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3 years ago

URGENT, please!!

Mathematics

1 answer:

lakkis [162]3 years ago

7 0

The equation of the parabola is:

$y = 24x^2$

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The <em>equation </em>of a parabola of vertex (h,k) and focus (0,f) is given by:

$y = 4p(x - h)^2 + k^2$

Vertex at the origin means that $h = 0, k = 0$ .
Focus (0,6) means that $p = 6$

Thus, the equation of the parabola is:

$y = 4p(x - h)^2 + k^2$

$y = 4(6)(x - 0)^2 + 0^2$

$y = 24x^2$

A similar problem is given at brainly.com/question/15165354

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Which of the following terms is best described as the point halfway between

zysi [14]

The answer should be A midpoint

6 0

2 years ago

Stacey is selling tickets to the school play. The tickets are $8 for adults and $3 for children. She sells twice as many adult t

Leona [35]

48 adult tickets and 24 children tickets were sold.

Step-by-step explanation:

Given,

Cost of one adult ticket = $8

Cost of one child ticket = $3

Total worth of sold tickets = $456

Let,

Number of adult tickets sold = x

Number of child ticket sold = y

According to given statement;

8x+3y=456 Eqn 1

x = 2y Eqn 2

Putting value of x from Eqn 1 in Eqn 2

$8(2y)+3y=456\\16y+3y=456\\19y=456$

Dividing both sides by 19

$\frac{19y}{19}=\frac{456}{19}\\y=24$

Putting y=24 in Eqn 2

$x=2(24)\\x=48$

48 adult tickets and 24 children tickets were sold.

Keywords: linear equation, substitution method

Learn more about linear equations at:

#LearnwithBrainly

6 0

3 years ago

PLEASE ANSWER ASAP!!

Rufina [12.5K]

Answer:

The instantaneous rate of increase of f(x) at $x_{0} = 3$ is 3.
One possible equation of this line is y = 3x - 16.
The line is tangent to the graph of y = f(x). The slope of the line is the same as the instantaneous rate of increase of f(x) at $x_{0} = 3$ .

Step-by-step explanation:

$\begin{aligned}&\lim_{h\to 0}{\frac{f(3+h)-f(h)}{h}}\\ =&\lim_{h\to 0}\frac{1}{h} \cdot [(3^{3} + 3 \times 3^{2}h +3\times 3h^{2} + h^{3})- 4(3^{2} + 2\times 3h + h^{2}) + 2 \\[-1em] &\phantom{\lim_{h\to 0}\frac{1}{h}\cdot []} -(3^{3} -4\times 3^{2} + 2)]\\ = &\lim_{h \to 0}\frac{h^{3} + 5h^{2} +3h}{h}\\=& \lim_{h \to 0}{h^{2}} + \lim_{h \to 0}{5h} + \lim_{h\to 0}{3}\\ =& 3\end{aligned}$ .

$f(3) = 3^{3} - 4\times 3^{2} + 2 =-7$ .

In other words, the graph of y = f(x) passes through the point (3, -7) where $x = 3$ .

The point-slope form of a line in a cartesian plane is:

$y - y_0 = m (x - x_0)$ .

For this line,

$(3, -7)$ is the point on the line, while

$3$ is the slope of the line.

The equation of this line will thus be

$y - (-7) = 3(x - 3)$ .

That's equivalent to

$y = 3x - 16$ .

Refer to the diagram attached. The line touches the graph of y = f(x) at x = 3 without crossing it. The line here is thus a tangent to the graph of y = f(x) at x = 3. The slope of the line represents the instantaneous rate of increase of f(x) at $x_{0} = 3$ .