Juan and his little brother Miquel ran around a circular track together. Juan ran on the inner track, which has a radius of 30 feet. Miquel ran on the outer track which has a radius of 40 feet. How much further did Miquel run than Juan after two loops around the track? A. 31.4 ft. B. 62.8 ft. C. 125.6 ft. D. 219.8 ft.

Step-by-step explanation:

Using the formula for finding the circumference of a circle expressed as:

where:

r is the radius of the circular track

If Juan ran on the inner track, which has a radius of 30 feet, the area of the trach is expressed as:

If Miquel ran on the outer track which has a radius of 40 feet, the area of the outer track will be expressed as:

To know  how much further did Miquel run than Juan after two loops around the track, we will take the difference in the circumference as shown:

Hence Miguel has ran  125.6 ft further after two loops around the track

C

Step-by-step explanation:

Mathematically, to calculate the distance run around the tracks, we need to know the circumferences of the tracks

The circumference of a circle is 2 π r

For the 40 feet track, circumference will be 2 * π * 40 = 80 π feet

In two loops, distance ran will be 2 * 80 π feet = 160 π feet

For the 30 feet track , circumference will be 2 * π * 30 = 60 π feet

In two loops, distance will be 2 * 60 π = 120 π feet

Thus, how much further Miguel ran will be the difference between the two loops

= 160 π - 120 π = 40 π feet

The distance here here if we substitute for π will be 40 * 22/7 = 125.71 ft

The closer answer to this is option C

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

47.28 or 47.2857143

step-by-step explanation:

you just divide 331 by 7 and you get that answer. ( i think so tho)