(x-h)^2=4p(y-k)
vertex is (h,k)
p is the distance from focus to vertex and distance from vertex to directix (vertex is in middle of directix and focus)
if p is positive, the parabola opens up and the focus is above the directix
if p is negative, the parabola opens down and the focus is below the directix
we see the directix is over the focus (1>-1) so the parabola opens down and p is negative
distance from (5,-1) to y=1 is 2 units
2/2=1
p=-1 since p is negative
1 up from (5,-1) is (5,0)
veretx is (5,0)
(x-5)^2=4(-1)(y-0)
(x-5)^2=-4y is the equation
The square root of 81 is 9, the square root of 100 is 10. 89 is between 81 and 100, therefore the square root of 89 must be between 9 and 10.
Count how many decimal places you need to move to the right until you get to:
1.203 and then multiply that by 10 raised to the power of the number of places you moved the decimal point...in this case it had to move 10 places so:
1.203X10^-10
A) y = 2x – 7 and f(x) = 7 – 2xIncorrect. These equations look similar but are not the same. The first has a slope of 2 and a y-intercept of −7. The second function has a slope of −2 and a y-intercept of 7. It slopes in the opposite direction. They do not produce the same graph, so they are not the same function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5. B) 3x = y – 2 and f(x) = 3x – 2Incorrect. These equations represent two different functions. If you rewrite the first equation in terms of y, you’ll find the equation of the function is y = 3x + 2. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5. C) f(x) = 3x2 + 5 and y = 3x2 + 5Correct. The expressions that follow f(x) = and y = are the same, so these are two different ways to write the same function: f(x) = 3x2 + 5 and y = 3x2 + 5. D) None of the aboveIncorrect. Look at the expressions that follow f(x) = and y =. If the expressions are the same, then the equations represent the same exact function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.
Answer:
Wow this hard
Step-by-step explanation:
X∞
k=1
k(k + 2)
(k + 3)2
is convergent or divergent. If it is convergent, find its sum.
Answer: This series diverges. To see this, I will show that the terms in the sequence do not
go to zero:
lim
k→∞
k(k + 2)
(k + 3)2
= lim
k→∞
k
2 + 2k
k
2 + 6k + 9
.
Dividing numerator and denominator by k
2 yields
lim
k→∞
1
k
2
1 + 2
k
1
k
2
1 + 6
k +
9
k
2
= lim
k→∞
1 + 2
k
1 + 6
k +
9
k
2
= 1.
Therefore, using the nth term test (a.k.a. Test for Divergence), the series diverges
