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2 years ago

George created a table based on two charged objects.

Mathematics

1 answer:

docker41 [41]2 years ago

4 0

Answer:

Two negative charges will not attract each other.

Step-by-step explanation:

According to the law of electrostatic induction, it states that "Like charges repel, unlike charges attracts.

Charges can either be positive or negative. For the charges to repel, charges with the same sign must be brought together e.g positive-positve or negative-negative.

For the charges to attract, charges with different sign must be brought together e.g positive-negative or negative-positive.

Based on the conclusion above, it can be seen that the table is incorrect because two negatively charged particle will always repel not attract.

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Can somebody help me with these problems please

mario62 [17]

Answer:

11. A. $\frac{12}{13}$

12. D. $\frac{35}{12}$

Step-by-step explanation:

11: Sin is just the side opposite of the angle divided by the hypotenuse of the triangle

Opposite of A = 36

Hypotenuse of the triangle = 39

36/39 = $\frac{12}{13}$

12. Tan is the side opposite of the angle divided by the side adjacent to the angle

Opposite of C = 35

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35/12 = $\frac{35}{12}$

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