Answer:
Step-by-step explanation:
The general solution will be the sum of the complementary solution and the particular solution:
In order to find the complementary solution you need to solve:
Using the characteristic equation, we may have three cases:
Real roots:
Repeated roots:
Complex roots:
Hence:
Solving for 
:
Since we got complex roots, the complementary solution will be given by:
Now using undetermined coefficients, the particular solution is of the form:
Note: 
was multiplied by x to account for 
and 
in the complementary solution.
Find the second derivative of in order to find the constants 
and 
:
Substitute the particular solution into the differential equation:
Simplifying:
Equate the coefficients of and on both sides of the equation:
So:
Substitute the value of the constants into the particular equation:
Therefore, the general solution is:
10.5x + 3y = 811.5
x + y = 97
y = 97 - x
3y = 291 - 3x
7.5x + 291 = 811.5
7.5x = 811.5 - 291
x = 520.5 / 7.5
x = 69.4
69 were sold at the original price
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that the areas of the kitchen, playroom, and dining room are in the ratio 4 : 3 : 2 and that the combined area of these three rooms is 189 square feet.
Therefore, Kitchen area = 4/(4+3+2) × 189 = 4/9 × 189 = 84 square feet
Playroom area = 3/(4+3+2) × 189 = 3/9 × 189 = 63 square feet
Dining room area = 2/(4+3+2) × 189 = 2/9 × 189 = 42 square feet
Answer:
y = 4x + 8
Step-by-step explanation:
The linear equation can be written in the form y = mx + b. "y" and "x" stay as they are. The "m" is the slope or rate of change. The b is the y-intercept.
Hope it helps!!!
(May I have brainliest if it's correct please?)
Answer:
30
Step-by-step explanation:
3 pieces each 1 dekameter long
1 dekameter = 10 meters
Convert dekameters to meters
3 pieces each 10 meters long
Multiply
Glenn has 30 meters of lanyard
Divide
He can cut 30 1-meter pieces
Hope this helps :)
