When triangle ABC is rotated about side AB, what figure is formed?
1 answer:
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Answer:
When we have a rational function like:
The domain will be the set of all real numbers, such that the denominator is different than zero.
So the first step is to find the values of x such that the denominator (x^2 + 3) is equal to zero.
Then we need to solve:
x^2 + 3 = 0
x^2 = -3
x = √(-3)
This is the square root of a negative number, then this is a complex number.
This means that there is no real number such that x^2 + 3 is equal to zero, then if x can only be a real number, we will never have the denominator equal to zero, so the domain will be the set of all real numbers.
D: x ∈ R.
b) we want to find two different numbers x such that:
r(x) = 1/4
Then we need to solve:
We can multiply both sides by (x^2 + 3)
Now we can multiply both sides by 4:
Now we only need to solve the quadratic equation:
x^2 + 3 - 4*x - 4 = 0
x^2 - 4*x - 1 = 0
We can use the Bhaskara's formula to solve this, remember that for an equation like:
a*x^2 + b*x + c = 0
the solutions are:
here we have:
a = 1
b = -4
c = -1
Then in this case the solutions are:
x = (4 + 4.47)/2 = 4.235
x = (4 - 4.47)/2 = -0.235
Answer:
a)
b)
c)
Step-by-step explanation:
Data given
x: 500, 700, 750, 590 , 540, 650, 480
y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50
Part a
We want to create a linear model like this :
Wehre
And:
With these we can find the sums:
And the slope would be:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
And the line would be:
Part b
The correlation coefficient is given by:
For our case we have this:
n=7
The determination coefficient is given by:
Part c