Answer:
Therefore the solution is = k{-7,5,1} where k ∈R
Step-by-step explanation:
Given that,
f₁(x) =x
f₂(x)= x²
f₃(x)= 7x - 5x²
Also,
g(x) = c₁f₁(x)+c₂f₂(x)+c₃f₃(x)
Putting the values of f₁(x), f₂(x) and f₃(x).
g(x) = c₁.x+c₂x²+c₃(7x-5x²)
Given condition that g(x)= 0
∴ c₁.x+c₂x²+c₃(7x-5x²)=0
⇒(c₁+7c₃)x +(c₂-5c₃)x² = 0
Comparing the coefficients of x and x²
∴c₁+7c₃=0 and c₂-5c₃ =0
Let c₃= k [k∈R]
Then c₁ = -7k and c₂=5k
Therefore the solution is = { c₁,c₂,c₃}
= {-7k, 5k, k}
=k{-7,5,1}
Let, the original price = x
x = 45 * 125 /100
x = 45 * 1.25
x = 56.25
So, your final answer is $56.25
Hope it helped
The answer is [ all real numbers ]
The domain are the input values which makes the function defined and real.
Since we don't have any constraints or any undefined points, the domain could be literally anything. Thus proves out answer.
Best of Luck!
The formula to use is
V = pi*r^2*h
V = volume of cylinder
pi = 3.14 approximately, but we'll leave it as pi
r = radius
h = height
In this problem,
r = 1 since the diameter is 2
h = 4
Plug those two values into the formula
V = pi*r^2*h
V = pi*1^2*4
V = pi*1*4
V = pi*4
V = 4pi
Answer: Choice C