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3 years ago

Which of these is the area of a sector of a circle with r = 18”, given that its arc length is 6π?

1 answer:

8 0

The formulas for arc length and area of a sector are quite close in their appearance. The formula for arc length, however, is related to the circumference of a circle while the area of a sector is related to, well, the area! The arc length formula is $AL= \frac{ \beta }{360} *2 \pi r$ . Notice the "2*pi*r" which is the circumference formula. The area of a sector is $A s= \frac{ \beta }{360} * \pi r ^{2}$ . Notice the "pi*r squared", which of course is the area of a circle. In our problem we are given the arc length and the radius. What we do not have that we need to then find the area of a sector of the circle is the measure of the central angle, beta. Filling in accordingly, $6 \pi = \frac{ \beta }{360} *2 \pi (18)$ . Simplifying by multiplying by 360 on both sides and then dividing by 36 on both sides gives us that our angle has a measure of 60°. Now we can use that to find the area of a sector of that same circle. Again, filling accordingly, $A_{s} = \frac{60}{360} * \pi (18) ^{2}$ , and $A_{s} =54 \pi$ . When you multiply in the value of pi, you get that your area is 169.65 in squared.

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Calculus graph please help

tresset_1 [31]

Answer:

See Below.

Step-by-step explanation:

We are given the graph of y = f'(x) and we want to determine the characteristics of f(x).

Part A)

f is increasing whenever f' is positive and decreasing whenever f' is negative.

Hence, f is increasing for the interval:

$(-\infty, -2) \cup (-1, 1)\cup (3, \infty)$

And f is decreasing for the interval:

$\displaystyle (-2, -1) \cup (1, 3)$

Part B)

f has a relative maximum at x = c if f' turns from positive to negative at c and a relative minimum if f' turns from negative to positive to negative at c.

f' turns from positive to negative at x = -2 and x = 1.

And f' turns from negative to positive at x = -1 and x = 3.

Hence, f has relative maximums at x = -2 and x = 1, and relative minimums at x = -1 and x = 3.

Part C)

f is concave up whenever f'' is positive and concave down whenever f'' is negative.

In other words, f is concave up whenever f' is increasing and concave down whenever f' is decreasing.

Hence, f is concave up for the interval (rounded to the nearest tenths):

$\displaystyle (-1.5 , 0) \cup (2.2, \infty)$

And concave down for the interval:

$\displaystyle (-\infty, -1.5) \cup (0, 2.2)$

Part D)

Points of inflections are where the concavity changes: that is, f'' changes from either positive to negative or negative to positive.

In other words, f has an inflection point wherever f' has an extremum point.

f' has extrema at (approximately) x = -1.5, 0, and 2.2.

Hence, f has inflection points at x = -1.5, 0, and 2.2.

7 0

3 years ago

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x)

mamaluj [8]

Answer:

First option: $\left \{ {{y\leq -2x + 3} \atop {y \leq x + 3}} \right.$

Step-by-step explanation:

The missing graph is attached.

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

We can observe that:

1. Both lines have the same y-intercept:

$b=3$

2. The lines are solid, then the symbol of the inequality must be $\leq$ or $\geq$ .

3. Since both shaded regions are below the solid lines, the symbol is:

$\leq$

Based on this and looking at the options given, we can conclude that the graph represents the following system of inequalities:

$\left \{ {{y\leq -2x + 3} \atop {y \leq x + 3}} \right.$

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3 years ago

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What is 22% expressed as a fraction in simplest form?

nata0808 [166]

22% when expressed as a fraction is 22/100.
to write this in the simplest form, we have to keep dividing both numerator and denominator by a common number.
22/100 , both are divisible by 2. therefore when 22/100 is divided by 2
 $\frac{22/2}{100/2} = \frac{11}{50}$ 
then we get 11/50. this cannot be divided any further by a common factor to both. therefore simplest form is 11/50

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3 years ago

What is the principle square root of 1600? A. -40 B. 40 C. both

WINSTONCH [101]

The answer is B 40........

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3 years ago

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Please help!!!!!!!!!!

lapo4ka [179]

Answer: 18.7

Step-by-step explanation: