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3 years ago

What is the length of the arc intercepted by an angle of 10 degrees on a circle with a radius of 10 meters?

1 answer:

soldier1979 [14.2K]3 years ago

3 0

$\displaystyle\\
\texttt{Length of the arc }= 2\pi R\times \frac{10}{360} = \frac{2\pi \times 10}{36} = \frac{20\pi}{36} = \boxed{\frac{5\pi}{9}~m}$

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Determine whether the improper integral converges or diverges, and find the value of each that converges.

Ksju [112]

Answer:converge at $I=\frac{1}{3}$

Step-by-step explanation:

Given

Improper Integral I is given as

$I=\int^{\infty}_{3}\frac{1}{x^2}dx$

integration of $\frac{1}{x^2}$ is - $\frac{1}{x}$

$I=\left [ -\frac{1}{x}\right ]^{\infty}_3$

substituting value

$I=-\left [ \frac{1}{\infty }-\frac{1}{3}\right ]$

$I=-\left [ 0-\frac{1}{3}\right ]$

$I=\frac{1}{3}$

so the value of integral converges at $\frac{1}{3}$

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3 years ago

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satela [25.4K]

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3 years ago

On Thursday, the high temperature was 60 degrees Fahrenheit. On Friday, the high was 72 degrees Fahrenheit

disa [49]

Answer: 120 percent increase

Step-by-step explanation:

72/60 = 1.2

1.2 times is also 120 percent

3 0

3 years ago

3(x - 5) – 3 = 5(x - 2) + 2x

Arlecino [84]

Answer:

x=−2

Step-by-step explanation: Step 1: Simplify both sides of the equation.

3(x−5)−3=5(x−2)+2x

(3)(x)+(3)(−5)+−3=(5)(x)+(5)(−2)+2x(Distribute)

3x+−15+−3=5x+−10+2x

(3x)+(−15+−3)=(5x+2x)+(−10)(Combine Like Terms)

3x+−18=7x+−10

3x−18=7x−10

Step 2: Subtract 7x from both sides.

3x−18−7x=7x−10−7x

−4x−18=−10

Step 3: Add 18 to both sides.

−4x−18+18=−10+18

−4x=8

Step 4: Divide both sides by -4.

−4x

−4

x=−2

6 0

3 years ago

(x-1)³ find derivative using definition

kakasveta [241]

Step-by-step explanation:

definition of the derivative to differentiate functions. This tutorial is well understood if used with the difference quotient .

The derivative f ' of function f is defined ascthe above pic.

when this limit exists. Hence, to find the derivative from its definition, we need to find the limit of the difference quotient.

3 0

3 years ago

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