Which graph is a one-to-one function?

Please answer this in two minutes

LekaFEV [45]

Answer:

20/29

Step-by-step explanation:

SOH CAH TOA

so its opposite/hyp...

20/29

is the answer

3 0

3 years ago

Convert the decimal expansion 0.1777 into a rational number

Helen [10]

Answer:

The rational form of the given number 0.1777 = $\frac{1777}{10,000}$

Step-by-step explanation:

The rational number is expressed as a number on the form of $(\frac{p}{q} ) , q \neq 0$

Now,here the given number in decimal form = 0.1777

To remove the decimal, firstly count the number of digits AFTER DECIMAL.

Here, number of digits after decimal = 4

SO, the decimal can be removed and replaced by 1 , by dividing with 1,0000.

$\implies 0.1777 = \frac{01,777} {10,000} = \frac{1777}{10,000}$

Hence, the rational form of the given number 0.1777 = $\frac{1777}{10,000}$

5 0

2 years ago

If f(x) = 1/9x-2, what is f^-1(x)?

gavmur [86]

Answer:

9x-2

Step-by-step explanation:

f^-1(x)=1/f(x)=9x-2

8 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:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$