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2 years ago

In the Latin Club, there are six more girls than twice the number of boys.

Mathematics

2 answers:

Lena [83]2 years ago

8 0

Answer:

C because twice the number of boys is 22 and 22+6=28

Verdich [7]2 years ago

6 0

X=number of girls
Y=number of boys
X=2Y+6
X=2(11)+6
=22+6
=28

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elena-14-01-66 [18.8K]

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3 years ago

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Zarrin [17]

Answer:

3,4

Step-by-step explanation:

5 0

2 years ago

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

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

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

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to find the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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

Unit: Integration

5 0

2 years ago

Function Composition: Let the function <img src="https://tex.z-dn.net/?f=f%28x%29%3D%203%2B6x" id="TexFormula1" title="f(x)=

V125BC [204]

Answer:

Given

f(x) = 3 + 6x

Find the inverse of f(x):

x = 3 + 6f⁻¹(x)
6f⁻¹(x) = x - 3
f⁻¹(x) = (x - 3) / 6

f · f⁻¹( ∛5/6) =
f( f⁻¹( ∛5/6)) =
f((∛5/6 - 3)/6) =
3 + 6((∛5/6 - 3)/6) =
3 + ∛5/6 - 3 =
∛5/6

f · f⁻¹(x) =
f(f⁻¹(x)) =
f((x - 3)/6) =
3 + 6(x - 3)/6 =
3 + x - 3 =
x

4 0

2 years ago

On Saturday, the vacation resort offers a discount on water sports. To take

MakcuM [25]

Answer:

Let x be the discounting price of a surfing lessons per person

Let y be the discounted price of a surfing lessons per person

The cost of taking a surfing lesson and go parasailing is $130

x + y = 130--------------(i)

25 people take

Surfing lessons, and 30 people go parasailing and a total of $3,650 is collected

25x + 30y = 3650--------------(ii)

We solve for y using equ (i):

y = 130 - x ------------(iii)

Substitute equ (iii) to equ (ii) and solve for x

25x + 30(130 - x) = 3650

25x + 390 - 30x = 3650

-5x = -250

-x = 50

We solve for y using equ (iii):

y = 130 - x

y = 130 - 50

y = 80

So, the discounted price to take a surfing lesson is $50 and the discounted price to go parasailing is $80

3 0

2 years ago