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WINSTONCH [101]

3 years ago

9

What is the probability (rounded to the nearest whole percent) that a randomly selected gym member would buy grape vitamin water

but not passion fruit vitamin water? 11% 24% 9% 31%

1 answer:

joja [24]3 years ago

6 0

11% hands down people

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What is x if f ( x) = 23?

musickatia [10]

In the expression f(x)=23, x is not a variable. f(x) means “a function of x” or “f of x” and is in practice another way of substituting for the variable y, that is, we are saying:

y=23.

That means x is unspecified and could be anything. So on the xy plane, this is a straight horizontal line, 23 units above the x axis. That would be the best way to interpret this, although it is a little ambiguous.

Usually functions of x are expressed in terms of x, such as:

f(x) = x^2

6 0

3 years ago

Calculus 2. Please help

Anarel [89]

Answer:

$\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}}} \, dx = \infty$

General Formulas and Concepts:

<u>Algebra I</u>

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

<u>Calculus</u>

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integrals

Definite Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

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

U-Substitution

U-Solve

Improper Integrals

Exponential Integral Function: $\displaystyle \int {\frac{e^x}{x}} \, dx = Ei(x) + C$

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx$

<u>Step 2: Integrate Pt. 1</u>

[Integral] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \int\limits^1_0 {\frac{e^{-x^2}}{x} \, dx$
[Integral] Rewrite [Improper Integral]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \int\limits^1_a {\frac{e^{-x^2}}{x} \, dx$

<u>Step 3: Integrate Pt. 2</u>

<em>Identify variables for u-substitution.</em>

Set: $\displaystyle u = -x^2$
Differentiate [Basic Power Rule]: $\displaystyle \frac{du}{dx} = -2x$
[Derivative] Rewrite: $\displaystyle du = -2x \ dx$

<em>Rewrite u-substitution to format u-solve.</em>

Rewrite <em>du</em>: $\displaystyle dx = \frac{-1}{2x} \ dx$

<u>Step 4: Integrate Pt. 3</u>

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {-\frac{e^{-x^2}}{x} \, dx$
[Integral] Substitute in variables: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {\frac{e^{u}}{-2u} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}\int\limits^1_a {\frac{e^{u}}{u} \, du$
[Integral] Substitute [Exponential Integral Function]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(u)] \bigg| \limits^1_a$
Back-Substitute: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-x^2)] \bigg| \limits^1_a$
Evaluate [Integration Rule - FTC 1]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-1) - Ei(a)]$
Simplify: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{Ei(-1) - Ei(a)}{2}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \infty$

∴ $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx$ diverges.

Topic: Multivariable Calculus

7 0

3 years ago

Write the equation of this circle in standard form. A) (x - 2)2 + (y - 3)2 = 4

Vika [28.1K]

Answer:

$x^2 + y^2 -4x -6y + 9 = 0$

Step-by-step explanation:

To write a circle in standard form, expand the equation of the circle and move all terms to one side.

$(x-2)^2 + (y-3)^2 = 4\\x^2 -4x + 4 + y^2 -6y + 9 = 4\\x^2 +y^2 - 4x - 6y + 13 = 4\\x^2 + y^2 -4x -6y + 9 = 0$

8 0

3 years ago

What is the value of the expression?<br> 84-24428<br> 13<br> 115<br> 13.4<br> 152<br> O

timama [110]

Answer:

WWhat

Step-by-step explanation:

6 0

3 years ago

What is the answer to -12=2+5v+2v

katovenus [111]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

v = − 2

Step-by-step explanation: No the right answer? Let me know!

7 0

3 years ago