Answer:
The product of the complex number and its conjugate is a real number
Step-by-step explanation:
Volume of a sphere is
![\frac{4}{3} \pi {r}^{3}](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20)
plug in 70 ft for the radius to get 1,436,755 cubic ft then divide that by 4 since the prompt describes a quarter sphere, giving you a tank volume of 359,189 cubic ft.
Volume of a cylinder is
![\pi {r}^{2} h](https://tex.z-dn.net/?f=%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
from the second prompt we know the tanks are identical since they are said to be congruent which means the hight and radius are the same. Plug in 120 f for h and 35 ft for r to get the volume of a cylinder and then divide that by 2 to get the volume of a single tank. the volume of both tanks would be
![\pi {35}^{2} (120) = 461,814](https://tex.z-dn.net/?f=%5Cpi%20%7B35%7D%5E%7B2%7D%20%28120%29%20%3D%20461%2C814)
To show tank model is a sixth of the original so you divide the radius by 6 and perform the same calculation as in the first portion of the problem ro get the volume a quarter sphere
![\frac{4}{3} \pi {( \frac{70}{6} )}^{3} = 6,652 \: {ft}^{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7B%28%20%5Cfrac%7B70%7D%7B6%7D%20%29%7D%5E%7B3%7D%20%20%3D%206%2C652%20%5C%3A%20%20%7Bft%7D%5E%7B3%7D%20)
To get the percentage of the model relative to the original you divide the models volume by the full scale volume
![\frac{6652}{1436755} \times 100 = 0.46](https://tex.z-dn.net/?f=%20%5Cfrac%7B6652%7D%7B1436755%7D%20%5Ctimes%20100%20%20%3D%200.46)
which is less than 1% of the full scale volume.
Answer:
$2.50
Step-by-step explanation:
Let's set up a proportion using the following setup.
price / pens = price / pens
We know that it costs $4.00 for 8 pens.
$4.00 / 8 pens = price / pens
We don't know how much it costs for 5 pens. Therefore, we can say it costs $x for 5 pens.
$4.00 / 8 pens = $x / 5 pens
4/8=x/5
We want to solve for x (the cost for 5 pens). Therefore, we must get x by itself on one side of the equation. x is being divided by 5. The inverse of division is multiplication, so multiply both sides of the equation by 5.
5*(4/8)=(x/5)*5
5*(4/8)=x
5*0.5=x
2.5=x
x= $2.50
Ivan should pay $2.50 for 5 pens.
Answer:
angle COD is right answer