Answer:
20 but I am not sure.....
So we can start with the full of possibilities and eliminate them one by one.
The full set is {0,1,2,3,4,5,6,7,8,9}.
Now we know that any prime greater than 2 is odd as otherwise it would have 2 as a factor, so we can eliminate all of these digits that would be an even number, leaving:
{1,3,5,7,9}
We also know that any prime greater than 5 cannot be a multiple of 5 and that all numbers with 5 in the digits are a multiple of 5, so we can eliminate 5.
{1,3,7,9}
We know that 11,13,17 and 19 are all primes, so we cannot eliminate any more of these, leaving the set:
{1,3,7,9} as our answer.
Answer:
A. -4
Step-by-step explanation:
Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.
For the left hand limit;
The function at the left hand occurs at x<-1
f-(x) = x+3
f-(-1) = -1+3
f-(-1) = 2
For the right hand limit, the function occurs at x>-1
f+(x) = 2x-c
f+(-1) = 2(-1)-c
f+(-1) = -2-c
For the function f(x) to be continuous on the entire real line at x = -1, then
f-(-1) = f+(-1)
On equating both sides:
2 = -2-c
Add 2 to both sides
2+2 = -2-c+2
4 =-c
Multiply both sides by minus.
-(-c) = -4
c = -4
Hence the value of c so that f(x) is continuous on the entire real line is -4
Answer:
p^5 + q^5
Step-by-step explanation:
(p + q)^5
p^5 + q^5 Distribute the fifth power to the letters in the paranthesis
Part 1: The general form for this matches y^2 = -4cx, which implies that this opens to the left. (Imagine assigning any value of y, whether positive or negative, which would result in a positive left-hand value. Then to match this sign, the value of x must be negative so that the right-hand side becomes positive as well.)
Part 2: The distance from the vertex to the directrix is given by c. This equation has its vertex at the origin (0, 0). If it opens to the left, the directrix is a vertical line to the right of the origin. This equation is y^2 = -4(1/2)x, so c = 1/2, and the directrix has the equation x = 1/2.
Part 3: The focus is inside the parabola, but it is the same distance from the vertex as the directrix. This distance is 1/2 units, and it will be to the left of the vertex. So the focus is at (-1/2, 0).
