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strojnjashka [21]
3 years ago
6

Hideki is draining a 45-gallon aquarium at a rate of 15 gallons per minute. What is the initial value of the linear function tha

t represents this situation?
Mathematics
2 answers:
kkurt [141]3 years ago
8 0
3 min sence 15 will enter 45 3 times
Alexxx [7]3 years ago
3 0

Answer:

Hideki is draining a 45-gallon aquarium at a rate of 15 gallons per minute. Let's solve for the initial value of the linear function that represents thissituation.

=> 45 gallon aquarium at rate of 15 gallons per minute.

=> 45 gallon / 15 gallon = 3 minutes.

Therefore with the rate of 15 gallons per minutes, Hideki will be able to finish the 45 gallon aquarium in 3 minutes.

Step-by-step explanation:

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Ms. Fitzgerald had 2 1 /4 gallons of fruit punch. She served 3 /8 gallon of the fruit punch
Luda [366]

Answer:

1 7/8

Step-by-step explanation:

1/4=2/8

2+2/8-3/8= 1 7/8

8 0
2 years ago
A recipe for giant soap bubbles uses 1/2 cup dishwashing liquid and 4 1/2 cups of water. How many cups of water will be used wit
GREYUIT [131]

Answer: D. 13 1/2.​

Step-by-step explanation:

1/2*3= 1 1/2 cups of dishwashing liquid.

4 1/2*3= 13 1/2 cups of water will be used with 1 1/2 cups of dishwashing liquid.

7 0
2 years ago
What is the surface area of a rectangular prism that is 12cm by 3cm by 5cm?
Cerrena [4.2K]
A = 2lw + 2lh + 2hw
A = 2(12)(3) + 2(12)(5) + 2(5)(3)
A = 72 + 120 + 30
A = 222 cm squared

Hope this helps!! :)
3 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 ...

  • z₃ = 3 -2i
  • z₄ = 6 -2i

We can show whether or not these are on the circle by seeing if they satisfy the equation of the circle.

  |z -c| = 5

For z₃: |(3 -2i) -(2 +i)| = √((3-2)² +(-2-i)²) = √(1+9) = √10 ≠ 5 . . . NOT on circle

For z₄: |(6 -2i) -(2 +i)| = √((6 -2)² +(2 -i)²) = √(16 +9) = √25 = 5 . . . IS on circle

4 0
3 years ago
Update:
ohaa [14]

Answer:

Love vines!

Step-by-step explanation:

But vine left us while getting milk. And tick tock is like our step father that we've grew to love :)

4 0
3 years ago
Read 2 more answers
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