We are asked in the problem to evaluate the integral of <span>(cosec^2 x-2005)÷cos^2005 x dx. The function is an example of a complex function with a degree that is greater than one and that uses special rules to integrate the function via the trigonometric functions. For example, we integrate
2005/cos^2005x dx which is equal to 2005 sec^2005 x since sec is the inverse of cos. The integral of this function when n >3 is equal to I=</span><span>∫<span>sec(n−2)</span>xdx+∫tanx<span>sec(n−3)</span>x(secxtanx)dx
Then,
</span><span>∫tanx<span>sec(<span>n−3)</span></span>x(secxtanx)dx=<span><span>tanx<span>sec(<span>n−2)</span></span>x/(</span><span>n−2)</span></span>−<span>1/(<span>n−2)I
we can then integrate the function by substituting n by 3.
On the first term csc^2 2005x / cos^2005 x we can use the trigonometric identity csc^2 x = 1 + cot^2 x to simplify the terms</span></span></span>
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Find area of one triangle
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Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 9 x 11.75
Area of triangle = 52.875 ft²
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Find area of two triangles
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Area of 2 triangles = 52.875 x 2
Area of 2 triangles = 105.75 ft²
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Find the cost of the flower beds
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1 ft² = $4.25
105.75 ft² = 105.75 x 4.25
105.75 ft² = $449.44 (nearest hundredth)
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Answer: $449.44
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Answer:
The length around the figure in terms of r is 2r (
+ 4).
Step-by-step explanation:
The perimeter of an object is the total length of the boundary of the object.
The figure consists two similar semicircle and a rectangle.
Adding the two semicircles, a complete circle is formed. The circumference of a circle = 2r.
The rectangle has a length which is twice its height.
i.e l = 2h
But,
r = 
(the diameters of the semicircles equal the height of the rectangle)
⇒ h = 2r
Thus, one side length of rectangle = 2 × 2r (l = 2 × h)
= 4r
The length around the figure in terms of r is:
= 2r + 4r + 4r
= 2r + 8r
= 2r ( + 4)
The length around the figure in terms of r is 2r ( + 4).
Answer:
Step-by-step explanation:
Given
Convert from exponential to logarithm
(a) to (d)
Required
Which of the options is correct
Given that:
--- Exponential
The logarithm form is:
From (a) to (d), only option (c) is correct.
Because it follows the above pattern
i.e.
becomes
or
