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3 years ago

Find the diameter of a spherical beach ball with a volume of 36n

Mathematics

1 answer:

mestny [16]3 years ago

8 0

6 I don’t know I just needed to answer a question

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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

Greatest common factor between 84 and 56

s344n2d4d5 [400]

The greatest common factor is 28.

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Then the greatest common factor is 28.

3 0

3 years ago

Find the missing value

lubasha [3.4K]

Answer:

70.2

Step-by-step explanation:

6 0

3 years ago

PLEASE HELP ASAP!! WORDED QUADRATIC QUESTIONS!!!

Roman55 [17]

Answer:

x² - 5x = 14

x = -2 or x = 7

Step-by-step explanation:

x² - 5x = 14

x² - 5x - 14 = 0

(x+2)(x-7) = 0

x = -2 or x = 7

4 0

2 years ago

What is Bethany's score on the test if she got 23 out of 30 right? (Round to the nearest whole number.)

matrenka [14]

Answer:

77%

Step-by-step explanation:

23 divided by 30 is 0.766666, which percent-wise is rounded to 77% :)

3 0

2 years ago

Read 2 more answers