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:
0.6710
Step-by-step explanation:
The diameters of ball bearings are distributed normally. The mean diameter is 107 millimeters and the population standard deviation is 5 millimeters.
Find the probability that the diameter of a selected bearing is between 104 and 115 millimeters. Round your answer to four decimal places.
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 107 mm
σ is the population standard deviation = 5 mm
For x = 104 mm
z = 104 - 107/5
z = -0.6
Probability value from Z-Table:
P(x = 104) = 0.27425
For x = 115 mm
z = 115 - 107/5
z = 1.6
Probability value from Z-Table:
P(x = 115) = 0.9452
The probability that the diameter of a selected bearing is between 104 and 115 millimeters is calculated as:
P(x = 115) - P(x = 104)
0.9452 - 0.27425
= 0.67095
Approximately = 0.6710
Answer:
B.
Step-by-step explanation:
The graph that is going to show the function, has two parts: one for numbers equal or less than 3 and the other for numbers greater than 3
Then, for x≤3, the function is f(x) = 4. This is a constant so the graph is a horizontal line.
Additionally, for x>3, the function is f(x)=12x. This is a straight line with a positive slope.
So, the answer that follows these 2 conditions is B.
The answer is $1.80. You would take 25% of 3, which is 75, and subtract it from 3. That leaves you with $2.25, which you take 20% off, which is 0.45, and subtract that from 2.25. That leaves you with a grand total of $1.80. Hope that this helped!
Answer:
positive
Step-by-step explanation:
if you subtract a negative number, it’s the same as adding a positive number. If you add 2 positive numbers, you get a positive number, so the expression is positive.
