Answer:
The total area of the figure is 
Step-by-step explanation:
we know that
The area of the figure is equal to the area of the rectangle plus the area of the isosceles right triangle
<u>Find the area of rectangle</u>
Find the area of the isosceles right triangle
<u>Find the total area of the figure</u>
Working with the right side:
cot(<em>x</em>) + 2 tan(<em>x</em>) + tan³(<em>x</em>) = cos(<em>x</em>)/sin(<em>x</em>) + 2 sin(<em>x</em>)/cos(<em>x</em>) + sin³(<em>x</em>)/cos³(<em>x</em>)
… = (cos⁴(<em>x</em>) + 2 sin²(<em>x</em>) cos²(<em>x</em>) + sin⁴(<em>x</em>)) / (sin(<em>x</em>) cos³(<em>x</em>))
Factorize the numerator as a sum of squares:
<em>a</em>⁴ + 2 <em>a</em>² <em>b</em>² + <em>b</em>⁴ = (<em>a</em>² + <em>b</em>²)²
… = (cos²(<em>x</em>) + sin²(<em>x</em>))² / (sin(<em>x</em>) cos³(<em>x</em>))
Recall that
cos²(<em>x</em>) + sin²(<em>x</em>) = 1
… = 1 / (sin(<em>x</em>) cos³(<em>x</em>))
… = 1 / (sin(<em>x</em>) cos³(<em>x</em>)) • cos(<em>x</em>)/cos(<em>x</em>)
… = cos(<em>x</em>) / (sin(<em>x</em>) cos⁴(<em>x</em>))
… = cot(<em>x</em>) sec⁴(<em>x</em>)
List the multiples of both 12 and 9:
12, 24, 36, 48, 60
9, 18, 27, 36, 45
The lowest common multiple is 36.
This will make the fixtures and bulbs equal.
This means they bought 3 packages of light figures 3 x 12 = 36)
And bought 4 packages of bulbs ( 4 x 9 = 36)
Answer:
Volume = 126 cm^2
Step-by-step explanation:
You don't exactly know what the base looks like, but it doesn't matter. The volume of a Prism is Base * height.
Solution
V = Base (which is the Cross sectional Area) * Length
V = 21 cm^2 * 6 cm
V = 126 cm^2
It would be 4r + 3b because If one red marble worth four points and blue marble worth 3 points each then we need to multiply the total number of marbles and calculate the sum. It would give the total number of points.
