By definition, the area of a parallelogram is given by:
A = (1/2) * (b) * (h)
Where,
b: base of the parallelogram
h: height of the parallelogram
Substituting values we have:
A = (1/2) * (3.1 + 3.3) * (4.1)
A = 13.12 cm ^ 2
Answer:
The area of one piece of fabric is:
A = 13.12 cm ^ 2
Answer:
f'(x) = -1/(1 - Cos(x))
Step-by-step explanation:
The quotient rule for derivation is:
For f(x) = h(x)/k(x)
![f'(x) = \frac{h'(x)*k(x) - k'(x)*h(x)}{k^2(x)}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7Bh%27%28x%29%2Ak%28x%29%20-%20k%27%28x%29%2Ah%28x%29%7D%7Bk%5E2%28x%29%7D)
In this case, the function is:
f(x) = Sin(x)/(1 + Cos(x))
Then we have:
h(x) = Sin(x)
h'(x) = Cos(x)
And for the denominator:
k(x) = 1 - Cos(x)
k'(x) = -( -Sin(x)) = Sin(x)
Replacing these in the rule, we get:
![f'(x) = \frac{Cos(x)*(1 - Cos(x)) - Sin(x)*Sin(x)}{(1 - Cos(x))^2}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7BCos%28x%29%2A%281%20-%20Cos%28x%29%29%20-%20Sin%28x%29%2ASin%28x%29%7D%7B%281%20-%20Cos%28x%29%29%5E2%7D)
Now we can simplify that:
![f'(x) = \frac{Cos(x)*(1 - Cos(x)) - Sin(x)*Sin(x)}{(1 - Cos(x))^2} = \frac{Cos(x) - Cos^2(x) - Sin^2(x)}{(1 - Cos(x))^2}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7BCos%28x%29%2A%281%20-%20Cos%28x%29%29%20-%20Sin%28x%29%2ASin%28x%29%7D%7B%281%20-%20Cos%28x%29%29%5E2%7D%20%3D%20%5Cfrac%7BCos%28x%29%20-%20Cos%5E2%28x%29%20-%20Sin%5E2%28x%29%7D%7B%281%20-%20Cos%28x%29%29%5E2%7D)
And we know that:
cos^2(x) + sin^2(x) = 1
then:
![f'(x) = \frac{Cos(x)- 1}{(1 - Cos(x))^2} = - \frac{(1 - Cos(x))}{(1 - Cos(x))^2} = \frac{-1}{1 - Cos(x)}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7BCos%28x%29-%201%7D%7B%281%20-%20Cos%28x%29%29%5E2%7D%20%3D%20-%20%5Cfrac%7B%281%20-%20Cos%28x%29%29%7D%7B%281%20-%20Cos%28x%29%29%5E2%7D%20%3D%20%5Cfrac%7B-1%7D%7B1%20-%20Cos%28x%29%7D)
Answer:
First image:
C, D, and E are true.
Second image:
30 tbsp
Step-by-step explanation:
1 cup = 8 ounces
A is false.
1 quart = 4 cups
7 qt = 28 cups
28 + 4 = 32
32 < 34
B is false.
1 gallon = 8 pints
4 gallons = 32 pints
31 < 32
C is true.
1 gallon = 4 quarts
5 gallons = 20 quarts
20 < 21
D is true.
1 quart = 2 pints
15 quarts = 30 pints
30 = 30
1 ounce = 2 tablespoons
15 ounces = y tablespoons
![\frac{1}{2}: \frac{15}{y}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3A%20%5Cfrac%7B15%7D%7By%7D)
1 × y = 15 × 2
y = 30
30 tbsp
Answer:
that is a acute angel because 73 is less than a right but also less than a other angel