The volume of the mineral = increase in volume of the water whuich is 16 - 8 = 8mls.
Therefore the mineral's density = 9.6 / 8
= 1.2 g/ ml answer
Answer:
3.25 pounds
Step-by-step explanation:
x + 4 (1/2) + 3 (1/2) = 11
x + 4.25 + 3.5 = 11
x + 7.75 = 11
x = 11 - 7.75
x = 3.25 pounds
Answer:
vertex = (0, -4)
equation of the parabola:
Step-by-step explanation:
Given:
- y-intercept of parabola: -4
- parabola passes through points: (-2, 8) and (1, -1)
Vertex form of a parabola:
(where (h, k) is the vertex and is some constant)
Substitute point (0, -4) into the equation:
Substitute point (-2, 8) and into the equation:
Substitute point (1, -1) and into the equation:
Equate to find h:
Substitute found value of h into one of the equations to find a:
Substitute found values of h and a to find k:
Therefore, the equation of the parabola in vertex form is:
So the vertex of the parabola is (0, -4)
A) zeroes
P(n) = -250 n^2 + 2500n - 5250
Extract common factor:
P(n)= -250 (n^2 - 10n + 21)
Factor (find two numbers that sum -10 and its product is 21)
P(n) = -250(n - 3)(n - 7)
Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.
They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.
B) Maximum profit
Completion of squares
n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4
P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000
Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000
Maximum profit =1000 at n = 5
C) Axis of symmetry
Vertex = (h,k) when the equation is in the form A(n-h)^2 + k
Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000
Vertex = (5, 1000) and the symmetry axis is n = 5.
Answer:
The statement is true for every n between 0 and 77 and it is false for
Step-by-step explanation:
First, observe that, for n=0 and n=1 the statement is true:
For n=0:
For n=1:
From this point we will assume that
As we can see, and . Then,
Now, we will use the formula for the sum of the first 4th powers:
Therefore:
and, because ,
Observe that, because and is an integer,
In concusion, the statement is true if and only if n is a non negative integer such that
So, 78 is the smallest value of n that does not satisfy the inequality.
Note: If you compute for 77 and 78 you will obtain: