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MA_775_DIABLO [31]

3 years ago

10

All planets revolve around thensun in elliptical orbits. Uranus's furthest distance from the sun is approximately 3.004 x 10 km,

and its closest distance is approximately 2.749 x 10. Using this information, what is the average distance of Uranus from the sun?

1 answer:

boyakko [2]3 years ago

5 0

Add the two numbers 3004000000+2749000000 and divide by 2
which equals 2876500000 or 2.8765x10^9

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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

Escreva a equação na forma fatorada:b²+ 5b + 6 = 0 b² + 3b + 2b + 6 = 0 b. (b + 3) + 2. (b + 3) = 0 (b + 3 ). (b + 2 ) = 0

Fantom [35]

Respuesta:

(segundo + 3) (segundo + 2) = 0

Explicación paso a paso:

Dada la expresión cuadrática b² + 5b + 6, debemos factorizarla;

b² + 5b + 6 = 0

b² + 2b + 3b + 6 = 0

b (segundo + 2) +3 (segundo + 2) = 0

(segundo + 3) (segundo + 2) = 0

Por tanto, el factor requerido es (b + 3) (b + 2) = 0

6 0

3 years ago

The length of a rectangle is 8 less than the width. The perimenter is 44 meters. Find the dimension of the rectangle

kramer

Answer:

Length = 7

Width = 15

Step-by-step explanation:

L= x

W= x-8

2x+2(x-8)=44

6 0

3 years ago

If f(x)=x²+2x then find f(2) and f(8)

kobusy [5.1K]

Answer:

f(2) = 8, f(8) = 80

Step-by-step explanation:

$f(x)=x(x+2)$

$f(2)=2(2+2)=2(4)=8\\f(8)=8(8+2)=8(10)=80$

5 0

3 years ago

A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12 degrees . To the nea

Finger [1]

Answer:

Step-by-step explanation:

98.8

7 0

3 years ago