Samuel plans to install a fence around the perimeter of his yard. His yard is shaped like a square and has an area of 40,000 squ
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Answer:
The small tire would make about 127 rotations.
The large tire would make about 38 rotations.
b. Would you rather ride a bicycle made with two large wheels or two small wheels? Explain.
Two large wheels. Because the larger wheel makes a smoother ride and you spend less energy in order to move, compared to smaller wheels. Also, the larger the diameter, the further it can travel over one revolution.
A bicycle with would allow you to travel farther with each rotation of the pedal.
The larger one. Because in one rotation the larger wheel moves 188.49 inches and the smaller one 56.55 inches.
Step-by-step explanation:
- Big wheel 60 inches
- Small wheel 18 inches.
a. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.
Considering:
Large tire:
Small tire:
Answer:
We want to find a solution of the system:
x^2 + y^2 > 49
y ≤ –x^2 – 4
Here we do not have any options, so let's try to find a general solution.
First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:
(x - a)^2 + (y - b)^2 = R^2
If we look at our first inequality, we can write it as:
x^2 + y^2 > 7^2
So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.
From the other equation, we would get:
y ≤ –x^2 – 4
This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.
Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.
You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:
by looking at the graph, we can see a lot of points that are solutions, like:
(0, -10)
(0, -15)
(2, -10)
etc.
