Answer:
Step-by-step explanation:
We will call the dog's original weight d and the cat's c. according to the problem 1.2c=.9d
1.2c is the cat's weight increased by 20% and .9d is the dog's weight decreased by 10% Now we just solve this with algebra for the dog's original weight.
1.2c=.9d
(1.2/.9)c = d
(4/3)c = d
Now, this tells us that the dog's original weight was 4/3 of the cat's.or about 33.33% larger
It kinda looks like the question is then asking what the cat's current weight is in comparison to the dog's original. If that's the case we need just one more step. We want the dog's original weight and the cat's current weight in terms of the same variable. Well, we have that.
Current cat = 1.2c or 6/5, since we have the other in fractional form.
original dog = (4/3)c
Now, what do we multiply the first to get to the second? Well, we need common denominators. 15 is the lcm of 3 and 5, so we'll use that.
6/5 = 18/15 and 4/3 = 20/15
Nowwe want to know what we have to multiply 18 by to get to 20. some algebra will find that.
18x=20
x = 20/18
x = 10/9
that's about 1.11, so the dog's original weight is about 11% higher than the cat's current weight.
Hopefully that's the answer it wanted, if not or if there is something you didn't understand let me know.
Answer:
i) sin(2x) = 
ii) cot(x+360) = 
iii) sin(x-180) = 
Step-by-step explanation:
sec(x) = 2
Since cos(x) is reciprocal of sec(x), this means:
cos(x) = 
cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.
Part i)
sin(2x) can be simplified as:
sin(2x) = 2 sin(x) cos(x)
First we need to find the value of sin(x). According to Pythagorean identity:
Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:
So,
Part ii)
We have to find cot(x + 360)
An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.
cot(x + 360) = cot(x)
Using the values, we get:
Part iii)
We need to find the value of sin(x - 180)
sin(x - 180) = - sin(x)
Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.
So,
sin(x - 180) = 
To solve A =lw for l it means you want l on one side of the equals and anything not l on the other side. How are l and w put together? They are multiplied. We undo that multiplying with dividing.
A = l * w
A / w = l to divide both sides by w.
Thus l = A / w.
