Use the properties of limits and the facts given below to find each of the limits given

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times {2}^{3} [/tex]

[tex]v = 33.51 \: {m}^{3} [/tex]

[tex]v = \pi {r}^{2} h[/tex]

[tex]v = \pi \times {2}^{2} \times 6[/tex]

[tex]v = 75.40 \: {m}^{3} [/tex]

[tex]v = 75.40 + 33.51[/tex]

[tex]v = 108.91 \: {m}^{3} [/tex]

Hence, the volume of the given compound shape is 108.91 cubic meters.

sphere:

= 33.51 m^3

cylinder:

= 75.40 m^3

all together:

= 108.91 m^3

There are 258 ways to color the octagon such that no two adjacent vertices are the same color

The given parameters are:

Since no two adjacent vertices are the same color, we use the following  chromatic polynomial of an octagon equation

Ways = (r - 1)⁸ + (r -1)

Substitute 3 for r

Ways = (3 - 1)⁸ + (3 -1)

Evaluate

Ways = 258

Hence, there are 258 ways to color the octagon

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Answer:

10

Step-by-step explanation:

32 - 12 (because C is 12 years younger) = 20

20 / 2 (because twice Anna's age, so we do the inverse) = 10

Anna is 10 years old.

Hope this helps!

Answer:44

Step-by-step explanation:

Answer:

9 / 2 = 4.5

4.5 - 4 = 0.5

Answer:

[tex]f(x)=-2\cos(2x)+1[/tex]

Step-by-step explanation:

Recall the general cosine equation

Identify amplitude

[tex]\text{Amplitude}=\frac{\text{Max-Min}}{2}=\frac{3-(-1)}{2}=\frac{4}{2}=2[/tex]

Identify period and solve for b

[tex]\frac{3\pi}{2}-\frac{\pi}{2}=\pi\\ \\\frac{2\pi}{|b|}=\pi\\ \\2\pi=b\pi\\\\2=b[/tex]

Identify midline

[tex]y=d=1[/tex]

Final Equation

[tex]f(x)=-2\cos(2x)+1[/tex]

Also, the reason why [tex]a=-2[/tex] is because a cosine function starts at its maximum, but since it starts at its minimum, the value of [tex]a[/tex] must be negative and causes the wave to flip about the midline.

Answer:

4/19

Step-by-step explanation:

Jar a: 3/8

Jar b: 1/11

8+11 = 19

3+1= 4

4/19

Step-by-step explanation

Here ...I'm not too sure about the question as you have written

P = 2 ( 1 + 6 ) and ask to solve for L ...

.So I guess the question you have written is wrong .. ...and I guess there should be L in the place of 1.

...So let me correct the question....

P = 2 ( l + 6 )

P = 2l + 12

P - 2l = 12

- 2l = 12 - P

- 2l = - P + 12

Change the sign of both side of the equation...

2l = P + 12

divide both side by the same number...

L = ( P + 12 ) ÷ 2

[tex]l = \frac{1}{2} p - 12 \times \frac{1}{2} \\ [/tex]

Calculate the product of rational numbers...

[tex]l = \frac{1}{2} p - 6 \\ [/tex]

Answer:

Hope the picture will help you.....................

Answer:

[tex]0 < x < 6[/tex]

Step-by-step explanation:

This question asks to solve an inequality which can be written as:

[tex]\sqrt{x^2-6x+9} < 3[/tex]

Solve for x:

[tex]\sqrt{x^2-6x+9} < 3\\x^2-6x+9 < 9\\x^2-6x < 0\\x(x-6) < 0[/tex]

From here we can deduce that the inequality is [tex]0[/tex] when:

[tex]x = 0[/tex] or [tex]x = 6[/tex]

We can write the solution as:

[tex]0 < x < 6[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 6x + 9 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 3x - 3x+ 9 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{}(x - 3) - 3(x - 3) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x - 3)(x - 3) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x - 3) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: { (x - 3) {}^{} } [/tex]

Now, we have been given that value of x :

[tex]\qquad \sf  \dashrightarrow \:x < 3[/tex]

So, let's plug the value of x as 3 in the given expression ~

[tex]\qquad \sf  \dashrightarrow \:3 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:0[/tex]

Therefore, we can conclude that :

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 6x + 9 } < 0[/tex]

Value of the expression should be less than 0

Step-by-step explanation:

Q1. volume of a cylinder

Ans. The way you find a volume of a regular object is multiplying the base area by height Here the base area is a circle so formula would be pi times r square (πr^2). To get the volume multiply it by 4. Final answer would be π(3)^2*4

Answer:

[tex]2[/tex]

Step-by-step explanation:

[tex] {16}^{ \frac{1}{4} } \: is \: the \: same \: as \\ \\ \sqrt[4]{16} = \sqrt[4]{ {4}^{2} } [/tex]

Note we broke down the 16 into 4 squared*. This is because 4 squared is the same as 16. The four and the two would cancel each other leaving:

[tex] \sqrt[2]{4} \;\\ or \\ \: \sqrt [2]{{2}^{2}} [/tex]

Like before the two and the two would cancel each other out leaving:

[tex]2[/tex]

Answer:

C. 2

Step-by-step explanation:

edge

Check the picture below.

The length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have angle GHJ = 82 units

Length of GH = 12 units

We know:

s = 2πr(θ/360)

s = (2π)12(82/360)

s = 17.17 units

Thus, the length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.

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Answer:

13r+10

Step-by-step explanation:

1. Combine Like Terms

(2r+11r)+(7+3)

13r+10

Answer:

13r+10

Step-by-step explanation:

2r+7+11r+3

collect like terms

2r+11r+7+3

13r+10

Answer:

1 23/36

Step-by-step explanation:

hope this helped

Answer:

65 pictures because 24+36+3+2

✒️ Equation

••••••••••••••••••••••••••••••••••••••

A. To find the x - intercept, let y = 0.

[tex]\tt \: \: \large \tt \: \begin{array}{|c|} \hline \tt \: 4x \: - \: 3y \: = \: \tt\underline{\green{ 12 }} \\ \tt 4x \: - \: 3(0) \: = \: \tt\underline{\blue{ 12 }} \\ \tt4x \: - \: 0 \: = \: \tt\underline{\pink{ 12 }} \\ \tt \tt\underline{\red{ \: x \: = \: 3 }} \\ \\ \tt \: x ↬\: the \: intercept\\ \tt\\ \hline\end{array} \: \\ [/tex]

[tex] \\ [/tex]

To find the y - intercept, let x = 0

[tex]\large \tt \: \begin{array}{|c|} \hline \tt 4x \: - \: 3y \: = \: \tt\underline{\green{ 12 }} \\ \tt 4(0) \: - \: 3y \: = \: \tt\underline{\blue{ 12 }} \\ \tt \: 0 \: - \: 3y \: = \: \tt\underline{\pink{ 12 }} \\ \tt \tt\underline{\red{ y \: = \: - 4 }} \\ \\ \tt \: x ↬\: the \: intercept \\ \ \\ \hline\end{array} \: [/tex]

[tex] \\ [/tex]

B. Replace x with 0 and solve for y. Then replace y with 0 and solve for x.

[tex]\large \tt \: \begin{array}{|c|} \hline \tt y \: - \: intercept: \: y \: = \: \frac{1}{3}(0) \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \tt = \tt\underline{\red{ 0 }} \\ \\ \tt \: x \: and \: y ↬ intercepts: (0,0)\\ \\ \tt \: x \: ↬ \: intercepts: \: 0 = \: \frac{1}{3} x \\ \quad\quad \quad \quad\quad\quad\quad\quad\quad \: \tt \tt\underline{\red{ \: 0 \: = \: x }} \ \\ \\ \hline\end{array} \\ [/tex]

[tex] \\ [/tex]

The equation in b is a linear equation in the form y = mx, where m is any real number. the graph of any equation in the form y = mx is always a line that passes through the origin, which means that both the x - and - y - intercepts are (0,0).

[tex]\large \tt \: \begin{array}{|c|} \hline \tt intercept \: for \: m \: of \: y \: = \: \tt\underline{\red{ mx }} \\ \hline\end{array}[/tex]

[tex] \\ [/tex]

C. Replace y with 0, then solve for the x.

[tex]\large \tt \: \begin{array}{|c|} \hline \tt x ↬ \: intercept : \: 0 \: = \: 2x \: \ + 5 \\ \\ \tt - 5 \: = \: 2x\\ \\ \tt \: \frac{ - 5}{2} \: = \: x\\ \\ \tt \: x \: ↬ \: intercept \ \\ \hline\end{array}[/tex]

Now, replace x with 0, and then solve for y.

[tex]\large \tt \: \begin{array}{|c|} \hline \tt y ↬ \: intercept: \: y \: = \: 2(0) \: + \: 5 \\ \\ \tt \: y \: = \: 0 \: + \: 5 \\ \\ \tt \: y \: = \: 5 \\ \\ \tt y ↬ \: intercept \ \\ \\ \hline\end{array}[/tex]

The equation in 11c is written in the form y = mx + b. note than in the form, when x is replaced by 0 to find the y↬intercept. you are left with the constant b.

[tex]\large \tt \: \begin{array}{|c|} \hline \tt \: the \: y ↬ intercept \: of \: y \: = \: mx \: + \: b \\ \hline\end{array}[/tex]

If the equation is in the form y = mx + b, where m and b are real numbers, then the y ↬intercept is b.

[tex] \\ [/tex]

D. Remember that the graph of y = 6 is horizontally line parallel to the x axis that passes through the y axis at (0,6). since the line is parallel to x axis, it will not incest tha x-axis. Hence, there is no x ↬ intercept.

[tex] \\ \\ \\ [/tex]

[tex]\pmb{(ノ‥)ノ}\qquad\qquad\qquad\qquad\boxed{\tt{[05-12-2022]}} \\ \qquad\qquad\qquad\qquad\qquad\qquad\boxed{\tt{[03:11 \: am]}}[/tex]

Answer:Angle BCE

Step-by-step explanation:

look across from point C

Answer:

[tex]2x - 2y = 24 \\ 2(x - y) = 24 \\ x = 12 + y......eq(1) \\ 4x + 7y = - 40......eq(2) \\ substituting \: the \: value \: of \: x \: in \: eq(2) \\ 4(12 + y) + 7y = - 40 \\ 48 + 4y + 7y = - 40 \\ 11y = - 40 - 48 \\ y = \frac{ - 88}{11} \\ y = - 8 \\ putting \: the \: value \: of \: y \: im \: eq(1) \\ x = 12 - 8 \\ = 4[/tex]

Step-by-step explanation:

3x-2y=24......eqi

x+2y=48........eqii

now solving eq i&ii

4x=72

x=72/4

x=18

now putting the value of x in eqii

18+2y=48

2y=48-18

y=30/2

y=15

Answer:

135 cubes

Step-by-step explanation:

Volume of cuboid :

Volume of a small cube :

Number of cubes :

Answer:

52 miles

Step-by-step explanation:

since 1 unit is 26 miles and the distance from Daytona beach to Orlando on the map is 2 units just multiply 26 by 2 to get 52 miles

The area of the city park will be equal to 3952 square units.

The Area is defined as the space occupied by the two-dimensional geometry in a plane.

We have the following information:-

In City Park, the playground takes up 3/8 of the area:-

[tex]\rm PGA=\dfrac{3}{8}\times CP[/tex]

The soccer field area is 1/3 of the playground area.

[tex]\rm SF=\dfrac{1}{3}\times PGA[/tex]

The product 13×38 can be used to find the area of the soccer field

SF= 13  x  38=494 square units

Noe the PGA will be:-

PGA =3 x SF

PGA= 3 x494=1482 square unit

Now the area of the city park will be calculated as:-

[tex]\rm CP=\dfrac{8}{3}\times PGA\\\\\\CP=\dfrac{8}{3}\times 1482[/tex]

CP=3952 square unit

Hence the area of the city park will be equal to 3952 square units.

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Answer:

x/3+3=x/8+1/11

x+9/3=11x+8/88

88(x+9)=3(11x+8)

88x+729=33x+24

88x-33x=729-24

55x=705

x=705/55

x=12.80

The sides

12-3a

12-3a

4(2a-5)=8a-40

so for perimeter we + them

(12-3a)+(12-3a)+(8a-40)

=

2a-16

See below for the proof of the equation 4h² - 4dh + x² = 0 using the Pythagoras theorem

The Pythagoras theorem states that:

Hypotenuse² = Opposite² + Adjacent²

The question is incomplete, as the figure is not given.

So, I will complete the proof using the following parameters:

Substitute the above values in the following equation

Hypotenuse² = Opposite² + Adjacent²

So, we have:

(2√dh)² = x² + (2h)²

Evaluate the exponents

4dh = x² + 4h²

Subtract 4dh from both sides

0 = x² + 4h² - 4dh

Rewrite as:

4h² - 4dh + x² = 0

Hence, the equation has been proved

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Answer:

if this is 4.88/16 then the answer is 0.305.

Answer:

32π cm^3.

Step-by-step explanation:

The volume of a cone is 1/3 of the volume of a cylinder with the same base area and height.

So the empty space = 2/3 * 48π

= 32π cm^3.

Yes

Step-by-step explanation:

[tex] \cos( \alpha ) = \frac{base}{hypoteneuse} [/tex]

Its just correct..

#34.

If one's price be d

#35

So old area=150(100)=15000

New area increase

New area

Option C

#36

Prime numbers inbetween

#37

#38

1hr additional=1.5(2)=3$

Equation is

So

Option A

Answer:

here i have tried 2 question hope it help u