Is the function below below linear or non-linear y=-8x^2+9
2 answers:
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Answer:
Step-by-step explanation:
The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.
For the integral from [0, 2], the equation of the line is -3x + 6;
For the integral from [2, 3], the equation of the line is 3x - 6.
We integrate then:
and
sorry for the odd representation; that's as good as it gets here!
Using the First Fundamental Theorem of Calculus, we get:
(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5
Answer:
120 liters of 60% alcohol solution is needed
Step-by-step explanation:
Let's assume
x liters of 60% alcohol solution is added
so, we get solution as
we are given
40 liters of a 20% alcohol solution is
so, total alcohol solution is
now, we can find total solutions
total solutions is
now, it is making 50% solution
so, we get
now, we can solve for x
So,
120 liters of 60% alcohol solution is needed
Gradient of the line formed;
m=
m=
m=
y=mx+c
y=
Replacing for x and y;
1=-3/11*(-5)+c
1=15/11+c
c=1-15/11
c=-4/11
y=
m=
m=
m=
y=mx+c
y=
Replacing for x and y;
1=-3/11*(-5)+c
1=15/11+c
c=1-15/11
c=-4/11
y=