Answer:
they used a universal plank to measure 7 and 10
Step-by-step explanation:
The capsule describe consists of 2 hemispheres (same) and 1 cylinder. We need to sum up the volume of the cylinder and the 2 same hemispheres.
- <u>Volume of Cylinder:</u>
We are given the radius of the cylinder as 3 and the height as 6. The formula for volume of cylinder is . Plugging in 3 for r and 6 for h gives us,
.
- <u>Volume of Hemisphere(s):</u>
We are given the radius is 3 for the hemisphere. The formula for volume of a hemisphere is half of the volume of a sphere. The formula for hemisphere is shown below.
. Plugging in 3 for r gives us,
<em>Now, since we have 2 same hemispheres, we multiply this answer by 2 to get total volume of the 2 hemispheres.</em>
.
- <u>Total volume of the capsule:</u>
In decimal, taking 3.14 as , it is
Rounding to the nearest whole number gives us 283 millimeters squared.
ANSWER: Volume = and
Answer:
Surface area of the fish tank
Step-by-step explanation:
We have to find the surface area of the hospital tank.
As mentioned it does not have a cover.
The tank is in cuboid shape as it has different length ,width and height .
Surface area of a cuboid
But here we have to subtract the surface area of the cover,that is .
So the equation for the surface area of the cuboid can be re-framed as
Plugging the values of and and
Now
Surface area of the tank:
So the surface area of the fish tank in the hospital is
This is the same as showing the following system of equations doesn't have a solution:
or in matrix form,
The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.
And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:
(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)
So there are indeed no such scalars <em>c₁</em>, <em>c₂</em>, and <em>c₃</em>.