A soccer ball has an interior diameter of 22 cm. How many cubic centimeters of air does a soccer ball contain, rounded to the nearest tenth of a centimeter?​

Answer:

g(x) = 4x² - x

General Formulas and Concepts:

Algebra II

Functions

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

*Note:

Integrating a piecewise function requires you to integrate both parts.

Step 1: Define

Identify.

[tex]\displaystyle f(x) = \left \{ {{8x - 1 ,\ x \leq 4} \atop {31 ,\ x \geq 4}} \right.[/tex]

[tex]\displaystyle \int {f(x)} \, dx = \left \{ {{g(x) + C ,\ x \leq 4} \atop {31x + C ,\ x \geq 4}} \right.[/tex]

Step 2: Find function g(x)

We can see that the 2nd part of the piecewise function already has been integrated:

To find function g(x), we simply have the same setup:

The integration constant C is already included in the answer, so our answer is g(x) = 4x² - x.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration (Applications)

Answer:

It does not matter, since, from your second case, [tex]5\sqrt5 +11 = 11+5\sqrt5[/tex].

In general is a matter of personal preference but in general I like to start with a positive number (I like [tex]\sqrt2 -1[/tex] more than [tex]-1+\sqrt2[/tex] since if there's an equal sign before I'm guaranteed to have the two signs mesh together in a few steps).

If everything you are adding together is positive, I just go first come first served and pick a new term in order it appears in the previous passage.

Answer:

1230

Step-by-step explanation:

[tex]\frac{\pi }{3}[/tex] x 49 x 24 = 1230 cm^3

on this one, we proceed the same as the other, we start off by graphing them, Check the picture below.  Now, we have a solid horizontal line at y = 7, that'd be our boundary, and a parabola that has a vertex at the origin, that's our other boundary, from 0 to 7.

In this case, is a solid area from the curve to the axis of rotation, so we can simply use the "disk" method to get the volume, lemme do it in the same way as "area under the curve", assuming h(y) = 0 for the axis of rotation

[tex]\textit{area under the curve}\\ \stackrel{f(y)}{2\sqrt{3y}}~~ - ~~\stackrel{h(y)}{0}\qquad \implies 2\sqrt{3y} \\\\\\ \displaystyle\int_{0}^7\pi \left( 2\sqrt{3y} \right)^2 dy\implies \int_{0}^7\pi(12y)dy\implies 12\pi \int_{0}^7 y\cdot dy \\\\\\ 12\pi \cdot \left. \cfrac{y^2}{2} \right]_{0}^7\implies12\pi \cdot \cfrac{49}{2}\implies 294\pi[/tex]

Answer:

2nd option

Step-by-step explanation:

Repeatedly divide by 2 until the value 1 is reached

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1 ← finish here

Then

32 = 2 × 2 × 2 × 2 × 2

Answer: the answer is 600 or the letter C

Answer:

3) 600

Step-by-step explanation:

Answer:

[(P - (2 x l)] / 2

Step-by-step explanation:

[Perimeter - ( 2 x length) ] / 2

(64 - 2x22)/2 = 10 pulgadas de ancho

Answer:

Because if you didn't you would not know anything about the past.

Step-by-step explanation:

Yes

Answer:

C - qd

Step-by-step explanation:

qid means four times a day

tid means three times a day

qd means every other day (answer)

qod also means every other day (but since it's not recommended to use this notation, the answer should be qd)

Answer:

C. qd

Step-by-step explanation:

qd stands for quaque die in latin. translated to english it means every day.

Answer:

A = (0,1)

B = (1,-1)

C = (-1,-1)

Step-by-step explanation:

If this helped leave a brainliest

Answer:

-12.5

Step-by-step explanation:

-7x+8+11x=-42

-7x+11x=-42-8

4x=-50

x=-12.5

Hope this helped! :)

Hey There!

Question:-

[tex] \sf \: - 7x+8+11x= - 42[/tex]

We need to find the value of x.

Solution:-

[tex]\sf \longmapsto - 7x + 8 + 11x = - 42[/tex]

Combine Like terms:-

[tex]\sf \longmapsto \: ( - 7x+11x)+(8)= - 42[/tex]

On Simplification :-

[tex]\sf \longmapsto \: 4x +8 = - 42[/tex]

Subtract 8 from both sides:-

[tex]\sf \longmapsto \: 4x+8 - 8= - 42 - 8[/tex]

On Simplification:-

[tex]\sf \longmapsto \: 4x + 0 = - 42 - 8[/tex]

Note that (-) and (-) equals to (+).

[tex]\sf \longmapsto \: 4x = - 50[/tex]

Divide both sides by 4:-

[tex]\sf \longmapsto \: \dfrac{4x}{4} = \dfrac{ - 50}{4} [/tex]

On Simplification:-

[tex]\sf \longmapsto \: \dfrac{ \cancel2x}{ \cancel2} = \dfrac{ \cancel{- 50}}{ \cancel4} [/tex]

[tex]\sf \longmapsto \: x = \dfrac{ - 25}{2} [/tex]

Or in Decimal :-

[tex]\sf \longmapsto \: x = -12.5[/tex]

______________________________________

Henceforth, the value of x is :-

[tex]\boxed{\huge \red{x = - \dfrac{25}{2}}} [/tex]

In Decimal:-

[tex] \boxed{\huge\red{ x = -12.5}}[/tex]

________________________________

Please let me know if you have any questions.

~MisterBrian

Answer:

A

Step-by-step explanation:

:)

hope it helps

Answer:

p=2,-16

Step-by-step explanation:

move all terms to left side and set equal to zero. then set each factor equal to zero

Answer:

|-5| absolute be always + so 5

Answer:

[tex]5[/tex]

Step-by-step explanation:

Step 1:  Determine what absolute value does

Taking the absolute value of a number just returns how far a specific value is from 0.  So in this case we see a number -9 and although it's negative it's still 9 away from 0 therefore that would be the absolute value.

We are missing the absolute value of -5 or 5 so we know that taking the absolute value would just give us the distance from 0.  In this case that would just be 5.

Answer: [tex]5[/tex]

Answer:

22.53-9.99=12.54

12.54 divided by 6 = 2.09

Each pencil costs $2.09

Step-by-step explanation:

Answer:

-2F=7x

Step-by-step explanation:

F*-2= -2F       3x*3x=9x

-2F=9x-2x

-2F=7x

To combine like terms, you have to add the same variables and all

First You have to find if the Numbers are positive or Negative

2s is positive

4w is Negative because i has Minus sigh before it

5 is Positive because it has added sigh

6s s Positive because it has added sign

Second you have to find the Like terms

2s+6s=8s

so, the new equation is

8s-4w+5.

That is the simplest

If you have questions just ask me I went through it pretty fast

Check the picture below.

there are a few angles shaded, I'll call that angle at O ∡O, and that angle at "x" ∡x and the green angle at A, ∡A, and the angle at B, ∡B, just so you know which angle we're referring to.

well, first off let's notice that B and C are points of tangency, meaning we get right-angles as you see in the picture, if we run an angle bisector from ∡x, towards point O, we get two congruent triangles, lemme shorten that up some, 90 + 90 + ∡O +∡x = 360, which means that ∡O + ∡x = 180,  meaning that ∡O = 180 - ∡x, if that's so, the angle at point O across the shade, is 360 - ∡O or 360 - (180 - ∡x).

alrighty, by the inscribed angle theorem, ∡A is half of ∡O.

let's now focus on the triangle AOB, we'll be using half of ∡A and half of ∡O and ∡B on that triangle, let's proceed.

[tex]\measuredangle x + \measuredangle O=180\implies \measuredangle O=180-\measuredangle x \\\\\\ \measuredangle A = \cfrac{\measuredangle O}{2}\implies \measuredangle A = \cfrac{180-\measuredangle x}{2} \\\\\\ \stackrel{\textit{the angle across from }\measuredangle O~is}{360-\measuredangle O}\implies 360-(180 - \measuredangle x)\implies 180+\measuredangle x \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\large the sum of all three angles at }\triangle AOB}{\stackrel{\textit{half of }\measuredangle A}{\cfrac{1}{2}\cdot \cfrac{180-\measuredangle x}{2}}~~ + ~~\stackrel{\textit{half the angle across from }\measuredangle O}{\cfrac{180+\measuredangle x}{2}}~~ +~~\measuredangle B~~ =~~180} \\\\\\ \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B = 180[/tex]

now, let's multiply both sides by the LCD of all denominators, hmmmm in this case that'll be 4, so multiplying both sides by the LCD will do away with the denominators, so let's do so.

[tex]4\left( \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B \right) = 4(180) \\\\\\ (180-\measuredangle x)+2(180+\measuredangle x)+4\measuredangle B = 720 \\\\\\ (180-\measuredangle x)+(360+2\measuredangle x)+4\measuredangle B = 720\implies 540+\measuredangle x+4\measuredangle B = 720[/tex]

[tex]\measuredangle x+4\measuredangle B = 180\implies 4\measuredangle B = 180-\measuredangle x\implies \measuredangle B = \cfrac{180-\measuredangle x}{4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle B = 45 - \cfrac{\measuredangle x}{4}~\hfill[/tex]

Answer:

C.

Step-by-step explanation:

Pi = circumference / diameter.

Answer:

The bigger number is 13 and the smaller number is 5

Answer:

y=-3/2 x + 6Step-by-step explanation:

Answer:

Assuming that the question is asking how many employees there are, your answer would be 675.

Step-by-step explanation:

Answer:

m=1352

Step-by-step explanation:

(118.64-24)/0.07=m

Answer:

2

990

2

495

3

165

3

55

5

11

Step-by-step explanation:

Answer:

1) 2/x³ the secound option

2)1/x²⁴ the secound option

I think

My answer needs to be 32-25=7

Answer:

  g(x) = 4x² -x +64

Step-by-step explanation:

The integral of f(x) will be continuous. This means the value must be the same for x = 4- as for x = 4+.

For some constant c1, the integral in the region x ≤ 4 is ...

  ∫f(x)dx = (4x² -x +c1) +C = g(x) +C

The integral in the region x ≥ 4 is given as ...

  ∫f(x)dx = 31x +C

Evaluated at x=4, we must get the same value from either expression:

  4(4²) -4 +c1 +C = 31(4) +C

  60 +c1 = 124

  c1 = 64

__

In order to make the integral continuous at x=4, we must have ...

  g(x) = 4x² -x +64

Add the sales tax to the bill:

Bill with tax = 14.60 x 1.09 = $15.95

Multiply the total bill by the tip percentage:

Tip = 15.95 x 0.19 = 3.02

Tip = $3.02

Answer:

Expression D

Step-by-step explanation:

all other answers are above 15! hope this helps :D