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2 years ago

The gates for a concert opened 1 hour before the concert began. Six minutes

Mathematics

1 answer:

GalinKa [24]2 years ago

7 0

Answer:

Step-by-step explanation:

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

3 0

2 years ago

Solve the equation x2<br> 18x + 21 = -3x to the nearest tenth.

Bumek [7]

Answer:

1x=-29

2x=-1

Step-by-step explanation:

i hope its useful.

7 0

2 years ago

A choreographer uses a number line to position dancers for a ballet. Dancers A and B

kenny6666 [7]

First we will calculate the distance AB.
$AB=B-A=23-5=18.$
If C is 5/9 of the distance, mathematically speaking that means:
$C= \frac{5}{6} *AB= \frac{5}{6} *18=15.$
R: The coordonate of C is 15.

5 0

2 years ago

Read 2 more answers

An irrigation system waters in circular patterns.

Varvara68 [4.7K]

80x 40 x 20 feet is your answer! Hope this helps

3 0

2 years ago

Evaluate each expression (-21)+22+41

Marianna [84]

Answer:

Step-by-step explanation: