Ok, here we go. Pay attention. The formula for the arc length is
. That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is
(that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of
. Integrating that we have
from -1 to 2.
gives us
. Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly:
which simplifies to
. The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with
. And there you go!
Answer: A) 1/2
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
If the third term is 20, it means that
T3 = 20 = ar^(3 - 1)
20 = ar²- - - - - - - - - - 1
If the third term is 20, it means that
T5 = 5 = ar^(5 - 1)
5 = ar⁴- - - - - - - - - - 2
Dividing equation 2 by equation 1, it becomes
5/20 = r⁴/r²
1/4 = r^(4 - 2)
(1/2)² = r²
r = 1/2
9514 1404 393
Answer:
- y-intercept: (0, -6)
- x-intercepts: (-3, 0), (-1, 0), (1, 0)
Step-by-step explanation:
We notice the first pair of coefficients is the same as the last pair (with the sign changed). This means we can factor by grouping.
f(x) = (2x^3 +6x^2) -(2x +6)
f(x) = 2x^2(x +3) -2(x +3)
f(x) = 2(x^2 -1)(x +3) = 2(x -1)(x +1)(x +3)
The factors are made to be zero when x is 1, -1, or -3.
The x-intercepts are (1, 0), (-1, 0), (-3, 0).
The y-intercept is the constant, -6.
Answer: Your answer is 3,000,150 plz give brain list
Step-by-step explanation:
150
2,000,000
+1,000,000
___________
3,000,150
It would be, 6.72/3 = $2.24
