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3 years ago

Jack is placing glass bottles into boxes to recycle. He can fit 12 bottles in each box.

1 answer:

6 0

His estimation is not reasonable because if you can only fit 12 bottles in a box and he has 10 boxes then he could only fit 120 out of the 200 bottles so he is short on boxes

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Is 3.667 a rational number,interger,or whole number

steposvetlana [31]

Rational 3667/1000
^^^^^^^^^^^

4 0

3 years ago

rancho middle school has an average of 23 3/8 students per teacher write this mixed number as a decimal

Reika [66]

let's firstly convert it to an improper fraction.

$\bf \stackrel{mixed}{23\frac{3}{8}}\implies \cfrac{23\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{187}{8}}\implies 187\div 8\implies \stackrel{decimal}{23.375}$

6 0

3 years ago

Jude estimates that his index finger is 3 inches long. He calculates the circumference of one of his bongo drums to be 27 inches

anzhelika [568]

Answer: 9 finger lengths

Step-by-step explanation: Since the circumference is the middle line passing through (usually a circle....) 27/3 equals 9, which basically means that 9 of Jude's index fingers can pass through the circumference of one of his bongo drums. Hope this helps, 15402256.

7 0

3 years ago

Can someone help me do part two please? It’s very important send a picture or something. I don’t even care if you tell me the st

Nataly_w [17]

<h3>Explanation:</h3>

1. "Create your own circle on a complex plane."

The equation of a circle in the complex plane can be written a number of ways. For center c (a complex number) and radius r (a positive real number), one formula is ...

|z-c| = r

If we let c = 2+i and r = 5, the equation becomes ...

|z -(2+i)| = 5

For z = x + yi and |z| = √(x² +y²), this equation is equivalent to the Cartesian coordinate equation ...

(x -2)² +(y -1)² = 5²

2. "Choose two end points of a diameter to prove the diameter and radius of the circle."

We don't know what "prove the diameter and radius" means. We can show that the chosen end points z₁ and z₂ are 10 units apart, and their midpoint is the center of the circle c.

For the end points of a diameter, we choose ...

z₁ = 5 +5i
z₂ = -1 -3i

The distance between these is ...

|z₂ -z₁| = |(-1-5) +(-3-5)i| = |-6 -8i|

= √((-6)² +(-8)²) = √100

|z₂ -z₁| = 10 . . . . . . the diameter of a circle of radius 5

The midpoint of these two point should be the center of the circle.

(z₁ +z₂)/2 = ((5 -1) +(5 -3)i)/2 = (4 +2i)/2 = 2 +i

(z₁ +z₂)/2 = c . . . . . the center of the circle is the midpoint of the diameter

__₁₂₃₄

3. "Show how to determine the center of the circle."

As with any circle, the center is the <em>midpoint of any diameter</em> (demonstrated in question 2). It is also the point of intersection of the perpendicular bisectors of any chords, and it is equidistant from any points on the circle.

Any of these relations can be used to find the circle center, depending on the information you start with.

As an example. we can choose another point we know to be on the circle:

z₄ = 6-2i

Using this point and the z₁ and z₂ above, we can write three equations in the "unknown" circle center (a +bi):

|z₁ - (a+bi)| = r
|z₂ - (a+bi)| = r
|z₄ - (a+bi)| = r

Using the formula for the square of the magnitude of a complex number, this becomes ...

(5-a)² +(5-b)² = r² = 25 -10a +a² +25 -10b +b²

(-1-a)² +(-3-b)² = r² = 1 +2a +a² +9 +6b +b²

(6-a)² +(-2-b)² = r² = 36 -12a +a² +4 +4b +b²

Subtracting the first two equations from the third gives two linear equations in a and b:

11 -2a -21 +14b = 0

35 -14a -5 -2b = 0

Rearranging these to standard form, we get

a -7b = -5

7a +b = 15

Solving these by your favorite method gives ...

a +bi = 2 +i = c . . . . the center of the circle

4. "Choose two points, one on the circle and the other not on the circle. Show, mathematically, how to determine whether or not the point is on the circle."

The points we choose are ...