Answer:
The capacity of the mug is 1,527.43 cm^3
Step-by-step explanation:
In this question, we are asked to calculate the capacity of the hemisphere. This is same as calculating the volume of the hemisphere.
A hemisphere is a sharpe which is half a sphere. Meaning to get a hemisphere, we shall be diving a sphere into 2.
Mathematically, the volume of a hemisphere V = 2/3 * π * r^3
Since D = 18cm , r = D/2 = 18cm/2 = 9 cm
The volume V is thus = 2/3 * 22/7 * 9^3
V = 1,527.428 cm^ 3
To the nearest hundredth,
V = 1,527.43 cm^3
Step-by-step explanation:
√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))
Square and take the square root.
√[√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))]²
√[(1 + sin x) / (1 − sin x) + 2 + (1 − sin x) / (1 + sin x)]
Add the fractions using least common denominator.
√[((1 + sin x)² + (1 − sin x)²) / (1 − sin²x) + 2]
√[(1 + 2 sin x + sin²x + 1 − 2 sin x + sin²x) / (1 − sin²x) + 2]
√[(2 + 2 sin²x) / (1 − sin²x) + 2]
Use Pythagorean identity:
√[(2 + 2 sin²x) / (cos²x) + 2]
√[2 sec²x + 2 tan²x + 2]
√[2 sec²x + 2 (tan²x + 1)]
Use Pythagorean identity:
√[2 sec²x + 2 sec²x]
√[4 sec²x]
±2 sec x
If x is in the second quadrant, then sec x < 0.
-2 sec x
Two cups in a pint,at least here in the us
Answer:
The pin number is 1147
Step-by-step explanation:
We have given that:
Maritza remembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500.
Pin number is between 1000 and 1500
PIN is the product of two consecutive prime numbers.
Prime numbers are those numbers which are divisible by one or itself only.
So,
prime numbers are 1, 3, 5, 7,………29, 31,37, 41, …..
Multiply 29 x 31 = 899 which does not come in the range of 1000 and 1500.
Next,
31 x 37 = 1147 this is between 1000 and 1500
Next
37 x 41 = 1517, which is above 1500.
Thus the pin number is 1147....
Answer:
It would be 16!
Step-by-step explanation:
Step 1 : 6 times 24 is 144
Step 2 : 144/9
Answer 16!
