Answer:
1073.38
Step-by-step explanation:
975 × 0.01 = 9.75
9.75 + 975 = 984.75
984.75 × 0.09 = 88.6275
88.6275 + 984.75 = <u>1073.38</u>
Answer:
The function is a parabola of the form . The the formula for the axis of symmetry of a parabola is. So it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.
Answer:
See explanation below.
Step-by-step explanation:
The prime numbers are bold:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31
a) We can see that as we go higher, twin primes seem less frequent but even considering that, there is an infinite number of twin primes. If you go high enough you will still eventually find a prime that is separated from the next prime number by just one composite number.
b) I think it's interesting the amount of time that has been devoted to prove this conjecture and the amount of mathematicians who have been involved in this. One of the most interesting facts was that in 2004 a purported proof (by R. F. Arenstorf) of the conjecture was published but a serious error was found on it so the conjecture remains open.
Answer:
Part 1) The y-intercept is the point ![(0,-3)](https://tex.z-dn.net/?f=%280%2C-3%29)
Part 2) The x-intercepts are the points ![(-\sqrt{3},0)\ and\ (\sqrt{3},0)](https://tex.z-dn.net/?f=%28-%5Csqrt%7B3%7D%2C0%29%5C%20and%5C%20%28%5Csqrt%7B3%7D%2C0%29)
Step-by-step explanation:
we have
![y=x^{2}-3](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D-3)
This is a vertical parabola open upward
step 1
Find the y-intercept
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
![y=(0)^{2}-3](https://tex.z-dn.net/?f=y%3D%280%29%5E%7B2%7D-3)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
The y-intercept is the point (0,-3)
step 2
Find the x-intercepts
we know that
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
![x^{2}-3=0](https://tex.z-dn.net/?f=x%5E%7B2%7D-3%3D0)
solve for x
Adds 3 both sides
![x^{2}-3+3=0+3](https://tex.z-dn.net/?f=x%5E%7B2%7D-3%2B3%3D0%2B3)
![x^{2}=3](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D3)
take square root both sides
![x=(+/-)\sqrt{3}](https://tex.z-dn.net/?f=x%3D%28%2B%2F-%29%5Csqrt%7B3%7D)
so
The x-intercepts are the points ![(-\sqrt{3},0)\ and\ (\sqrt{3},0)](https://tex.z-dn.net/?f=%28-%5Csqrt%7B3%7D%2C0%29%5C%20and%5C%20%28%5Csqrt%7B3%7D%2C0%29)
The range of the function is {-34, -2, -20}
<h3>How to determine the range?</h3>
The function is given as:
f(x) = -2x^2 - 2
The domain is {-4, 0, 3}
Substitute the domain values in the function.
f(-4) = -2(-4)^2 - 2 = -34
f(0) = -2(0)^2 - 2 = -2
f(3) = -2(3)^2 - 2 = -20
This means that the range of the function is {-34, -2, -20}
Read more about range at:
brainly.com/question/10197594
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