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Anna007 [38]
2 years ago
7

Kathy slices through a circular cake. The cake has a diameter of 14 inches. The slice that Kathy made is straight and has a leng

th of 11 inches. Did Kathy cut along a radius, a diameter, or a chord of the circle
Mathematics
1 answer:
Tanzania [10]2 years ago
7 0

Answer: chord

Step-by-step explanation:

A chord is a straight line that's typically drawn from one particular edge of a circle to another.

In this case, the diameter is 14cm while the length of the line drawn is 11cm, therefore the diameter isn't a chord. It's not a radius as well as the diameter divided by 2 gives the radius which should be 7cm.

Therefore, it's a chord.

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Find the third side in simplest radical form:<br> 25
Gre4nikov [31]

Answer:

<h3>\boxed{  \bold{24}}</h3>

Step-by-step explanation:

\mathsf{given}

\mathsf{hypotenuse(h) = 25}

\sf{perpendicular (p) = 7}

\sf{base(b) = }?

Now, Using Pythagoras theorem

\sf{{h}^{2}  =  {p}^{2}  +  {b}^{2} }

plug the values

⇒\sf{  {25}^{2}  =  {7}^{2}  +  {b}^{2} }

Evaluate the power

⇒\sf{625 = 49 +  {b}^{2} }

Swap the sides of the equation

⇒\sf{49 +  {b}^{2}  = 625}

Move constant to right hand side and change it's sign

⇒\sf{ {b}^{2}  = 625 - 49}

Calculate the difference

⇒\sf{ {b}^{2}  = 576}

Squaring on both sides

⇒\sf{b = 24}

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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

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