Answer: 2 cups
Step-by-step explanation:
<u>Given</u>:
The given expression is 
We need to determine the value of x using either base - 10 or base - e logarithms.
<u>Value of x:</u>
Let us determine the value of x using the base - e logarithms.
Applying the log rule that if
then 
Thus, we get;

Applying the log rule,
, we get;

Expanding, we get;

Subtracting both sides by
, we get;

Subtracting both sides by
, we get;

Taking out the common term x, we have;



Thus, the value of x is 
Answer: 376.98192 mL
Step-by-step explanation:
We are going to use this equation.
V = π * r² * h
according to the question we have the value for r and h, if you replace the values into the equation we will get following product:
note: also keep in mind that value of π is 3.141516
V = π * r² * h
V = π * (4in)² * (10in)
V = 502.64256 in³
after we can divide this value in 4 equals parts
then we get the following equation:
502.64256 in³ / 4 = 125.66064 in³
after that that you can multiply this value by 3 to get the 3 parts of the cylinder vase for example:
125.66064 in³ * 3 = 376.98192 in³
and this result is the volume of water that we have to pour into the vase
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer:
Brainliest!!!
Step-by-step explanation:
see picture