Answer:
Rate of change = 3
Step-by-step explanation:
The rate of change is the slope.
Slope = 3
Answer:
![2(a^3+b^2+11)+1(3+a^3+b+11)=3a^3+2b^2+b+36](https://tex.z-dn.net/?f=2%28a%5E3%2Bb%5E2%2B11%29%2B1%283%2Ba%5E3%2Bb%2B11%29%3D3a%5E3%2B2b%5E2%2Bb%2B36)
Step-by-step explanation:
I assume that you need simplification of the given expression.
The given expression is:
![2(a^3+b^2+11)+1(3+a^3+b+11)](https://tex.z-dn.net/?f=2%28a%5E3%2Bb%5E2%2B11%29%2B1%283%2Ba%5E3%2Bb%2B11%29)
Using distributive property and multiplying 2 inside the parenthesis and 1 inside the other parenthesis. This gives,
![2(a^3+b^2+11)=2\times a^3+2\times b^2+2\times 11\\2(a^3+b^2+11)=2a^3+2b^2+22\\\\1(3+a^3+b+11)=1\times 3+1\times a^3+1\times b+1\times 11\\1(3+a^3+b+11)=3+a^3+b+11=a^3+b+14](https://tex.z-dn.net/?f=2%28a%5E3%2Bb%5E2%2B11%29%3D2%5Ctimes%20a%5E3%2B2%5Ctimes%20b%5E2%2B2%5Ctimes%2011%5C%5C2%28a%5E3%2Bb%5E2%2B11%29%3D2a%5E3%2B2b%5E2%2B22%5C%5C%5C%5C1%283%2Ba%5E3%2Bb%2B11%29%3D1%5Ctimes%203%2B1%5Ctimes%20a%5E3%2B1%5Ctimes%20b%2B1%5Ctimes%2011%5C%5C1%283%2Ba%5E3%2Bb%2B11%29%3D3%2Ba%5E3%2Bb%2B11%3Da%5E3%2Bb%2B14)
Therefore,
is equal to:
![2a^3+2b^2+22+a^3+b+14](https://tex.z-dn.net/?f=2a%5E3%2B2b%5E2%2B22%2Ba%5E3%2Bb%2B14)
Now, combining like terms using the commutative property of addition, we get:
![=(2a^3+a^3)+2b^2+b+(22+14)\\=3a^3+2b^2+b+36](https://tex.z-dn.net/?f=%3D%282a%5E3%2Ba%5E3%29%2B2b%5E2%2Bb%2B%2822%2B14%29%5C%5C%3D3a%5E3%2B2b%5E2%2Bb%2B36)
Therefore, the simplified form is ![3a^3+2b^2+b+36](https://tex.z-dn.net/?f=3a%5E3%2B2b%5E2%2Bb%2B36)
(i) The area of the cross section ABCDEFG is 1771.6cm³
(ii) The volume of the concrete lab is 212592 cm³
(iii) the total surface area of the concrete slab is 30284 cm²
(iv) The mass of the concrete slab is 40746.8 kg/m³.
Given, dimensions are 120 cm by 60 cm by
40 cm.
(i) area of cross section = 40 × 60 ₋ π(60 ₋10 ₋ 10)/2 . 1/2
= 1771.6 cm³
(ii) the volume of the concrete slab = 40 × 60 × 120 ₋ 1/2 π((60 ₋ 10 ₋10)/2)² . 120
= 212592 cm³
(iii) The total surface area is:
=40 × 120 × 2 ₊ 60 × 120 ₊ 1771.6 × 2 ₊ 10 × 120 × 2 ₊ 1/2 π(60 ₋ 10 ₋10) × 120
= 30284 cm²
(iv) Mass of the concrete slab given density is 2300 kg/m³
Mass = Volume × density
Mass = 17.716 m³ × 2300
= 40746.8 kg/m³
Hence we get the mass as 40746.8 kg/m³.
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This is a classic example of Scientific Notation.
5.3 x 10^5 actually equals 530,000
3.8 x 10^4 actually equals 38,000
Since it is asking for the sum of the numbers you are adding.
Your new equation look like this:
530,000 + 38,000
= 568,000
now all you have to do is count the decimal points. You start from the end zero and count the spaces in between until you get to the tenths place. (Right behind the first number) There are 5
So your answer will be:
B. 5.68 x 10^5.
The answer you are looking for is -17/44