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3 years ago

If the diameter of a circle is 5 centimeters, how long is the arc subtended by an angle measuring 60° ?

2 answers:

7 0

Arc length s is given by s = r*theta, where theta is the central angle in radians (not degrees).

Here the diam. is 5 cm, so the radius is 5/2 cm. 60 deg = sqrt(3) / 2. Thus,

the arc length is s = (5/2 cm)*sqrt(3) / 2. This simplifies to (5/4) sqrt(3).

Darina [25.2K]3 years ago

5 0

I think the answer will be 12 because 12 times 5 is 60°

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consider the function and then use calculus to answer the questions that follow 1 1/x 5/x^2 1/x^3 (a) Find the interval(s) where

boyakko [2]

Answer:

a) $X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)$

b) $Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0 )$

Step-by-step explanation:

From the question we are told that

The Function

$f(x)=1+\frac{1}{x} +\frac{5}{x^2} +\frac{1}{x^3}$

Generally the differentiation of function f(x) is mathematically solved as

$f(x)=1+\frac{1}{x} +\frac{5}{x^2} +\frac{1}{x^3}$

$f(x)=\frac{x^3+x^2+5x+1}{x^2}$

Therefore

$f'(x)=\frac{x^2+10x+3}{x^4}$

Generally critical point is given as

$f'(x)=0$

$\frac{x^2+10x+3}{x^4}=0$

$x=-5 \pm\sqrt{22}$

Generally the maximum and minimum x value for critical point is mathematically solved as

$f'(-5 \pm\sqrt{22})$

Where

Maximum value of x

$f'(-5 +\sqrt{22})$

Minimum value of x

$f'(-5 +\sqrt{22})$

Therefore interval of increase is mathematically given by

$f'(-5 -\sqrt{22}),f'(-5 +\sqrt{22})$

$f(x)$

Therefore interval of decrease is mathematically given by

$(-\infty,-5 -\sqrt{22}),f'(-5 +\sqrt{22},0),(0,\infty)$

Generally the second differentiation of function f(x) is mathematically solved as

$f''(x)=\frac{2(x^2+15x+6)}{x^5}$

Generally the point of inflection is mathematically solved as

$f''(x)=0$

$x^2+15x+6=0$

Therefore inflection points is given as

$x=\frac{1}{2} (-15 \pm \sqrt{201}$

$f''(x)>0,\frac{1}{2}(-15-\sqrt{201})$

a)Generally the concave upward interval X is mathematically given as

$X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)$

$f''(x)$

b)Generally the concave downward interval Y is mathematically given as

$Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0 )$

5 0

2 years ago

Mandy's science class counted the bones in an owl pellet.

Kamila [148]

Each of those bones pictures are equal to 2 bones. The question is asking, how many more rib bones than skull and jaw bones combined, so you’re gonna have to do some addition and subtraction.

You take the number of skull bones, which is 1(2), and add that to the number of jaw bones, which is 0. Giving you a total of 2 bones.

Then you are taking the rib bones 3(2) and finding out that you have 6.

So with that information, you can find out that there are 4 more rib more than skull and jaw bones combines (6-2=4)

8 0

2 years ago

20 gallons to 0.75 gallons express in simplest form

natta225 [31]

20 : 0.75 = 40 : 1.5 = 80 : 3

7 0

2 years ago

What is the volume, in terms of cubic inches, of a cone with a diameter of 8 inches and a height of 10 inches? Use 3.14 for LaTe

Ad libitum [116K]

Answer:

It is not 502.4 it was on 1 of my test its 669.9in3

Step-by-step explanation: