The circumference of a circle is C=2πR, where R is the radius of the circle and π≈3.14.
So if we open the circumference of the circle into a straight line segment, the length of this segment is C=2πR≈2*3.14*R=6.28R
4 rotations mean 4 circumferences that is 4 segments of length 6.28R,
which makes a linear distance of 4*6.28R=25.12R
i: the radius of the smaller wheel is R=r, thus it covers a distance of 25.12r feet
ii: the radius of the smaller wheel is R=2r, thus it covers a distance of 25.12*2r=50.24r (feet)
50.24r is twice 25.12r, thus the larger wheel traveled Twice the distance of the smaller one.
Answer: the larger covered twice the distance of the smaller.
1. the answer is 24. think of x as the original amount, and y as the new amount. y times 1.5 is x, and y+12 is x. reverse that to figure out y, which is what we need, and you have x/1.5 = y as well as x-12 = y. Use the equal values method and make an equation x/1.5=x-12. solve this equation to get x, which is 36. to figure out the new amount, y, you need to subtract 12, which would help you get 24 as your final answer.
2. once again, create an equation. let's call team 1 x and team 2 y. team one has 1/4th as many as team 2, so that would be x=1/4y. An easier way to write that is 4x=y. after 6 people quit team two, that would be y-6. after the transfer, that would be y-6-12, and x+12 for the teams. they are equal after these, so y-6-12=x+12. solve this equation to get y-18= x+12. if you recall earlier, y was 4 times x, so substitute that into y to get 4x-18=x+12. Solve the equation to get 10 people on team one originally. your final answer is 10 people.
Answer:
x=13
Step-by-step explanation:
Answer:
x=35, y=21
Step-by-step explanation:
A way to rewrite the first equation is
after cross-multiplying, we get 3x=5y.
If we solve for one variable, we can substitute it into the other equation.
Let's solve for x.
3x=5y
x=(5/3)y
Now, we can substitute x=(5/3)y in the equation x+y=56.
(5/3)y+y=56
(8/3)y=56
y=21
Going back to x+y=56, we can now plug back in y, knowing that it is 21.
x+21=56
x=35.