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cestrela7 [59]
2 years ago
7

An ant is walking around the perimeter of a circular wreath with a radius of 8 inches. If the ant walked 21 inches, how many rad

ians is the central angle that intercepts the ants path?
Mathematics
1 answer:
Butoxors [25]2 years ago
6 0

The movement of the ant illustrates the length of an arc

The measure of the central angle is 2.625 radians

<h3>How to determine the central angle</h3>

The radius of the arc is given as:

r = 8

The distance walked is given as:

L = 21

The length of an arc is

L = r\theta

So, we have:

21 = 8\theta

Divide both sides by 8

\theta = \frac{21}{8}

Divide

\theta = 2.625

Hence, the measure of the central angle is 2.625 radians

Read more about length of arc at:

brainly.com/question/2005046

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eden purchased a home for $156,200. The home appreciates about 4.5% each year. what is the value of the home after 17 years?
e-lub [12.9K]

Answer:

590,088

Step-by-step explanation:

So you divide 156,200 by 4.5 then once you have that times it bye the 17 years I think

6 0
2 years ago
Its length is
melamori03 [73]

Answer:

$100

Step-by-step explanation:

40x30=1200

1200/12=100

7 0
3 years ago
Write the standard form of the equation for the circle that passes through the points (2,31),(-15,14),(33,0)
stepladder [879]

Answer:

Step-by-step explanation:

Begin with the standard form of a circle as a conic:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

For a circle, A and C will be the exact same, and B will equal 0.  If B is non-zero, the equation represents a rotation of a conic, which is reserved for college-level courses.  Shortening this, then:

x^2+y^2+Dx+Ey+F=0 is good enough for us for this.  Start with the first point on the circle, (2, 31) and fill in the equation above with x and y:

2^2+31^2+2D+31E+F=0 which simplifies down to:

(1):2D+31E+F=-965

Do the same with the next point on the circle, (-15, 14):

-15^2+14^2-15D+14E+F=0 which simplifies down to:

(2):-15D+14E+F=0

Do the same with the last point, (33, 0):

33^2+0^2+33D+0E+F=0 which simplifies down to:

(3):33D+F=-1089

Now we will add (1) and (2) to get (4):

 2D + 31E + F = -965

-15D + 14E + F = -421

Multiply the top equatio by -1 to get rid of the F terms:

 -2D - 31E - F = 965

-15D + 14E + F = -421

which simplifies to

(4): -17D - 17E = 544

Now add (2) and (3) to get (5):

-15D + 14E + F = -421

33D           + F = -1089

Multiply the bottom equation by -1 to get rid of the F terms:

-15D + 14E + F = -421

-33D          - F = 1089

which simplifies to

(5): -48D + 14E = 668

Now add (4) and (5) together and eliminate the E terms:

-17D - 17E = 544

-48D + 14E = 668

In order to eliminate the E terms, multiply the top equation by 14 and the bottom equation by 17 to solve for D:

-238D - 238E = 7616

-816D + 238E = 11356

Which gives you that

D = -18

Now plug the value for D into (4) to find E:

-17(-18) - 17E = 544 and

306 - 17E = 544 and

-17E = 238 so

E = -14

Now plug the values for both D and E into (1) to find F:

2(-18) + 31(-14) + F = -965 and

-36 - 434 + F = -965 and

-470 + F = -965 so

F = -495

Now we can fill in the standard form of the conic:

x^2+y^2-18x-14y=495

but we're not done til we complete the square on both the x terms and the y terms (and I am assuming you know how to complete the square):

(x^2-18x+81)+(y^2-14y+49)=495+81+49 which simplifies to

(x-9)^2+(y-7)^2=625

The second choice down matches that equation, but the center they have there is not correct.  The center of that circle is (9, 7) and they have it as being (7, 10) with a radius of 5.  The radius is 25.  The center is wrong in the equation that represents the circle as is the radius.  Maybe let someone know that...

4 0
3 years ago
Read 2 more answers
Answer this<br> PLz i needs to get this done there will be more questions stay alert thank you
Zarrin [17]

The answer is 89,760 feet.

6 0
2 years ago
Help me with this please!!
ser-zykov [4K]

Answer:

-1.3

Step-by-step explanation:

The graph shows the straight line passing through the points (3,-1) and (-3,7).

The slope of the line passing through the points (x_1,y_1) and (x_2,y_2) is

\dfrac{y_2-y_1}{x_2-x_1}

In your case, the slope is

\dfrac{7-(-1)}{-3-3}\\ \\=\dfrac{7+1}{-6}\\ \\=-\dfrac{8}{6}\\ \\=-\dfrac{4}{3}\\ \\\approx -1.3

The rate of change is -1.3

8 0
3 years ago
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