PLEASE HELP!!!
1. A sphere has a radius of 2x+3. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S=4πr^2 for the surface area of a sphere.
2. A carpenter is putting a skylight in a roof. If the roof measures (10x+9) by (7x+7) and the skylight measures (x+5) by (3x+3), what is the area of the remaining roof after the skylight is built?
1. So in your formula replace the r with (2x+3)
that is...
S = 4(PI)(2x+3)(2x +3)
Now use the distributive property to simplify...
2. total area - sky light = area remaining
(10x+9)(7x+7) - (x+5)(3x+3) = remaining area.
Use the distributive property to expand both sets of brackets then collect like terms.
Sure, I can help you with these problems! Let's break them down step by step:
1. To find the surface area of a sphere, we use the formula S = 4πr^2, where S represents the surface area and r represents the radius of the sphere. In this problem, the radius is given as 2x+3.
To find the total surface area polynomial, we need to substitute the given radius into the formula and simplify the expression.
Therefore, the total surface area of the sphere can be found by using the formula S = 4π(2x+3)^2. Let's simplify it:
S = 4π(2x+3)^2
S = 4π(4x^2 + 12x + 9)
S = 16πx^2 + 48πx + 36π
So the polynomial representation of the total surface area of the sphere is 16πx^2 + 48πx + 36π.
2. To find the area of the remaining roof after the skylight is built, we need to calculate the area of the original roof and subtract the area of the skylight.
The area of the original roof can be found by multiplying its length and width, which are given as (10x+9) and (7x+7) respectively. So the area of the original roof is (10x+9)(7x+7).
Similarly, the area of the skylight can be found by multiplying its length and width, which are given as (x+5) and (3x+3) respectively. So the area of the skylight is (x+5)(3x+3).
To find the area of the remaining roof, we need to subtract the area of the skylight from the area of the original roof:
Area of remaining roof = Area of original roof - Area of skylight
= (10x+9)(7x+7) - (x+5)(3x+3)
You can expand, simplify, and combine like terms to get the final polynomial expression representing the area of the remaining roof.
I hope this explanation helps you understand how to approach these problems!