Option C:
x = 90°
Solution:
Given equation:
<u>To find the degree:</u>
Subtract 1 + cos²x from both sides.
Using the trigonometric identity:
Let sin x = u
Factor the quadratic equation.
u + 2 = 0, u – 1 = 0
u = –2, u = 1
That is sin x = –2, sin x = 1
sin x can't be smaller than –1 for real solutions. So ignore sin x = –2.
sin x = 1
The value of sin is 1 for 90°.
x = 90°.
Option C is the correct answer.
Answer:
(x + 5) m
Step-by-step explanation:
From the question given above, the following data were obtained:
Area (A) = (x² + 8x + 15) m²
Width (W) = (x + 3) m
Length (L) =?
The lenght of the rectangle can be obtained as follow:
A = L × W
x² + 8x + 15 = L (x + 3)
Divide both side by x + 3
L = x² + 8x + 15 / x + 3
L = (x + 5) m
Please attached photo for explanation.
Therefore, the length of the rectangle is: (x + 5) m
Answer:
Train A's unit rate is 67 km per hour.
Train B's unit rate is 75 km per hour.
Train B is faster than Train A
Step-by-step explanation:
Train A
Distance traveled by Train A is represented by :
where represents distance traveled in kilometers and
is the time in hours.
To find the unit rate of Train A, we will plugin and get the distance traveled by Train A in 1 hour which will be the unit rate of Train A in km/hr.
So, distance traveled by Train A in 1 hour = 67 km
∴ Train A's unit rate is 67 km per hour.
Train B
For Train B, we are given the table for the time in hours and distance traveled in that duration.
Taking time =2 hours the distance traveled by Train B= 75 km
To find distance traveled in 1 hour we apply unitary method.
So
So, distance traveled by Train B in 1 hour = 75 km
∴ Train B's unit rate is 75 km per hour.
Difference in units rates =
On comparing their unit rate i.e. the speed of the trains we find out that Train B is faster than Train A by 8 km/hr