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andriy [413]
3 years ago
9

Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's rate in mil

es per hour if there are 5,280 feet in a mile. Which girl bikes faster? (also can I get an explanation so I actually learn something lol)

Mathematics
2 answers:
topjm [15]3 years ago
5 0
That’s my work on the picture, the answer is nina because she rode the further distance in the shorter amount of time, i just did the converting but if you needed to you could show the unit rate too, let me know if you want me to add the work for the unit rate part

earnstyle [38]3 years ago
4 0

Step-by-step explanation:

question 1 = what is nina's rate in miles/hour

question 2 = which girl bikes faster

we need to find miles/hour but we are given feet/second so lets first convert our measurements.

63,360 / 5,280 = 12 miles

3,400 / 60 = 56 2/3 minutes     56 2/3 / 60 = 17/18 hour

so we know nina travels 12 miles in 17/18 hour, meaning she travels about 12.7 miles/hour

12.7 miles/hour is greater than 10 miles/hour meaning nina bikes faster

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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

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t = 0

Or

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It reaches the ground when t = 2 seconds.

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

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3 years ago
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