Answer:
Step-by-step explanation:
The need is to find the area of the elongated plus sign inside the rectangle. The area of the rectangle itself is not needed. That elongated plus sign is where we will run into trouble. The center of that plus sign is included in both the vertical strip and the horizontal strip. So when we go to find the area of the plus sign, we include the center in one or the other, NOT BOTH. I included the area in the vertical strip so I eliminated it in the horizontal strip, creating 2 shorter strips on either side of the center.
The area for the vertical strip, including the center:
A = 3 * 26 (3 is the width and 26 is the length)
A = 78 square meters
Now for the horizontal strip...
The horizontal strip minus the center is
14 - 3 = 11; divide that 11 in half and we get the length of each short horizontal strip on either side of the center to be 5.5 meters long. Therefore, each short strip measures 5.5 (we have 2 of them).
A = 3(5.5) + 3(5.5) and
A = 16.5 + 16.5
A = 33
The sum of the long vertical and the 2 shorter horizontal areas is
78 + 33 = 111
Therefore, the total area of the colored portion is 111 square meters.
Hello,
twice as many means that the number of crayons is multiplied by 2, which would give 2C
she also has 3 more than that so you would add 3 (+3)
this would give you the expression 2C+3
hope this helped :)
Answer:
1:27 (D)
Step-by-step explanation:
Given:
Sphere A has a diameter of 2
Sphere A is dilated to create sphere B
Scale factor = 3
Volume of a sphere = 4/3 πr³
Radius = r = diameter/2 = 2/2
r = 1
Volume of sphere A = 4/3 ×π(1)³
Volume of sphere A = 4/3 × π
Volume of sphere B = 4/3 πR³
Since the diameter was dilated, the diameter of B = diameter of A × scale factor
diameter of B = 2×3 = 6
Radius of B = R = diameter/2 = 3
Volume of sphere B = 4/3 × π(3)³
Volume of sphere B = (4/3)(27)π
Ratio of the volume of sphere A to volume of sphere B
= [4/3 ×π]: [(4/3)(27)π]
= (4π/3)/[(4π/3)×27] = 1/27
= 1:27
4 : 3 ratio
Break it down to inches and simplify
1.Disc method.
In this method the volume is given by:
![\boxed{V=\pi\int\limits_a^b\big[f(x)\big]^2}](https://tex.z-dn.net/?f=%5Cboxed%7BV%3D%5Cpi%5Cint%5Climits_a%5Eb%5Cbig%5Bf%28x%29%5Cbig%5D%5E2%7D)
so:
![V=\pi\int\limits_1^3x^4\,dx=\boxed{\pi\int\limits_1^3\big[x^2\big]^2\,dx}](https://tex.z-dn.net/?f=V%3D%5Cpi%5Cint%5Climits_1%5E3x%5E4%5C%2Cdx%3D%5Cboxed%7B%5Cpi%5Cint%5Climits_1%5E3%5Cbig%5Bx%5E2%5Cbig%5D%5E2%5C%2Cdx%7D)
A) Function
over the interval
![[1,3]](https://tex.z-dn.net/?f=%5B1%2C3%5D)
B) We use disk method and f(x) is function of variable x, so we <span>rotate the curve about the x-<span>axis.
2. Shell method.
In this case volume is given by:
</span></span>
So there will be:
A) Function
over the interval
B) We use shell method and f(x) is function of variable x, so we <span>rotate the curve about the y-<span>axis.</span></span>
