Place each pair of angles in the correct column (Look at the picture)
1 answer:
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the maximum height is the y-value of the vertex.
h(x) = -2x² + 20x + 48
<em> a=-2, b=20, c=48</em>
h(5) = -2(5)² + 20(5) + 48
= -50 + 100 + 48
= 50 + 48
= 98
Answer: 98 meters
Answer:
Peculiar purples would be more abundant
Step-by-step explanation:
Given that eculiar Purples and Outrageous Oranges are two different and unusual types of bacteria. Both types multiply through a mechanism in which each single bacterial cell splits into four. Time taken for one split is 12 m for I one and 10 minutes for 2nd
The function representing would be
i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
a) Here P0 =3, time t = 60 minutes.
i) I bacteria P =
ii) II bacteria P =
b) Since II is multiplying more we find that I type will be more abundant.
The difference in two hours would be
c) i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
d) At time 36 minutes we have t = 36
Peculiar purples would be
The rate may not be constant for a longer time. Hence this may not be accurate.
e) when splits into 2, we get
where P0 is initial and t = interval of time
Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in ,
and -3. The last root gives us the factor (x+3). Hence, our polynomial is
where is a polynomial with rational coefficients and roots
and
. The root
gives us a factor
, but in order to obtain rational coefficients we must consider the factor
.
An analogue idea works with . For convenience write
. This gives the factor
. Hence,
Notice that . So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is
Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type will introduce in the expression, we need to multiply by its conjugate
. Hence, we will obtain
that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.