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Mathematics

1 answer:

Paha777 [63]3 years ago

3 0

Answer:

FH ~ 10.02

Step-by-step explanation:

1. Approach

One should first find the circumference of the given circle. Then one should find how large the fraction of the circumference one is supposed to find is. Finally, one should multiply the fraction of the circumference one is supposed to find by the total circumference.

2. Circumference of the circle

The formula for circumference is;

$2r$ π

Substitute in the given values;

It is given that the radius is, hence

2 (7) π

14π

3. Find the fraction of the circumference one is supposed to find

It is given that the angles over the measure of the total degrees of angles in a circle are equal to the arc surrounding the angles of the circumference. Essentially;

$\frac{angles}{360}=\frac{arc}{circumference}$

Substitute in the given information and solve;

$\frac{82}{360}=\frac{arc}{14pi}$

arc = $\frac{41}{180}*14pi$

arc = $\frac{287}{90}*pi$

arc ~ 10.02

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Elanso [62]

Answer:

a) domain: (0, ∞)

b) range: (-∞, ∞)

c) increasing everywhere

d) concave downward

Step-by-step explanation:

a) Your knowledge of the log function tells you it is defined for positive arguments. 9x > 0 means x > 0. The domain is all positive real numbers.

b) Your knowledge of the log function tells you it has output values ranging from -∞ to +∞. The range is all real numbers.

c) The function is monotonically increasing.

d) Since the output does not increase as fast as the input (the first derivative is decreasing), the function is concave downward.