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3 years ago

I believe the answer is B can someone confirm

Mathematics

2 answers:

stellarik [79]3 years ago

6 0

Answer:

yes you are right

Step-by-step explanation:

B is correct

Usimov [2.4K]3 years ago

4 0

Answer:

Looks right, b is right

Step-by-step explanation:

The rest are false

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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

3 years ago

A pool has a depth of 12 feet and a width of 14 feet.If it holds 1680 cubic feet of water, what is the length of the pool?

Novay_Z [31]

12 x 14 x L = 1680

168 x L = 1680

L = 1680 / 168

L = 10 feet

3 0

3 years ago

Find the VOLUME of this composite solid.

Black_prince [1.1K]

Answer:

(294π +448) cm³ ≈ 1371.6 cm³

Step-by-step explanation:

The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.

The cylinder volume is ...

V = πr²h = π(7 cm)²(6 cm) = 294π cm³

The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...

V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³

Then the total volume of the composite figure is ...

(294π +448) cm³ ≈ 1371.6 cm³

8 0

3 years ago

Sin 2x=

loris [4]

Answer:

A,C

Step-by-step explanation:

sin 2x=sin (x+x)=sinx cos x+cos x sin x=2 sin x cos x

or =2 cos x sin x

[sinx cox=cos x sin x ]

6 0

3 years ago

5<br>X Х please find the answer<br>20

Daniel [21]

Answer:

2 or 4

Step-by-step explanation:

Since I do not quite understand what you mean by X X, I could think of two answers. If you are doing 5 times X=20, then X = 4, but if you are trying to do 5 times x times x, then x=2.

3 0

3 years ago