“an architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying a finish to the exterior of the spheres need to know the surface area of each sphere. the finishing process costs $92 per square meter. the surface area of a sphere is equal to 4πr2, where r is the radius of the sphere.“in the table, select the value that is closest to the cost of finishing a sphere with a 5.50-meter circumference as well as the cost of finishing a sphere with a 7.85-meter circumference. make only two selections, one in each column.”circumference 5.50 m circumference 7.85 m finishing cost$900$1,200$1,800$2,800$3,200$4, 500

Part 1) The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900

Part 2) The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800

Step-by-step explanation:

Step 1

Find the radius of each sphere

we know that

The circumference of a circle is equal to

Find the radius of the sphere with a 5.50-meter circumference

For

assume

substitute and solve for r

Find the radius of the sphere with a 7.85-meter circumference

For

assume

substitute and solve for r

step 2

Find the surface area of each sphere

The surface area of sphere is equal to

Find the surface area of sphere with a 5.50-meter circumference

For

assume

substitute

Find the surface area of sphere with a 7.85-meter circumference

For

assume

substitute

step 3

Find the cost of finishing each sphere

we know that

To find out the cost , multiply the surface area by $92 per square meter

Find the cost of sphere with a 5.50-meter circumference

therefore

The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900

Find the cost of sphere with a 7.85-meter circumference

therefore

The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

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'.