Answer:
False
Step-by-step explanation:
The answer is in its name. Its a property of equality meaning it makes sure that both sides are equal to each other
tan2x*cotx - 3 = 0
We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx
==> sin2x/cos2x *cosx/sinx = 3
Now we know that sin2x = 2sinx*cosx
==> 2sinxcosx/cos2x * cosx/sinx = 3
Reduce sinx:
==> 2cos^2 x/ cos2x = 3
Now we know that cos2x = 2cos^2 x-1
==> 2cos^2 x/(2cos^2 x -1) = 3
==> 2cos^2 x = 3(2cos^2 x -1)
==> 2cos^2 x = 6cos^2 x - 3
==> -4cos^2 x= -3
==> 4cos^2 x = 3
==> cos^2 x = 3/4
==> cosx = +-sqrt3/ 2
<span>==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6</span>
Answer:
A) between 7:40 and 7:45
Step-by-step explanation:
Given,
The maximum time taken by her to walk to school = 15 minutes,
Since, the school starts on 8:00 AM,
Also, 15 minutes before 8:00 AM = 7:45 AM,
Thus, the maximum time at which she has to leave home = 7: 45 AM,
Hence, the reasonable estimate of the time she should leave home to get to school by 8:00 is between 7:40 and 7:45.
OPTION A would be correct.
84 sq. ft of the wall has to be covered with paint or wallpaper.
Step-by-step explanation:
- Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × width
Area of the wall = 8 × 16 = 128 ft²
Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)
Area of the fireplace = 5 × 3 = 15 ft²
Area of the mirror = 4 × 2 = 8 ft²
- Step 2: Calculate the area to be painted or covered with wallpaper
Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)
= 128 - 44
= 84 ft²
Propane costs $3.50 per hundred pounds,
and there is a $6 monthly delivery fee.
A family has budgeted $85 for their propane this month.
Let 'x' hundreds of pounds can the family use without going over budget
Here family has budgeted $85 for their propane.
So the cost for Propane = $ 3.5x
One month delivery fee $6
Therefore cost + delivery charge not exceed $85
So 3.5x + 6 ≤ 85
3.5x=85-6 =79
x = 22.57
Therefore 22 hundreds of pounds can the family use without going over budget
