Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.
Answer:
57 inches
Step-by-step explanation:
The height, width, and diagonal of the TV screen form a right triangle.
Use the pythagorean theorem, a² + b² = c², and solve for c, the hypotenuse/diagonal of the TV.
a² + b² = c²
30² + 48² = c²
900 + 2304 = c²
3204 = c²
56.6 = c
Round this to the nearest inch:
56.6
= 57
So, the diagonal of the TV screen is 57 inches
Not entirely sure, but it seem the answer could be B.) It will not be spread out vertically across the entire coordinate plane because in step 5, Nancy selected an incorrect scale on the y-axis.
Given:
Circular racetrack with a diameter of 1/2 mile
Find: how far does a car travel in one lap around the track?
We need to find the circumference of the racetrack.
Circumference is multiplying pi to the diameter of the racetrack.
Circumference = 3.14 * 1/2 mile
Circumference = 3.14/2 mile
Circumference = 1.57 miles rounded to the nearest tenth is 1.60 miles.
Answer:
Annika was 14 days late with her book.
Step-by-step explanation:
The first four days would cost Annika 1.0 dollar (4x0.25), then we need to divide the rest of the ammount by 0.30 to calculate for how many days she paid the 0.30 dollar fine.
4.00 - 1.00 = 3.00
3.00/0.30 = 10
Therefore, Annika was 4 +10 = 14 days late with her book.
