All categories

3 years ago

Find the length of the arc shown in brown. Leave your answer in terms of pi.

Mathematics

2 answers:

just olya [345]3 years ago

8 0

The central angle that captures the brown arc is 120°. To find out what fraction of the total circumference the brown arc is, we can find the ratio of this 120° angle to the total central angle of a circle, which is 360°. So we have:

$\frac{120}{360} = \frac{1}{3}$

Now we know the brown arc is $\frac{1}{3}$ of the total circumference. The circumference is π*diameter, so in this case it’s 24π.

Finally, we do:

$\frac{1}{3}*24 \pi =8 \pi \text{ feet}$

dlinn [17]3 years ago

5 0

Answer:1. a central angle

2. c 270

3.d. Two times r equals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.

4. c 155

5. c 70

6.b 55

7. c 19 in

8. a 183.3 ft

9. b 8 pi ft

10. b 33 pi in

Step-by-step explanation:

You might be interested in

What is the probability that the next flood will occur four years from now?

Mrac [35]

1 in 100 or 1/100 would be the probability

6 0

3 years ago

Your coach said to spin no less than 27 minutes practicing each day if you practice for 9 in the morning how many more minutes d

Fudgin [204]

Answer:

Step-by-step explanation:

first find the total 27min then you find the amount he already practiced 9min. now you have everything you need. if you here, how many more, it usually means subtract. so 27-9=D is the formulated answer

8 0

3 years ago

I need help with this 9/2 divided by 2/9

wlad13 [49]

Answer:

20.25

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Turn .055 into fraction

Slav-nsk [51]

Write 0.055 as
0.055
1

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

0.055
1

The factors of 55 are: 1 5 11 55
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The Greatest Common Factor (GCF) for both 55 and 1000 is: 5
Now to reduce the fraction we divide both the numerator and denominator by the GCF value.

=
0.055 x 1000
1 x 1000
=
55
1000

In order to reduce the fraction find the Greatest Common Factor (GCF) for 55 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.

Answer ( 55/1000
= 11/200)

8 0

2 years ago

Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the ve

Akimi4 [234]

A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is $\mathbf 0$ . We have

$\nabla\times\mathbf f(x,y,z)=-2e^{-x}\,\mathbf k$

so this vector field is not conservative.

- - -

Another way of determining the same result: We want to find a scalar function $f(x,y,z)$ such that its gradient is equal to the given vector field, $\mathbf f(x,y,z)$ :

$\nabla f(x,y,z)=\mathbf f(x,y,z)$

For this to happen, we need to satisfy

$\begin{cases}f_x=ye^{-x}\\f_y=e^{-x}\\f_z=2z\end{cases}$

From the first equation, integrating with respect to $x$ yields

$f_x=ye^{-x}\implies f(x,y,z)=-ye^{-x}+g(y,z)$

Note that $g$ *must* be a function of $y,z$ only.

Now differentiate with respect to $y$ and we have

$f_y=-e^{-x}+g_y=e^{-x}\implies g_y=2e^{-x}\implies g(y,z)=2ye^{-x}+\cdots$

but this contradicts the assumption that $g(y,z)$ is independent of $x$ . So, the scalar potential function does not exist, and therefore the vector field is not conservative.

8 0

3 years ago