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3 years ago

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1 answer:

deff fn [24]3 years ago

6 0

Download photomath. step by step equation solver

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Your station charges $16.50 for a lubrication job. As a promotion you sell six coupons for lubrication jobs for $90. What percen

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Multiply 6 by $16.50 to get the total amount = $99

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3 years ago

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A mystery element has 18 protons. Which one of the following statements is true about the element?

Xelga [282]

Answer:

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Step-by-step explanation:

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3 years ago

A 20-gallon container is filled halfway with a mixture that is $90\%$ vinegar and $10\%$ water. How many gallons of water must b

Yuki888 [10]

Answer:

5 gallons of water must be added.

10 gallons to start with

adding 'x' gallons of water final volume = 10 + x

.9 (10) = amount of vinegar

.1(10) = amount of water

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2 years ago

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

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

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

$4.9t(t - 2) = 0$

$4.9t = 0$

$t = 0$

Or

$t - 2 = 0$

$t = 2$

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.

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3 years ago

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2 years ago