7. In how many ways can the same 5-question True / False quiz be
1 answer:
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Answer:
Step-by-step explanation:
The x-intercept exists when y = 0; the coordinate that results from our x-intercept is (4, 0).
The y-intercept exists when x = 0; the coordinate that results from our y-intercept is (0, -2).
We can use these 2 coordinates to find the slope of the line we need to write:
Now we can use that slope along with one of our points to write the equation of the line. I am going to use the point-slope form, then we will solve it for y to put it into slope-intercept. Let's use the coordinate (4, 0). Keep in mind that regardless of which point we choose to use to write our equation, we will get the same equation.
y - 0 = 1/2(x - 4) and
y = 1/2x - 2
That's your equation!
Answer:
(-∞, -2) and (2, ∞)
Step-by-step explanation:
ƒ(x) = x³ -12x + 10
f'(x) = 3x² - 12
Set 3x² - 12 = 0
x² - 4 = 0
x² = 4
x = ±2
The points x = -2 and x = + 2 divide the number line into three intervals:
(-∞, -2), (-2, +2), and (+2, ∞).
a. Interval (-∞, -2)
x < -2, so f'(x) > 0 when -∞ < x < -2
The function is increasing in (-∞, -2).
b. Interval (-2, 2)
|x| < 2, so f'(x) <0
The function is decreasing in (-2, 2).
c. Interval (2, ∞)
x > 2, so f'(x) > 0 when 2 < x < ∞
The function is increasing in (2, ∞).
Thus, the function is increasing in the intervals (-∞, -2) and (2, ∞).
Answer:
(a) at t=2, the particle is moving toward the origin
(b) a(t) = 70(8 -9t^2)/(3t^2 +8)^3; a(2) = -0.245
(c) the particle approaches x = 1/3 as t gets large
Step-by-step explanation:
(a) The function x(t) is negative for -3 < t < 3, so at t = 2, the particle is to the left of the origin.
The velocity of the particle is given by the derivative of the position function:
Then, at t=2, the expression is positive, indicating the particle is moving toward the origin.
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(b) The acceleration is the derivative of the velocity, so is ...
Then at t=2, the acceleration is ...
a(2) = 70(8 -9·4)/(3·4+8)^3 = 70(-28)/8000
a(2) = -0.245
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(c) As t gets large, the value of x(t) approaches t^2/(3t^2) = 1/3.