Answer:
-20/3 & -40/3
Step-by-step explanation:
Let’s say that the 1st number is X and the 2nd number is Y.
Given that x:y = 1:2 => x/y = 1/2 => 2x = y
and a-5/y+4 = 5/4 (The first number is decreased by 5 and the second number is increased by 4.)
=> 4(x - 5) = 5 (y + 4)
=> 4x - 20 = 5y + 20
=> 4x - 5y = 40
As, 2x = y , 4x = 2y
=> 2y - 5y = 40
=> -3y = 40
=> y = -40/3 ; x = y/2 = -20/3
This might be confusing but I hope this helps :)
So you add whats in parentheses first which gives you -11 then you end up with -11(-3)
Which will equal 33 Thats your final awnser...
33
Answer:
The diameter of the sphere is 6 centimeters
Step-by-step explanation:
we know that
The surface area of a sphere is
![SA=4\pi r^{2}](https://tex.z-dn.net/?f=SA%3D4%5Cpi%20r%5E%7B2%7D)
The volume of the sphere is
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
Equate both formulas
![\frac{4}{3}\pi r^{3}=4\pi r^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D%3D4%5Cpi%20r%5E%7B2%7D)
Simplify
![\frac{1}{3}r^{3}=r^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dr%5E%7B3%7D%3Dr%5E%7B2%7D)
![\frac{r^3}{r^2}=3](https://tex.z-dn.net/?f=%5Cfrac%7Br%5E3%7D%7Br%5E2%7D%3D3)
![r=3\ cm](https://tex.z-dn.net/?f=r%3D3%5C%20cm)
Remember that the diameter is two times the radius
so
![D=2r=2(3)=6\ cm](https://tex.z-dn.net/?f=D%3D2r%3D2%283%29%3D6%5C%20cm)
therefore
The diameter of the sphere is 6 centimeters
For this case we have a function of the form:
![y = A * (b) ^ x](https://tex.z-dn.net/?f=%20y%20%3D%20A%20%2A%20%28b%29%20%5E%20x%20%20)
Where,
A: starting salary
b: salary growth rate
x: number of years
y: salary after x years.
Substituting values we have:
![100000 = A * (1.04) ^ {10}\\](https://tex.z-dn.net/?f=%20100000%20%3D%20A%20%2A%20%281.04%29%20%5E%20%7B10%7D%5C%5C%20)
From here, we clear the value of A.
We have then:
![A=\frac{100000}{1.04^{10}}](https://tex.z-dn.net/?f=%20A%3D%5Cfrac%7B100000%7D%7B1.04%5E%7B10%7D%7D%20%20)
![A=67556.42](https://tex.z-dn.net/?f=%20%20A%3D67556.42%20%20)
Answer:
the lowest salary that i should request in order to meet my goal is:
A=67556.42