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3 years ago

Which absolute value equation represents the graph? PLEASE HELP

Mathematics

1 answer:

storchak [24]3 years ago

3 0

Answer:

Step-by-step explanation:

i just looked up the question

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a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and

fomenos

Answer:

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

$x(t) = -4.9t^{2} + 9.8t$

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format $x(t) = at^{2} + bt + c$

The vertex is the point $(t_{v}, x(t_{v}))$ , in which

$t_{v} = -\frac{b}{2a}$

In this question:

$x(t) = -4.9t^{2} + 9.8t$

So $a = -4.9, b = 9.8$

Vertex:

$t_{v} = -\frac{9.8}{2*(-4.9)} = 1$

The time taken for the upward motion is 1 second.

$x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9$

It reaches a maximum height of 4.9 meters.

Downward motion:

From the vertex to the ground.

The ground is t when x = 0. So

$-4.9t^{2} + 9.8t = 0$

$4.9t^{2} - 9.8t = 0$

$4.9t(t - 2) = 0$

$4.9t = 0$

$t = 0$

$t - 2 = 0$

$t = 2$

It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

5 0

3 years ago

What is the area of the figure below? PLEASE HELP

viktelen [127]

Answer:

Step-by-step explanation:

This can be broken down into a square and a rectangle.

A=5(5)+(12)(8-5)

A=25+12(3)

A=25+36

A=61 u^2

6 0

3 years ago

Read 2 more answers

Identify Like terms : 3y2, 2/3x, -3/4y2, 5x, 12x2

wel

3y^2 and -3/4y^2
5x and 2/3x
12x^2

4 0

3 years ago

How are the two angles below related? Drawing not to scale. Drawing is not to scale.

Phoenix [80]

we know that

Two angles are supplementary if their sum is equal to $180$ degrees

in this problem we have

$Angle\ 1=45\°$

$Angle\ 2=135\°$

$Angle\ 1+Angle\ 2=180\°$

therefore

the answer is

The two angles are supplementary

5 0

3 years ago

Read 2 more answers

The profit that a vendor makes per day by selling x elephant ears is given by the function P(x)= -0.004x^2+3.2x-200. Find the nu

dezoksy [38]

Answer:

The number of elephant ears that must be sold to maximize profit is 400.

Step-by-step explanation:

Given that,

The profit that a vendor makes per day is given by

P(x)= - 0.004x² +3.2 x -200

where x is number of elephant ears.

P(x)= - 0.004x² +3.2 x -200

Differentiating with respect to x

P'(x)= - 0.008x+3.2

Again differentiating with respect to x

P''(x) = -0.008

For maximum or minimum P'(x)=0

- 0.008x+3.2=0

⇒0.008x=3.2

$\Rightarrow x=\frac{3.2}{0.008}$

⇒ x = 400

$P''(x)|_{x=400} = -0.008$

Since at x=400, P''(x)<0, the profit is maximize.

P(400) = -0.004×400²+3.2×400-200

=440

The number of elephant ears that must be sold to maximize profit is 400.

3 0

3 years ago