped!

Answer:

Step-by-step explanation:

x + x + 10 + 3x = 180

5x + 10 = 170

5x = 170

x = 36°

3(36)= 108° the largest angle

When given the base of and height of a triangle, you can use this formula:

[tex]area = \frac{1}{2} bh[/tex]

Plug in the known values:

[tex]area = \frac{1}{2} (18)(6)[/tex]

Solve:

[tex]area = \frac{1}{2} \times 108[/tex]

[tex]area = 54[/tex]

Add units:

[tex]area = 54cm^{2} [/tex]

Answer:

x= 4 i think

Step-by-step explanation: -24 divided by 3 equals 8 subtract for and there is your answer

Answer:

D

Step-by-step explanation:

I answer this already.  XD

Answer:

D

Step-by-step explanation:

sorry i needed these points XD

Answer:

153:108

1.42

1 [tex]\frac{5}{12}[/tex]

1.42 is the approximate value of the ratio [tex]\frac{153}{108}[/tex].

The ratio is the number of times one value contains or is contained within the other in a quantitative relationship between two numbers.

The ratio of 153:108 is given.

Other forms of the ratio are

[tex]\frac{153}{108}=\frac{17}{12}[/tex]

[tex]=1.41666...\approx 1.42[/tex] (rounded to the hundredth place.

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Answer: Pick anyone that suits you

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{Eight \ subtracted \ from \ the \ product \ of \ three \ and \ a \ number.}}[/tex]

Step-by-step explanation:

[tex]\sf 3n-8[/tex]

n is a number.

8 is subtracted from the product of 3 and a number.

The verbal expression would be :

Eight subtracted from the product of three and a number.

Answer: 11 9/35

Step-by-step explanation: just add the whole number to the fraction.

Answer & Step-by-step explanation:

[tex]11+\frac{9}{35}[/tex]

Add the whole number to the fraction:

[tex]11 \frac{9}{35}[/tex]

:Done

Answer:

x = 45°, y = 53°, z = 82°

Step-by-step explanation:

x is the first angle, y is the second, and z is the third.

The sum of the second and third, which is denoted by y + z, is 3 times the measure of the first, which is just x. So, we have:

y + z = 3 * x

Additionally, the third angle, z, is 29 more than the second, y, so:

z = 29 + y

We also know that the sum of the three is 180, so:

x + y + z = 180

Let's substitute y + z in the last equation with 3 * x:

x + y + z = 180

x + 3x = 180

4x = 180

x = 45

Now, we know that y + z = 3 * 45 = 135. We also know that z = 29 + y, so substitute 29 + y in for z in y + z = 135:

y + z = 135

y + (29 + y) = 135

2y + 29 = 135

2y = 106

y = 53

Finally, use this value of y to solve for z:

z = 29 + y

z = 29 + 53 = 82

Thus, the angles are x = 45°, y = 53°, and z = 82°.

~ an aesthetics lover

Answer:

a

The  population is  2000

b

The  sample is  36

c

No this is not a random sample  

Step-by-step explanation:

From this question we are told that

   A computer outlet store receives a shipment of 2000 computer chips

  The  number of unites chosen by the owner is  n=  36

Generally the population for this statistical test is  N  =  2000

This is because the 2000 is the entire pool from which a statistical sample is drawn

  Generally 36  is  the sample  because this is the number that will be statistically tested and its result will be generalized for every other element of the population

 Now if the 36 chips are all selected from the top then the sample  is not a random sample because in a sample each element of the sample  have an equal likelihood of been selected from the population but in the case of the question each element are selected base it accessibility

One example is the idea of two parts of a book that open up. Each flat part is a plane and the two planes intersect along the spine of the book.

Another example would be a wall intersecting with the floor. Both are flat surfaces.

A third example would be a laptop's screen as one plane and the keyboard as the other plane. They intersect at the hinge of the laptop.

For each example, the surface has a finite amount of area and it doesn't extend forever in all four directions. Theoretically, a plane is where the flat surface extends in all four directions infinitely. Though of course, real life has limitations but the idea is still applicable in a way.

Note how for each example, the two planes intersect to form a line. Also, each plane must be flat without bending or curving in any way.

An expression is a combination of numbers, variables, and functions such as addition, subtraction, multiplication or division, etc.

The expression for the product of d and 4 is d x 4.

An expression is a combination of numbers, variables, and functions such as addition, subtraction, multiplication or division, etc.

Example:

3 added to 2 will be 3 + 2.

4 times 3 is 4 x 3.

4 less than 6 is 6 - 4.

We have,

The product of d and 4.

This can be written as:

= d x 4

Thus the expression for the product of d and 4 is d x 4.

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Answer:

  a = 3x^2 +9x

Step-by-step explanation:

Put the given dimensions in the formula and simplify. The distributive property is useful.

  a = (1/2)bh

  a = (1/2)(6x)(x+3) = 3x(x +3)

  a = 3x^2 +9x

Answer:

8,0

8,-9

2,1

Step-by-step explanation:

It is always going to be the opposite.

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , thus

L(- 8, 0 ) → L'(8, 0 )

M(- 8, 9 ) → M'(8, 9 )

N(- 2, - 1 ) → N'(2, - 1 )

Answer:

[tex]\sqrt{4}, \ \sqrt{9} \text{ are rational numbers.}[/tex]

Step-by-step explanation:

Hello,

[tex]\sqrt{n^2}=n \ for \ n\geq 0\\\\\text{For instance}\\\\\sqrt{2^2}=2=\sqrt{4}\\\\\sqrt{3^2}=3=\sqrt{9}[/tex]