The answer
according to the figure, we can solve this problem only by applying sines rule:
that is
sinA/a = sinB/b = sinC /c
As we observe, sin A /54 = sin B/27 = sin C/ c, and c = AB
besides, sinC > sinB > sinA , so the only answer possible is
<span>27 < AB < 81</span>
Answer:
for what bro
Step-by-step explanation:
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We have been given the function 
We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.
Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.
Therefore, the range of the function is given by y>0
B is the correct option.
Steps in multiplying fractions. Remember: finding common denominator is not necessary in multiplying fractions.
Common denominators are only needed in adding and subtracting fractions.
14/15 * 5/2
Step 1. Multiply the numerators.
14 * 5 = 70
Step 2. Multiply the denominators
15 * 2 = 30
Step 3. Simplify the fraction.
70/30 = 2 10/30 = 2 1/3
*the fraction 10/30 can still be simplified by dividing both numbers by 10. Hence, 1/3.
Steps in Dividing fractions.
24/60 ÷ 8/15
Step 1. Get the reciprocal of the 2nd fraction. Reciprocal means the reverse of the fraction. Simply swap the places of the numbers.
Reciprocal of 8/15 is 15/8.
Step 2. Multiply the 1st fraction to the reciprocal of the 2nd fraction. Follow steps in multiplying fractions.
24/60 * 15/8 = (24*15) / (60*8) = 360/480
Step 3. Simplify the fraction.
360/480 = 9 / 12 = 3/4
360 ÷ 40 = 9 ; 9 ÷ 3 = 3
480 ÷ 40 = 12 ; 12 ÷ 3 = 4
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>
