Answer:
Step-by-step explanation:
y=mx+b where m is the slope of the line so the slope of this line is 2/3
Answer:
6.2832 square units (rounded off to four decimal values)
Step-by-step explanation:
Area of a semicircle =
× π × r²
r (radius) = 2 units
For our semicircle the area =
× π × 2² = 6.28318530718 square units
Or 6.2832 square units (rounded off to four decimal values)
Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)
If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.
On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.
For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.
Then the range of F(x) is the interval [-π, π].
-6, because you can see a pattern in which the x coordinate of each pair is reversed to the opposite value, from positive to negative.
Hi there!

To derive an equation given the points, we can use the slope formula:

Plug in the corresponding coordinates:

Simplify:

Therefore, we have:
y = -4x + b
Plug in the x and y values for a coordinate to solve for b:
2 = -4(1) + b
2 = -4 + b
b = 6
The equation is:
y = -4x + 6. The correct answer is D.