The root sof this quadratic equation are -4 and 2.5.
The roots of any quadratic can be found by using the quadratic equation. The equation is below for you.

In this equation you use the number attached to x^2 as the a, which in this case is -2. The number attached to x as b, which is in this case -3. And the number at the end as c, which is 20. From there you solve for the answers.



Now you separate and get the two separate answers. First the positive.


4
Now the negative


-2.5
Tan 2° = x / 1 mile, where x is the vertical change
0.03492 = x / 1 mile
x = 1 mile · 0.03429 = 0.03492 miles
1 mile = 5,280 feet
0.03492 · 5,280 = 184.38 ft
Answer: The vertical change is 184.38 feet
It is given in the question that
Suppose the supply function for product x is given by

And we have to find how much of product x is produced when px = $600 and pz = $60.
And for that, we have to substitute 600 for px and 60 for pz, and on doing so, we will get

And that's the required answer .
Answer:
0.99865
Step-by-step explanation:
The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.
To solve the above question, we would be using the z score formula
The formula for calculating a z-score
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
In the above question,
x is 115 liters
μ is 100
σ is the population standard deviation is unknown. But we were given variance in the question.
Standard deviation = √Variance
Variance = 9
Hence, Standard deviation = √9 = 3
We go ahead to calculate our z score
z = (x-μ)/σ
z = (115 - 100) / 3
z = 15/ 3
z score = 5
Using the z score table of normal distribution to find the Probability of having a z score of 5
P(x = 115) = P(z = 5) =
0.99865
Therefore the probability that this year it will produce 115 liters of wine = 0.99865
Answer:
As per the given statement:
The region bounded by the given curves about the y-axis,
, y=0, x = 0 and x = 1
Using cylindrical shell method:
The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;
where 
where x is the radius of the cylinder
f(x) is the height of the cylinder.
From the given figure:
radius = x
height(h) =f(x) =y=
a = 0 and b = 1
So, the volume V generated by rotating the given region:
![V =2 \pi \int_{0}^{1} x ( 13e^{-x^2}) dx\\\\V=2\pi\left [ -\frac{13}{2}e^{-x^2} \right ]_{0}^{1}\\\\V=2\pi\left (-\frac{13}{2e}-\left(-\frac{13}{2}\right) \right )\\\\V=-\frac{13\pi }{e}+13\pi](https://tex.z-dn.net/?f=V%20%3D2%20%5Cpi%20%5Cint_%7B0%7D%5E%7B1%7D%20x%20%28%2013e%5E%7B-x%5E2%7D%29%20dx%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%5B%20-%5Cfrac%7B13%7D%7B2%7De%5E%7B-x%5E2%7D%20%5Cright%20%5D_%7B0%7D%5E%7B1%7D%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%28-%5Cfrac%7B13%7D%7B2e%7D-%5Cleft%28-%5Cfrac%7B13%7D%7B2%7D%5Cright%29%20%5Cright%20%29%5C%5C%5C%5CV%3D-%5Cfrac%7B13%5Cpi%20%7D%7Be%7D%2B13%5Cpi%20)
therefore, the volume of V generated by rotating the given region is 