write the equation of the linear function that passes through the point (2,-2) and (-3, 13)

Question

y=___x+____

Answer 1

First, we need to find the slope (m) of the line using the two given points:

m = (y2 - y1) / (x2 - x1)
m = (13 - (-2)) / (-3 - 2)
m = 15 / -5
m = -3

Now that we have the slope, we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)
y - (-2) = -3(x - 2)
y + 2 = -3x + 6
y = -3x + 4

Therefore, the equation of the linear function that passes through the points (2,-2) and (-3,13) is:

y = -3x + 4

Answer 2

find the volume of the between the cylinder and the cone. note the cone is touching the top of the cylinder.
the height of the cylinder is 13 inches and the diameter is 60 inches

use 3.14 for pi.

Answer 3

To find the volume between the cylinder and the cone, we first need to find the volume of both shapes and then subtract the volume of the cone from the volume of the cylinder.

1. Volume of the Cylinder:
Given that the height of the cylinder is 13 inches and the diameter is 60 inches, we can calculate the radius of the cylinder as half of the diameter:
Radius = 60 / 2 = 30 inches

The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * 30^2 * 13
V_cylinder = 3.14 * 900 * 13
V_cylinder = 35310 cubic inches

2. Volume of the Cone:
Since the cone is touching the top of the cylinder, the height of the cone will be equal to the height of the cylinder (13 inches).

The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h
V_cone = (1/3) * 3.14 * 30^2 * 13
V_cone = (1/3) * 3.14 * 900 * 13
V_cone = 39390 cubic inches

3. Volume between the Cylinder and Cone:
Volume between cylinder and cone = Volume_cylinder - Volume_cone
Volume between cylinder and cone = 35310 - 39390
Volume between cylinder and cone = -4079.6 cubic inches

Therefore, the volume of the space between the cylinder and the cone is approximately 4079.6 cubic inches.

Answer 4

are you sure?

Answer 5

Apologies for the mistake in the calculation. Let's correct that:

1. Volume of the Cylinder:
Given radius (r) = 30 inches and height (h) = 13 inches:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * 30^2 * 13
V_cylinder = 3.14 * 900 * 13
V_cylinder = 35490 cubic inches

2. Volume of the Cone:
Since the cone is touching the top of the cylinder, the height of the cone will be equal to the height of the cylinder (13 inches).

V_cone = (1/3) * π * r^2 * h
V_cone = (1/3) * 3.14 * 30^2 * 13
V_cone = (1/3) * 3.14 * 900 * 13
V_cone = 12285 cubic inches

3. Volume between the Cylinder and Cone:
Volume between cylinder and cone = Volume_cylinder - Volume_cone
Volume between cylinder and cone = 35490 - 12285
Volume between cylinder and cone = 23205 cubic inches

Therefore, the corrected volume of the space between the cylinder and the cone is 23205 cubic inches. Thank you for your understanding.

Answer 6

what is the total volume of the shape below if the height of the cylinder is 5 inches, the radius of the cylinder is 6 inches and the height of cone is 6 inches? use 3.14 for pi. round to the nearest hundredth.

Answer 7

To find the total volume of the shape, we need to calculate the volume of the cylinder and the volume of the cone separately, then add them together.

1. Volume of the Cylinder:
Given radius (r) = 6 inches and height (h) = 5 inches:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * 6^2 * 5
V_cylinder = 3.14 * 36 * 5
V_cylinder = 565.2 cubic inches

2. Volume of the Cone:
Given radius (r) = 6 inches and height (h) = 6 inches:
V_cone = (1/3) * π * r^2 * h
V_cone = (1/3) * 3.14 * 6^2 * 6
V_cone = (1/3) * 3.14 * 36 * 6
V_cone = 226.08 cubic inches

3. Total Volume:
Total Volume = Volume_cylinder + Volume_cone
Total Volume = 565.2 + 226.08
Total Volume ≈ 791.28 cubic inches

Therefore, the total volume of the shape is approximately 791.28 cubic inches when rounded to the nearest hundredth.