If segment DE is 12, what is segment BC?

Answer:

[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]

General Formulas and Concepts:

Alg I

Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]

Pre-Calc

[Right Triangle Only] Pythagorean Theorem: a² + b² = c²

a is a legb is a legc is hypotenuse

Trigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]

Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]

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

TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]

Calc

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]

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

U-Substitution

U-Trig Substitution: x² + a² → x = atanθ

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]

Step 2: Identify Sub Variables Pt.1

Rewrite integral [factor expression]:

[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]

Identify u-trig sub:

[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]

Later, back-sub θ (integrate w/ respect to x):

[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]

Step 3: Integrate Pt.1

[Int] Sub u-trig variables:                                                                                 [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]:                                                                           [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents:                                                                                [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor:                                                                                                      [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]:                                                                                              [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents:                                                                                [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]:                                                                          [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]:                                                                                         [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]:                                                                                            [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]:                                                                                              [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]:                                                                          [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]:                                                                          [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]  

Step 4: Identify Sub Variables Pt.2

Determine u-sub for trig int:

u = 2θ

du = 2dθ

Step 5: Integrate Pt.2

[Ints] Rewrite [Int Prop - MC]:                                                                       [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub:                                                                                                     [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]:                                                             [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub:                                                                                 [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]:                                                                                           [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply:                                                                                                 [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub:                                                                                             [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]

Step 6: Triangle

Find trig values:

[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]

[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]

tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:

sinθ = opposite / hypotenuse

cosθ = adjacent / hypotenuse

Leg a = 2

Leg b = 9x

Leg c = ?

Sub variables [PT]:                                                                                         [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents:                                                                                      [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides:                                                  [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite:                                                                                                           [tex]c = \sqrt{81x^2 + 4}[/tex]

Substitute into trig ratios:

[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]

[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]

Step 7: Integrate Pt.3

[Exp] Sub variables [TR]:                                                                               [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply:                                                                                                 [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute:                                                                                             [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]

Answer:

8(34a-1)

Step-by-step explanation:

Hope this helps :)

Answer:

8(34a-1)

Step-by-step explanation:

Answer:

for stunt performers and this is lady's work ( paragraph 6)

Answer:

x = -0.441 and x = -2.359

Step-by-step explanation:

The given equation is :

[tex]2(5x+7)^2-13=33[/tex]

Adding 13 to both sides of the equation.

[tex]2(5x+7)^2-13+13=33+13\\\\2(5x+7)^2=46\\\\(5x+7)^2=23[/tex]

So,

[tex]5x+7=\sqrt{23}\\\\5x+7=\pm4.795\\\\5x=4.795-7, 5x=-4.795-7\\\\5x=-2.205, 5x = -11.795\\\\x=-0.441, x=-2.359[/tex]

So, the solution of the given equation is x = -0.441 and x = -2.359.

Sorry don’t know
Joking so i will round to 1 sig fig
So 60 and 10 product is times
60x10=600
when estimating say what you are rounding to

Answer:

300

Step-by-step explanation:

if you mean, 245.320

Answer:

False

Step-by-step explanation:

ir doesn't add up from what i saw

Answer:

-5 3/5

Step-by-step explanation:

John's error was in adding the whole number and fractional portions separately, the fractions must be converted to improper fractions with common denominators to be added or subtracted properly so

(-7 4/5) + (2 1/5), convert to improper fractions

-39/5 + 11/5, both fractions have common denominator so we can continue

-39 + 11 = -28, so -39/5 + 11/5 = -28/5, convert back to proper fractions

-28/5 = (-25/5) + (-3/5) = -5 3/5

Answer: TRUE!

Step-by-step explanation: Hope this helps!

Answer: True

Step-by-step explanation:

What kind of math is this?

Following order of operations:

3^2 = 9

(10-2) = 8

Now you have :

9 + 8 x 5 -4

Multiplication is next:

9 + 40 -4

Now just add and subtract from left to right:

9 + 40 = 49

49-4 = 45

The answer is 45

Step-by-step explanation:

So first you solve whats inside of the parenthesis 10 -2 aand get 8 then you figure 3^2 which is 9 then multiplie 8 times 5 and get 40. 9 + 40 - 4 is what it is so far then add 9 to 40 which is 49 then subtract 4 and get 45!

Answer:

The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

The height of the bullet after t seconds is given by:

[tex]h(t) = -16t^2 + 720t[/tex]

When does the bullet reach a height of 4,000 feet?

This is t for which [tex]h(t) = 4000[/tex]. So

[tex]4000 = -16t^2 + 720t[/tex]

[tex]16t^2 - 720t + 4000 = 0[/tex]

Dividing by 16

[tex]t^2 - 45t + 250 = 0[/tex]

So [tex]a = 1, b = -45, c = 250[/tex]

[tex]\bigtriangleup = b^{2} - 4ac = (-45)^2 - 4(1)(250) = 1025[/tex]

[tex]t_{1} = \frac{-(-45) + \sqrt{1025}}{2} = 38.5[/tex]

[tex]t_{2} = \frac{-(-45) - \sqrt{1025}}{2} = 6.49[/tex]

The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.

y=x^2
substitute the values into the original equation
0=4^2
0=16
No it does not satisfy the equation because 0 does not equal to 16

1 - 0.082 = 0.918
Multiply by 0.918

Answer:

d = 17

Step-by-step explanation:

The given arithmetic sequence is :

31, 48, 65, 82, ...

We need to find the common difference for this sequence.

First term, a₁ = 31

Second term, a₂ = 48

Common difference = a₂-a₁

= 48-31

= 17

So, the common difference for this arithmetic sequence is equal to 17.

Answer:

<BAC=1/2 <BOC=1/2 X=X/2(INSCRIBED ANGLE IS HALF OF CENTRAL ANGLE)

Answer:

b) 200

Step-by-step explanation:

The correct answer is b) 200

1) El IVA del balón es de $ 20.

2) El precio final del balón es $ 145.

1) El Impuesto al Valor Agregado (IVA) es un impuesto indirecto que se aplica sobre el precio de compra del artículo comprado, es decir, se trata de un impuesto indirecto al consumo.

El porcentaje por concepto del impuesto varía de país en país. No obstante, el valor más común en países hispanoparlantes se ubica en torno al 16 % del precio de compra del artículo.

El IVA del balón se determina mediante la siguiente operación aritmética:

[tex]\Delta C = 0.16\cdot (125)[/tex]

[tex]\Delta C = 20[/tex]

El IVA del balón es de $ 20.

2) El precio final del producto es la suma del precio de compra y el IVA, es decir:

[tex]C = 125 + 20[/tex]

[tex]C = 145[/tex]

El precio final del balón es $ 145.  

Para aprender más sobre impuestos, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/24907444

Nota - El enunciado reporta numerosos errores tipográficos y está incompleto, el enunciado correcto y completo es el siguiente:

Un balón de fútbol tiene un precio de $ 125 + IVA.

1) ¿Cuánto es el IVA del balón? a) 20, b) 145, c) 325

2) ¿Cuál es el precio final con IVA del balón? a) 125, b) 200, c) 145

Answer:

2

Step-by-step explanation:

hope this helps

please give brainliest. Thanks! :)

Answer:

-26, -29, -32

Have a great day!

Step-by-step explanation:

Answer: Constant of proportionality is $6 for one pair and cost of dry cleaning 11 pairs of pants is $66.

11 pairs of pants would equal $66

$18/3=6
$6 per one pair of pants
6 times 11= 66
$66

Hope this helps! Have a great day :)

Answer:

0.098-0.607-0.78-4.003-5.6

Step-by-step explanation:

The numbers in orders that starting with the smallest should be considered as the 0.098-0.607-0.78-4.003-5.6.

Calculation of the listing numbers:

Since the list of the number should be like

0.78

0.607

5.6

0.098

4.003

So here we sequence the numbers from the smallest to the largest

So it should be like 0.098-0.607-0.78-4.003-5.6.

Hence, The numbers in orders that starting with the smallest should be considered as the 0.098-0.607-0.78-4.003-5.6.

Learn more about numbers here: https://brainly.com/question/24571514

Answer:
Faris' arrival time = 3:30 pm + 3 h 54 mnt = 7:24 pm
Step-by-step explanation:
Driving distance between Manchester to London = 195 miles
Coach left Manchester = 3.30 pm
Average speed of coach = 50 mph
Total time taken by the coach to reach the Manchester to London = 195÷50 = 3.9 h
0.9 h = 0.9×60 mnt = 54 mnt
Now,
3.9 h = 3 h 54 mnt
Hence Faris' arrival time in London = 3.30 pm + 3 h 54 mnt = 7.24 pm

Step-by-step explanation:

$9 because 1 third of 3 third would be $3

Answer:

You cannot get a positive answer for this, nor can you divide. You could however divide 1/12 by 1/4 to get 1/3.

Step-by-step explanation

The number whose 1/3 is 1/12 is 4.

What is Division?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

let 1/3 divided by x equals 1/12.

So, 1/3 ÷ x = 1/12

and, 1/3 (1/x) = 1/12

1/x = 3/12

1/x = 1/4

x = 4

So, the required number is 4.

Learn more about Fraction here:

https://brainly.com/question/10354322

#SPJ2

Answer:

3000

Step-by-step explanation:

100%-> 5000

60%->3000

Radius is half d so r us 4.5
Formula is 2x pi x r
So 28.3 to 3 s.f.

Answer:

n = -7

Step-by-step explanation:

3n-27-2n-8=6n

n-35=6n

-35=5n

n=-7

Answer:

45 dollar's ezzzzzzzzzzzzz

Answer:

B. (3,2)

Step-by-step explanation:

Step 1) When shifting from A(1,2) to B(4,4), the point shifted 3 units to the right (which means x=3) and 2 units upwards (which means y=2).

Step 2) So when you apply the same movements to point C(0,0), the new point will be (3,2).

See the diagram below. Step 1 is the graph on the left. Step 2 is the graph on the right. The movement is colored in green. Hope this helps!

Answer:

2 2/9

hope it's helpful ❤❤❤

THANK YOU.❤