Answer:
The domain is (-∞ , ∞)
The domain is continuous
Step-by-step explanation:
Here, we want to identify the domain of the linear function
The domain in this case can be represented by the set of all real numbers.
When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis
Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books
Thus, the domain here will be (-∞ , ∞)
On if the domain is discrete or continuous, we can see that the domain is continuous.
The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous
Answer:
Step-by-step explanation:
The answer to this question is 12+6sqrt3.
This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.
Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.
The square root of 108 simplified=6sqrt3.
Then you add them together and get 12+6sqrt3.
The other diagonal would be 13 feet as well because it is a rectangle.
To solve this problem, all we have to do is to thoroughly
analyze the situation step by step.
First let us work on the remaining 10 gallons of water in
the tank. We are given that 2 / 3 of the water initially in the tank leaked
out. Therefore this means that we are left with 1 / 3 the original amount of
water which is 10 gallons, hence:
(1 / 3) Vi = 10 gallons
where Vi is the initial volume of water inside the tank,
calculating for Vi:
Vi = 3 (10 gallons)
Vi = 30 gallons
We are also given that this initial volume of water is
just 3 / 4 of the total capacity of the tank, therefore:
(3 / 4) Vc = Vi
where Vc is the volume capacity of the tank, calculating
for Vc:
Vc = 4 Vi / 3
Vc = 4 (30 gallons) / 3
Vc = 40 gallons
Answer:
<span>Capacity of the fish tank is 40 gallons</span>
Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.
We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA
D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA
Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A
This verifies the identity.
